| {"text": "(*\n Copyright (C) 2019 Susi Lehtola\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: lda_exc *)\n(* prefix:\n lda_c_chachiyo_mod_params *params;\n\n assert(p->params != NULL);\n params = (lda_c_chachiyo_mod_params * )(p->params);\n*)\n\n(* Functional is based on Chachiyo correlation *)\n$include \"lda_c_chachiyo.mpl\"\n(* .. but with a different scaling function *)\ng := z -> (opz_pow_n(z,2/3) + opz_pow_n(-z,2/3))/2:\ng_zeta := zeta -> 2*(1 - g(zeta)^3):\n\nf_chachiyo := (rs, zeta) -> e0(rs) + (e1(rs) - e0(rs))*g_zeta(zeta):\nf := (rs, zeta) -> f_chachiyo(rs, zeta):\n", "meta": {"hexsha": "674b609a4590226593f055ffd0c13667c89bfeb9", "size": 720, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_chachiyo_mod.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_chachiyo_mod.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_chachiyo_mod.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 28.8, "max_line_length": 68, "alphanum_fraction": 0.6569444444, "num_tokens": 242, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9449947148047776, "lm_q2_score": 0.7931059609645724, "lm_q1q2_score": 0.7494809413916852}} |
| {"text": "# If X ~ Exponential(λ) then k*exp(X) ~ Pareto(λ, k)\n\n# Proof:\n\nPDF_exponential := (alpha, x) -> exp(-x/alpha)/alpha;\n\nPDF_pareto := (lambda, k, x) -> lambda * k ^ lambda / x ^ (lambda + 1);\n\n\nsimplify(PDF_exponential(1/lambda, log(x/k))*diff(log(x/k), x));\n\nsimplify(PDF_pareto(lambda, k, x));", "meta": {"hexsha": "64c89a62fb4c2661ed79a48d151fb02cf2f30935", "size": 294, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "tests/RoundTrip/t_exponential_to_pareto.proof.mpl", "max_stars_repo_name": "vmchale/hakaru", "max_stars_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 327, "max_stars_repo_stars_event_min_datetime": "2015-01-03T08:56:51.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-24T12:12:06.000Z", "max_issues_repo_path": "tests/RoundTrip/t_exponential_to_pareto.proof.mpl", "max_issues_repo_name": "vmchale/hakaru", "max_issues_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 155, "max_issues_repo_issues_event_min_datetime": "2015-05-05T17:57:22.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T15:43:39.000Z", "max_forks_repo_path": "tests/RoundTrip/t_exponential_to_pareto.proof.mpl", "max_forks_repo_name": "vmchale/hakaru", "max_forks_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 38, "max_forks_repo_forks_event_min_datetime": "2015-01-23T16:25:37.000Z", "max_forks_repo_forks_event_max_datetime": "2021-03-14T15:09:12.000Z", "avg_line_length": 24.5, "max_line_length": 71, "alphanum_fraction": 0.619047619, "num_tokens": 106, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9559813463747182, "lm_q2_score": 0.7826624789529375, "lm_q1q2_score": 0.7482107303864037}} |
| {"text": "\n { InformerScen.mpl }\n\nTITLE\n InformerScen;\n\nSTOCHASTIC \n\nTREE\n TwoStage;\n\nSCENARIOS\n scen := 1..10;\n\nRANDOM DATA\n Demand[scen] := (210, 290, 335, 370, 415, 450, 460, 495, 540, 585);\n\nPROBABILITIES\n prob[scen] := (0.03, 0.134, 0.086, 0.188, 0.226, 0.08, 0.056, 0.132, 0.06, 0.008);\n\nDATA\n Budget := 1500;\n ProdCost := 0.81;\n SellPrice := 0.90;\n Margin := SellPrice - ProdCost;\n\nDECISION VARIABLES\n Production;\n\nSTAGE2 VARIABLES\n Shortfall;\n Excess;\n\nMODEL\n\n MAX Profit = Margin * Production \n - Margin * Shortfall\n - SellPrice * Excess;\n\nSUBJECT TO\n\n BudgetLimit: Production * ProdCost <= Budget;\n\n Balance: Production + Shortfall - Excess = Demand;\n\nEND\n\n\n--------------------------------------------------------------------------------------\nVarCount = 3\nConCount = 2\nStageCount = 2\nVarStages[vars] := (1,2,2)\nConStages[cons] := (1,2)\n\nScenCount = 10\nRandomCount = 10\n\nTreeType = TWOSTAGE\nTreeStage[scen] := (1,2,2,2,2,2,2,2,2,2)\n\nProbData[scen] := (0.03, 0.134, 0.086, 0.188, 0.226, 0.08, 0.056, 0.132, 0.06, 0.008)\n\nRandomScen[random] := (1, 2, 3, 4, 5, 6, 7, 8, 9, 10)\nRandomVar[random] := (RHS, RHS, RHS, RHS, RHS, RHS, RHS, RHS, RHS, RHS)\nRandomCon[random] := (2, 2, 2, 2, 2, 2, 2, 2, 2, 2)\nRandomData[random] := (210, 290, 335, 370, 415, 450, 460, 495, 540, 585)\n--------------------------------------------------------------------------------------\n\n", "meta": {"hexsha": "08e51d24c44aafb7e953db35560872568c6f0176", "size": 1445, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Stochastic/InformerScen.mpl", "max_stars_repo_name": "BjarniMax/mpl-models", "max_stars_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Stochastic/InformerScen.mpl", "max_issues_repo_name": "BjarniMax/mpl-models", "max_issues_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Stochastic/InformerScen.mpl", "max_forks_repo_name": "BjarniMax/mpl-models", "max_forks_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 20.6428571429, "max_line_length": 87, "alphanum_fraction": 0.5224913495, "num_tokens": 554, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9184802395624257, "lm_q2_score": 0.8104789018037399, "lm_q1q2_score": 0.7444088558889908}} |
| {"text": "macro(Multiply=LinearAlgebra[Multiply]):\nmacro(Copy=LinearAlgebra[Copy]):\nmacro(mInverse=LinearAlgebra[Modular][Inverse]):\n\n\n\n# DoublePlusOneLift : Computes a sparse inverse expansion of the matrix A by using Double Plus One Lifting\n#\n# Input :\n#\t\tA : Integer matrix n x n\n#\t\tX : Integer which must be relatively prime with the determinant of A and >= max(10000, 3.61 * n^2 * ||A||)\n#\t\tn : Dimension of A\n#\t\tk : Determines the number of the times to lift and the precision of the inverse, i.e. X^(2^(k+1)-1)\n#\n# Precondition : gcd(X, det(A)) = 1 and X >= max(10000, 3.61 * n^2 * ||A||)\n#\n# Output:\n#\t\tA_0 : It is the inverse of A modulo X (Initialisation of the inverse)\n#\t\tR : A table from 0 to k needed for the sparse inverse expansion\n#\t\tM : A table from 0 to k - 1 needed for the sparse inverse expansion\n#\n# All together it will be : (...(A_0(I + R_0 * X_0) + M_0 * X_0^2) * (I + R_1 * X_1) + M_1 * X_1^2)...) = A^(-1) mod X^(2^(k+1)-1\n#\nDoublePlusOneLift := proc(A, X, n, k)\n\tA_0 := mInverse(X, A):\n\tR[0] := map(iquo, 1 - Multiply(A, A_0), X):\n\tfor i from 0 to (k - 1) do\n\t\tR_bar := Multiply(R[i], R[i]):\n\t\tM[i] := map(modp , Multiply(A_0, R_bar), X):\n\t\tR[i+1] := map(iquo, R_bar - Multiply(A, M[i]), X):\n\tod:\n\treturn A_0, eval(R), eval(M):\nend proc:\n\n\n# XadicRepresentationMatrixCreate : Computes the X-adic representation of a matrix and stores it compactly in a new larger one\n#\n# Input :\n#\t\tA : Input integer matrix n x m\n#\t\tX : Integer for the X-adic representation\n#\t\tn, m : Dimensions of A\n#\t\tp : Length of the X-adic representation to output\n#\n# Output :\n#\t\tA_xadic : Integer matrix n x (m*p) where every vertical slice contains one term from the X-adic representation of A\n#\nXadicRepresentationMatrixCreate := proc(A, X, n, m, p)\n\tA_xadic := Matrix(n, m*p):\n\tfor i to n do\n\t\tfor j to m do\n\t\t\ttemp := convert(A[i, j], 'base', X):\n\t\t\tfor k to min(p, nops(temp)) do\n\t\t\t\tA_xadic[i, j + m * (k - 1)] := temp[k]:\n\t\t\tod:\n\t\tod:\n\tod:\n\treturn A_xadic:\nend proc:\n\n\n# XadicRepresentationMatrixCollapse : Computes the actual matrix from its X-adic representation\n#\n# Input :\n#\t\tA_xadic : Input integer matrix n x (m*p) containing the X-adic representation of A\n#\t\tX : Integer for the X-adic representation\n#\t\tn, m : Dimensions of A to output\n#\t\tp : Length of the input X-adic representation\n#\n# Output :\n#\t\tA : Integer matrix n x m collapsed from its X-adic representation\n#\nXadicRepresentationMatrixCollapse := proc(A_xadic, X, n, m, p)\n\tA := Matrix(n, m):\n\tfor i to n do\n\t\tfor j to m do\n\t\t\tsum := 0:\n\t\t\tfor k to p do\n\t\t\t\tsum := sum + A_xadic[i, j + m * (k - 1)] * X^(k - 1)\n\t\t\tod:\n\t\t\tA[i, j] := sum:\n\t\tod:\n\tod:\n\treturn A:\nend proc:\n\n\n# SwiftRightXadic : Multiplies an X-adic representation by X^swift, i.e., \n#\tslides the vertical slices of the matrix swift times at the right\n#\n# Input :\n#\t\tA : Input integer matrix n x (m*p) containing an X-adic representation\n#\t\tswift : Exponent of X, i.e., A will be multiplied by X^swift\n#\t\tn, m : Dimensions of each slice in A\n#\t\tp : Length of the X-adic representation, i.e., number of slices\n#\n# Output :\n#\t\tA_slided : Integer matrix n x (m*p) containing the input X-adic representation multiplied by X^swift\n#\nSwiftRightXadic := proc(A, swift, n, m, p)\n\tA_slided := Matrix(n, m*p):\n\tif swift < p then\n\t\tA_slided[1..n, swift*m+1..m*p] := A[1..n, 1..m*(p-swift)]:\n\tfi:\n\treturn A_slided:\nend proc:\n\n\n# SwiftRightAndMultiply : Computes the product of 2 matrices A, B, multiplied by X^swift\n#\n# Input :\n#\t\tA : Integer matrix n x n\n#\t\tB : Integer matrix n x (m*p) containing an X-adic representation\n#\t\tswift : Exponent of X, i.e., A*B will be multiplied by X^swift\n#\t\tn: Dimension of A, and the number of rows in B\n#\t\tm : Number of collumns of each slice in B\n#\t\tp : Length of the X-adic representation in B, i.e., number of slices\n#\n# Output :\n#\t\tC : Integer matrix n x (m*p) containing the X-adic representation of A * B * X^swift\n#\nSwiftRightAndMultiply := proc(A, B, swift, n, m, p)\n\tC := Matrix(n, m*p):\n\tif swift < p then\n\t\tC[1..n, swift*m+1..m*p] := Multiply(A, B[1..n, 1..m*(p-swift)]):\n\tfi:\n\treturn C:\nend proc:\n\n\n# CleanUpXadic : Cleans up an X-adic representation, i.e., \n#\tscans the matrix, looking for overflowed elements which will reduce mod X, and it will forward the carry to the next slice\n#\n# Input :\n#\t\tA : Input integer matrix n x (m*p) containing an X-adic representation to be cleaned up\n#\t\tX : Integer for the X-adic representation\n#\t\tn, m : Dimensions of each slice in A\n#\t\tp : Length of the X-adic representation, i.e., number of slices\n#\n# Output :\n#\t\tA : Integer matrix n x (m*p) containing the input X-adic representation that has been cleaned up\n#\nCleanUpXadic := proc(A, X, n, m, p)\n\tfor k to p-1 do\n#\t\tA[1..n, 1+m*k..m*(k+1)] := A[1..n, 1+m*k..m*(k+1)] + map(iquo, A[1..n, 1+m*(k-1)..m*k], X):\n#\t\tA[1..n, 1+m*(k-1)..m*k] := map(modp, A[1..n, 1+m*(k-1)..m*k], X):\n\t\tfor i to n do\n\t\t\tfor j to m do\n\t\t\t\tentry := A[i, j + m * (k - 1)]:\n\t\t\t\tif entry >= X then\n\t\t\t\t\tA[i, j + m * (k - 1)] := modp(entry, X):\n\t\t\t\t\tA[i, j + m * k] := A[i, j + m * k] + iquo(entry, X):\n\t\t\t\tfi:\n\t\t\tod:\n\t\tod:\n\tod:\n\t# Take care of the last slice as well\n#\tA[1..n, 1+m*(p-1)..m*p] := map(modp, A[1..n, 1+m*(p-1)..m*p], X):\n\tfor i to n do\n\t\tfor j to m do\n\t\t\tA[i, j + m * (p - 1)] := modp(A[i, j + m * (p - 1)], X):\n\t\tod:\n\tod:\n\treturn A:\nend proc:\n\n\n# ApplyDPOL : Applies the Double Plus One Lifting formula to a matrix B\n#\n# Input :\n#\t\tA_0, R, M : The output from the DoublePlusOneLift procedure, i.e., matrices that form the expansion of the inverse of a matrix A\n#\t\tB : Integer matrix n x (m*p) containing an X-adic representation on which the Double Plus One Lifting formula will be applied\n#\t\tX : Integer for the X-adic representation\n#\t\tn: Dimension of A_0, R[i], M[i], and the number of rows in B\n#\t\tm : Number of collumns of each slice in B\n#\t\tp : Length of the X-adic representation in B, i.e., number of slices\n#\t\tk : Length of the lists R and M\n#\n# Precondition : p <= 2^(k+1) - 1\n#\n# Output :\n#\t\tExpansion : Integer matrix n x (m*p) containg the X-adic representation of A^(-1) * B, where A is represented by its sparse inverese expansion here\n#\nApplyDPOL := proc(A_0, R, M, B, X, n, m, p, k)\n\tExpansion := Matrix(n, m*p):\n\tFactor := Copy(B):\n\tfor i from k-1 by -1 to 0 do\n\t\tExpansion := CleanUpXadic(Expansion + SwiftRightAndMultiply(M[i], Factor, 2^(i + 2) - 2, n, m, p), X, n, m, p):\n\t\tFactor := CleanUpXadic(Factor + SwiftRightAndMultiply(R[i], Factor, 2^(i + 1) - 1, n, m, p), X, n, m, p):\n\tod:\n\tExpansion := CleanUpXadic(Expansion + Multiply(A_0, Factor), X, n, m, p):\n\treturn Expansion:\nend proc:\n\n\n\n# SolveLinearSystem : Solves a linear system A*x=B <=> x=A^(-1)*B over the integers\n#\n# Input :\n#\t\tA : Integer matrix n x n\n#\t\tB : Integer matrix n x m\n#\t\tn: Dimension of A, and the number of rows in B\n#\t\tm : Number of collumns in B\n#\n# Output :\n#\t\tSolution : Integer matrix n x m containg the solution x of the linear system A*x=B\n#\nSolveLinearSystem := proc(A, B, n, m)\n\n\tX := 10007:\n\tk := 5:\n\tp := 2^(k+1)-1:\n\n\tA_0, R, M := DoublePlusOneLift(A, X, n, k):\n\n\tB_xadic := XadicRepresentationMatrixCreate(B, X, n, m, p):\n\n\tSolution_xadic := ApplyDPOL(A_0, R, M, B_xadic, X, n, m, p, k):\n\n\tSolution := XadicRepresentationMatrixCollapse(Solution_xadic, X, n, m, p):\n\n\treturn Solution:\n\nend proc:\n", "meta": {"hexsha": "1b78fcf252a9095682b32c8d0f1a1ff0710a6e7e", "size": 7252, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "doubleplusone.mpl", "max_stars_repo_name": "stavrosbir/matrix_lifting", "max_stars_repo_head_hexsha": "ab83de773dede8575badee909845ce1e314d435e", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "doubleplusone.mpl", "max_issues_repo_name": "stavrosbir/matrix_lifting", "max_issues_repo_head_hexsha": "ab83de773dede8575badee909845ce1e314d435e", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "doubleplusone.mpl", "max_forks_repo_name": "stavrosbir/matrix_lifting", "max_forks_repo_head_hexsha": "ab83de773dede8575badee909845ce1e314d435e", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 32.375, "max_line_length": 150, "alphanum_fraction": 0.639547711, "num_tokens": 2486, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9324533126145178, "lm_q2_score": 0.7981867753392728, "lm_q1q2_score": 0.7442719027502048}} |
| {"text": "with(simplex);\n\nConstraints := [\n# conservation of units at each node\ne13+e14 = 300, # CHI\ne23+e24 = 300, # DC\ne13+e23 = 300, # HOU\ne14+e24 = 300, # BOS\n# maximum flow on individual edges\n0 <= e13, e13 <= 200,\n0 <= e14, e14 <= 200,\n0 <= e23, e23 <= 280,\n0 <= e24, e24 <= 350\n];\n\nCost := 7*e13 + 6*e14 + 4*e23 + 6*e24;\n# Invoke linear programming to solve problem\nminimize (Cost, Constraints, NONNEGATIVE);", "meta": {"hexsha": "c351ac1d883b95f198d41e68cb6ac84de528621d", "size": 405, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Code/Maple/Chapter-8/Commands.mpl", "max_stars_repo_name": "konny0311/algorithms-nutshell-2ed", "max_stars_repo_head_hexsha": "760b0b8a296fb6be923c89406f61e773a48c59db", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 522, "max_stars_repo_stars_event_min_datetime": "2016-02-21T18:44:23.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-31T09:29:04.000Z", "max_issues_repo_path": "Code/Maple/Chapter-8/Commands.mpl", "max_issues_repo_name": "linfachen/algorithms-nutshell-2ed", "max_issues_repo_head_hexsha": "17bd6e9cf9917727501f9eeadbfb2100f94eede0", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 3, "max_issues_repo_issues_event_min_datetime": "2020-04-09T01:52:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-13T08:18:55.000Z", "max_forks_repo_path": "Code/Maple/Chapter-8/Commands.mpl", "max_forks_repo_name": "linfachen/algorithms-nutshell-2ed", "max_forks_repo_head_hexsha": "17bd6e9cf9917727501f9eeadbfb2100f94eede0", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 216, "max_forks_repo_forks_event_min_datetime": "2015-10-16T16:50:10.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-10T00:57:20.000Z", "avg_line_length": 22.5, "max_line_length": 44, "alphanum_fraction": 0.6345679012, "num_tokens": 160, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9473810511092412, "lm_q2_score": 0.7853085758631159, "lm_q1q2_score": 0.7439864640463}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: work_gga_x *)\n\n$define gga_x_rpw86_params\n$include \"gga_x_pw86.mpl\"\n\nmalpha := 0.02178:\nmbeta := 1.15:\nmuLV := 0.8491/9:\n\nf0 := s -> \n + (1 + muLV*s^2)/(1 + malpha*s^6) \n + malpha*s^6*f0_pw86(s)/(mbeta + malpha*s^6):\n\nf := x -> f0(X2S*x):\n\n", "meta": {"hexsha": "e1642ccf295593a99f21692df6087d203b10219b", "size": 496, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_lv_rpw86.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-4.2.3/maple/gga_x_lv_rpw86.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-4.2.3/maple/gga_x_lv_rpw86.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 20.6666666667, "max_line_length": 68, "alphanum_fraction": 0.6310483871, "num_tokens": 188, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9273632956467158, "lm_q2_score": 0.8006920020959543, "lm_q1q2_score": 0.7425323738616713}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: gga_exc *)\n\nbeefvdw_coeffs := [\n 1.516501714e0, 4.413532099e-1, -9.182135241e-2, -2.352754331e-2,\n 3.418828455e-2, 2.411870076e-3, -1.416381352e-2, 6.975895581e-4,\n 9.859205137e-3, -6.737855051e-3, -1.573330824e-3, 5.036146253e-3,\n -2.569472453e-3, -9.874953976e-4, 2.033722895e-3, -8.018718848e-4,\n -6.688078723e-4, 1.030936331e-3, -3.673838660e-4, -4.213635394e-4,\n 5.761607992e-4, -8.346503735e-5, -4.458447585e-4, 4.601290092e-4,\n -5.231775398e-6, -4.239570471e-4, 3.750190679e-4, 2.114938125e-5,\n -1.904911565e-4, 7.384362421e-5\n]:\n\nbeefvdw_k := 4:\nbeefvdw_xi := p -> 2*p/(beefvdw_k + p) - 1:\n\nwith(orthopoly):\nbeefvdw_f := x -> add(beefvdw_coeffs[i]*P(i-1, beefvdw_xi(X2S^2*x^2)), i=1..30):\n\nf := (rs, zeta, xt, xs0, xs1) -> gga_exchange(beefvdw_f, rs, zeta, xs0, xs1):\n", "meta": {"hexsha": "72382e2ec7d220dec99089373a71898d3d8729c8", "size": 1048, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_beefvdw.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_beefvdw.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_beefvdw.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 36.1379310345, "max_line_length": 80, "alphanum_fraction": 0.6679389313, "num_tokens": 519, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9615338112885302, "lm_q2_score": 0.7718434978390747, "lm_q1q2_score": 0.7421536201954759}} |
| {"text": "\r\n\r\n { Planning.mpl }\r\n\r\n { Aggregate production planning for 12 months }\r\n\r\nTITLE\r\n Production_Planning;\r\n\r\nINDEX\r\n product := 1..3;\r\n\r\n month := (January,February,March,April,May,June,July,\r\n August,September,October,November,December);\r\nDATA\r\n price[product] := (105.09, 234.00, 800.00); [$/Boxes]\r\n Demand[month,product] := 1000 DATAFILE(Demand.dat); [Boxes/month]\r\n ProductionCapacity[product] := 1000 (10, 42, 14); [Boxes/month]\r\n ProductionCost[product] := (94.0, 188.10, 653.20); [$/Boxes]\r\n InventoryCost := 8.8; [$/Boxes/month]\r\n\r\nDECISION VARIABLES\r\n Inventory[product,month] -> Invt; [Boxes]\r\n Production[product,month] -> Prod; [Boxes/month]\r\n Sales[product,month] -> Sale; [Boxes/month]\r\n\r\n\r\n\r\nMACRO\r\n Revenues := SUM(product,month: price * Sales); [$]\r\n\r\n TotalCost := SUM(product,month: ProductionCost[product] * Production[product,month]\r\n + InventoryCost * Inventory[product,month]); [$]\r\n\r\n\r\nMODEL\r\n\r\n\r\n MAX Profit = Revenues - TotalCost;\r\n\r\n\r\nSUBJECT TO\r\n\r\n InvtBal[product,month] : Inventory = Inventory[month-1] + Production - Sales;\r\n\r\n\r\n\r\nBOUNDS\r\n Sales < Demand ;\r\n\r\n Production < ProductionCapacity ;\r\n\r\n Inventory[month=January..November] < 90000 ;\r\n Inventory[month=December] = 20000 ;\r\n\r\nEND\r\n\r\n", "meta": {"hexsha": "90e4746751255b278d2640856f109c047cb28b03", "size": 1544, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Planning.mpl", "max_stars_repo_name": "BjarniMax/mpl-models", "max_stars_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Planning.mpl", "max_issues_repo_name": "BjarniMax/mpl-models", "max_issues_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Planning.mpl", "max_forks_repo_name": "BjarniMax/mpl-models", "max_forks_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.6206896552, "max_line_length": 89, "alphanum_fraction": 0.5310880829, "num_tokens": 404, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9449947086083139, "lm_q2_score": 0.7853085859124002, "lm_q1q2_score": 0.7421124583118957}} |
| {"text": "######################################################################\n\n# A full tree on A is a tree that contains A, and also contains {a}\n# for all a in A.\n# (Definition defn-full-trees)\n\n`is_element/full_trees` := (A::set) -> proc(TT)\n local a;\n global reason;\n\n if not(`is_element/trees`(A)(TT)) then\n reason := [convert(procname,string),\"TT is not a tree\",TT,reason];\n return false;\n fi;\n if not(member(A,TT)) then\n reason := [convert(procname,string),\"The full set A is not in TT\",A,TT];\n return false;\n fi;\n\n for a in A do\n if not(member({a},TT)) then\n reason := [convert(procname,string),\"The singleton {a} is not in TT\",a,TT];\n return false;\n fi; \n od;\n\n return true;\nend;\n\n`is_equal/full_trees` := eval(`is_equal/trees`);\n`is_leq/full_trees` := eval(`is_leq/trees`);\n\n# A full tree TT on A is binary if every non-minimal set in TT has\n# precisely two children. This holds iff |TT| = 2|A|-1.\n\n`is_binary/full_trees` := (A) -> proc(TT)\n return evalb(nops(TT) = 2*nops(A)-1);\nend:\n\n`list_elements/full_trees`:= proc(A::set)\n local n,a,A1,TTT1,TTT,TT1,T1;\n\n # Degenerate cases for small A \n if A={} then return []; fi;\n if nops(A)=1 then return [{A}]; fi;\n\n # If A is not too small, we write it as {a} union A1. Then we recursively\n # choose a random tree on A1, and attach a to it.\n\n n := nops(A);\n a := A[n];\n A1 := A minus {a};\n TTT1 := `list_elements/full_trees`(A1);\n\n TTT := [];\n for TT1 in TTT1 do\n for T1 in TT1 do\n TTT := [op(TTT),`attach_to_tree`(A1)(TT1,T1,a,true)];\n if n > 2 and nops(T1) > 1 then\n TTT := [op(TTT),`attach_to_tree`(A1)(TT1,T1,a,false)];\n fi;\n od;\n od;\n \n return TTT;\nend:\n\n# A000311 from OEIS\n\n`count_elements/full_trees` := proc(A::set)\n local n,i,j,k;\n n := nops(A);\n if n = 0 then\n return 0;\n elif n = 1 then\n return 1;\n else\n return \n add(\n (n+k-1)!*\n add(\n 1/(k-j)! * \n add(\n (2^i*(-1)^(i)*Stirling2(n+j-i-1,j-i))/((n+j-i-1)!*i!),\n i=0..j),\n j=1..k),\n k=1..n-1);\n fi;\nend;\n\n`random_element/full_trees`:= (A::set) -> proc()\n local n,a,A1,T0,T1,T,above;\n\n # Degenerate cases for small A \n if A={} then return FAIL; fi;\n if nops(A)=1 then return {A}; fi;\n\n # If A is not too small, we write it as {a} union A1. Then we recursively\n # choose a random tree on A1, and attach a to it.\n\n n := nops(A);\n a := A[rand(1..n)()];\n A1 := A minus {a};\n if n = 2 then\n above := true;\n else\n above := evalb(rand(0..1)() = 1);\n fi;\n\n T0 := `random_element/full_trees`(A1)();\n T1 := select(U -> nops(U) > 1,T0);\n\n if above then\n T := T0[rand(1..nops(T0))()];\n else\n T := T1[rand(1..nops(T1))()];\n fi;\n\n T := `attach_to_tree`(A1)(T0,T,a,above);\n \n return T;\nend;\n\n", "meta": {"hexsha": "7909d6adb7ce4bfd9b29af1083a3944bd3b9453f", "size": 2647, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/full_trees.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/full_trees.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/full_trees.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 21.3467741935, "max_line_length": 78, "alphanum_fraction": 0.5810351341, "num_tokens": 918, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9111797003640646, "lm_q2_score": 0.8128673246376009, "lm_q1q2_score": 0.740668205299028}} |
| {"text": "# real 3 metric for BSSN in spherical symmetry.\nNdim_ := 3:\nx1_ := x:\nx2_ := theta:\nx3_ := phi:\ncomplex_ := {}:\ng11_ := A(x)*exp(4*phi(x)):\ng12_ := 0:\ng13_ := 0:\ng22_ := x^2*B(x)*exp(4*phi(x)):\ng23_ := 0:\ng33_ := x^2*B(x)*(sin(theta))^2*exp(4*phi(x)):\n", "meta": {"hexsha": "65048995b32c4d5bb73acb8d7ae04c2b9358f60b", "size": 252, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "metrics/spher_3_met.mpl", "max_stars_repo_name": "rmanak/bssn_spher", "max_stars_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "metrics/spher_3_met.mpl", "max_issues_repo_name": "rmanak/bssn_spher", "max_issues_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "metrics/spher_3_met.mpl", "max_forks_repo_name": "rmanak/bssn_spher", "max_forks_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 19.3846153846, "max_line_length": 47, "alphanum_fraction": 0.5515873016, "num_tokens": 117, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9674102524151827, "lm_q2_score": 0.7634837689358857, "lm_q1q2_score": 0.7386020256211602}} |
| {"text": "\n { DakotaScen.mpl }\n\n\nTITLE\n DakotaScen;\n\n\nINDEX\n product := (Desk, Tble, Chair);\n resource := (Lumber, Finishing, Carpentry);\n\nSTOCHASTIC \n\nTREE\n TWOSTAGE;\n\nSCENARIOS\n scen := 1..3;\n\nPROBABILITIES\n Prob[scen] := (0.3, 0.4, 0.3);\n\nRANDOM DATA\n Demand[product,scen] := (50, 150, 250, \n 20, 110, 250, \n 200, 225, 500);\n\nDATA\n Cost[resource] := (2, 4, 5.2);\n ProdReq[resource, product] := (8, 6, 1, \n 4, 2, 1.5, \n 2, 1.5, 0.5);\n Price[product] := (60, 40, 10);\n\n Budget := 8000; \n\n\nDECISION VARIABLES\n Acquire[resource]\n\nSTAGE2 VARIABLES\n Produce[product];\n\n\nMODEL\n Max Profit = SUM(product: Price * Produce) \n - SUM(resource: Cost * Acquire);\n\nSUBJECT TO\n MaxBudget[resource]: Cost * Acquire <= Budget;\n\n MaxProduce[product]: Produce <= Demand;\n\n MinAcquire[resource]: SUM(product: ProdReq * Produce) <= Acquire;\n\nEND\n", "meta": {"hexsha": "4fc0a5715c0721d0232c85da6bcf367a26cbd13c", "size": 1005, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Stochastic/DakotaScen.mpl", "max_stars_repo_name": "BjarniMax/mpl-models", "max_stars_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Stochastic/DakotaScen.mpl", "max_issues_repo_name": "BjarniMax/mpl-models", "max_issues_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Stochastic/DakotaScen.mpl", "max_forks_repo_name": "BjarniMax/mpl-models", "max_forks_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 17.3275862069, "max_line_length": 68, "alphanum_fraction": 0.5243781095, "num_tokens": 329, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9334308110294984, "lm_q2_score": 0.7905303112671295, "lm_q1q2_score": 0.7379053495894785}} |
| {"text": "\r\n { Diet.mpl }\r\n\r\n{\r\n This model determines a least cost diet which meets the daily\r\n allowances of nutrients for a man weighing 154 lbs.\r\n\r\n Reference: G. B. Dantzig, Linear Programming and Extensions,\r\n Princeton University Press, Princeton, New Jersey, 1963.\r\n}\r\n\r\n\r\nTITLE\r\n Stiglers_nutrition_model\r\n\r\nINDEX\r\n nutrients = (Calorie,Protein,Calcium,Iron,Avitamin\r\n Thiamine,Riboflavin,Niacin,Cvitamin) : 10\r\n\r\n foods = (WheatFlour,CornMeal,EvapMilk,Margarine,\r\n Cheese,Lard,Liver,PorkRoast,Salmon,\r\n GreenBeans,Cabbage,Onions,Potatoes,Spinach,\r\n SweetPot,Peaches,Prunes,LimaBeans,NavyBeans) : 10\r\n\r\n\r\nDATA\r\n Required[nutrients] = ( 3 ! Calories [thousands]\r\n 70 ! Protein [grams]\r\n 0.8 ! Calcium [grams]\r\n 12 ! Iron [milligrams]\r\n 5 ! Avitamin [thousand ius]\r\n 1.8 ! Thiamine (B1) [milligrams]\r\n 2.7 ! Riboflavin (B2) [milligrams]\r\n 18 ! Niacin [milligrams]\r\n 75 ) ; ! Cvitamin [milligrams]\r\n\r\n\r\n A[foods,nutrients] = DATAFILE(nutri.dat) ! Nutritive values of foods\r\n ! per dollar expenditure.\r\n\r\nDECISION\r\n x[foods] -> \"\" ! dollars of food to be purchased daily\r\n\r\n\r\n\r\nMODEL\r\n\r\n MIN Cost = SUM(foods: x) ;\r\n\r\nSUBJECT TO\r\n\r\n NutrBal[nutrients] -> \"\" : SUM(foods: A*x) > Required[nutrients];\r\n\r\nEND\r\n\u001a", "meta": {"hexsha": "6b040cdabfe87b606273fe53387968bb22df6902", "size": 1740, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Diet.mpl", "max_stars_repo_name": "BjarniMax/mpl-models", "max_stars_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Diet.mpl", "max_issues_repo_name": "BjarniMax/mpl-models", "max_issues_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Diet.mpl", "max_forks_repo_name": "BjarniMax/mpl-models", "max_forks_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 31.6363636364, "max_line_length": 75, "alphanum_fraction": 0.4793103448, "num_tokens": 431, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9546474194456936, "lm_q2_score": 0.7718434978390747, "lm_q1q2_score": 0.7368384034280104}} |
| {"text": "################################\n# Derivation of BSSN equations\n# Using GR-Tensor\n# See bssn_spher.mw for interactive\n# version of this script\n################################\ngrtw();\ngrload(g,\"metrics/spher_3.mpl\");\ngrdisplay(g(dn,dn));\ngrcalc(g(up,up));\ngrdisplay(g(up,up));\ngrdef(`g_f{a b} := kdelta{a $x}*kdelta{b $x}*1 + kdelta{a $theta}*kdelta{b $theta}*x^2 + kdelta{a $phi}*kdelta{b $phi}*x^2*(sin(theta))^2`); grcalc(g_f(dn,dn)); grdisplay(g_f(dn,dn));\ngrdef(`g_f_inv{^a ^b} := kdelta{^a $x}*kdelta{^b $x}*1 + kdelta{^a $theta}*kdelta{^b $theta}*1/x^2 + kdelta{^a $phi}*kdelta{^b $phi}*1/(x^2*(sin(theta))^2)`); grcalc(g_f_inv(up,up)); grdisplay(g_f_inv(up,up));\ngrdef(`ChL_f{d a b} := 1/2*( g_f{b d ,a} + g_f{a d,b} - g_f{a b,d})`);\ngrdef(`MCh_f{^c a b} := g_f_inv{^c ^d} * ChL_f{d a b}`):\ngrcalc(MCh_f(up,dn,dn)); grdisplay(MCh_f(up,dn,dn));\ngrdef(`ChL{d a b} := 1/2*( g{b d ,a} + g{a d,b} - g{a b,d})`):\ngrdef(`MCh{^c a b} := g{^c ^d} * ChL{d a b}`):\ngrcalc(MCh(up,dn,dn));\ngralter(MCh(up,dn,dn),simplify,expand);\ngrdisplay(MCh(up,dn,dn));\ngrdef(`TG{^i} := g{^j ^k}*MCh{^i j k}`);\ngrcalc(TG(up));\ngrdisplay(TG(up));\ngrdef(`TG2{^i} := g{^j ^k}*(MCh{^i j k}-MCh_f{^i j k})`); grcalc(TG2(up)); gralter(TG2(up),simplify,expand); grdisplay(TG2(up));\ngrdef(`Lam{^a} := [Lamx(t,x),0,0]`);\ngrcalc(Lam(up)); grdisplay(Lam(up));\ngrdef(`GA{^i} := Lam{^i} + g{^j ^k}*MCh_f{^i j k}`); grcalc(GA(up)); grdisplay(GA(up));\ngrdef(`SS{i j} := 2*g{^l ^m}*MCh{^k l (i}*ChL{j) k m} + g{^l ^m}*MCh{^k i m}*ChL{k l j}`);\ngrcalc(SS(dn,dn));\ngralter(SS(dn,dn),simplify);\ngrdisplay(SS(dn,dn));\ngrdef(`RB{i j} := -1/2*g{^l ^m}*g{i j ,l ,m} + g{k (i}*GA{^k ,j)} + GA{^k}*ChL{(i j) k} + SS{i j}`);\ngrcalc(RB(dn,dn));\ngralter(RB(dn,dn),simplify,expand);\ngrdisplay(RB(dn,dn));\ngrdef(`CF{} := phi(t,x)`);\ngrcalc(CF);\ngrdef(`DCF{i} := CF{;i}`);\ngrcalc(DCF(dn));\ngrdisplay(DCF(dn));\ngrdef(`Rphi{i j} := -2*DCF{j ;i} - 2*g{i j}*DCF{^k ;k} + 4*DCF{i}*DCF{j} - 4*g{i j}*DCF{^k}*DCF{k}`);\ngrcalc(Rphi(dn,dn));\ngralter(Rphi(dn,dn),expand,simplify,expand);\ngrdisplay(Rphi(dn,dn));\ngrcalc(R(dn,dn)); grdisplay(R(dn,dn));\ngrdef(`RBtest{i j} := -1/2*g{^l ^m}*g{i j ,l ,m} + g{k (i}*TG{^k ,j)} + TG{^k}*ChL{(i j) k} + SS{i j}`);\ngrdef(`Rresid{i j} := RBtest{i j} - R{i j}`);\ngrcalc(Rresid(dn,dn));\ngralter(Rresid(dn,dn),simplify);\ngrdisplay(Rresid(dn,dn));\ngrdef(`Sh{^a}:=[beta(t,x),0,0]`);\ngrcalc(Sh(up));\ngrdisplay(Sh(up));\ngrdef(`Q{i j} := Sh{^k}*g{i j ,k} + g{i k}*Sh{^k ,j} + g{k j}*Sh{^k ,i} -2/3*g{i j}*vee*divbeta(t,x)`);\ngrcalc(Q(dn,dn));\ngrdisplay(Q(dn,dn));\ngrdef(`A{a b} := kdelta{a $x}*kdelta{b $x}*Axx(t,x)/1 + kdelta{a $theta}*kdelta{b $theta}*x^2*Athth(t,x) + kdelta{a $phi}*kdelta{b $phi}*x^2*(sin(theta))^2*Athth(t,x)`);\ngrcalc(A(dn,dn));grdisplay(A(dn,dn));\ngrdef(`P{i j} := Sh{^k}*A{i j,k} + A{i k}*Sh{^k ,j} + A{k j}*Sh{^k ,i} - 2/3*A{i j}*vee*divbeta(t,x)`):\ngrcalc(P(dn,dn));\ngrdisplay(P(dn,dn));\ngrdef(`Extc{} := K(t,x)`);\ngrcalc(Extc);\ngrdef(`Lapse{} := alpha(t,x)`);\ngrcalc(Lapse);\ngrdef(`S{i} :=[Sx(t,x),0,0]`);\ngrcalc(S(dn));\n\ngrdef(`DBS{} := divbeta(t,x)`);\ngrdef(`DGA{^i} := g{^l ^j}*Sh{^i ,l ,j} - 2*A{^i ^j}*Lapse{,j} + 2*Lapse*(MCh{^i j k}*A{^k ^j} - 2/3*g{^i ^j}*Extc{,j} - g{^i ^j}*S{j} + 6*A{^i ^j}*DCF{j}) + Sh{^j}*GA{^i ,j} - GA{^j}*Sh{^i ,j} +vee/3*(2*GA{^i}*divbeta(t,x)+g{^i ^l}*DBS{,l})`);\ngrcalc(DGA(up));\n\ngralter(DGA(up),simplify,expand,trigsin,factor,expand); \ngrdisplay(DGA(up));\ngrdef(`met{a b} := exp(4*CF)*(kdelta{a $x}*kdelta{b $x}*A(t,x) + kdelta{a $theta}*kdelta{b $theta}*B(t,x)*x^2 + kdelta{a $phi}*kdelta{b $phi}*B(t,x)*x^2*sin(theta)^2)`);\ngrcalc(met(dn,dn));\ngrdisplay(met(dn,dn));\n\ngrdef(`met_s{a b} := kdelta{a $x}*kdelta{b $x}*metxx(t,x) + kdelta{a $theta}*kdelta{b $theta}*x^2*metthetatheta(t,x) + kdelta{a $phi}*kdelta{b $phi}*x^2*(sin(theta))^2*metthetatheta(t,x)`);\ngrcalc(met_s(dn,dn));grdisplay(met_s(dn,dn));\ngrdef(`invmet_s{^a ^b}:=kdelta{^a $x}*kdelta{^b $x}*1/metxx(t,x) + kdelta{^a $theta}*kdelta{^b $theta}*1/(x^2*metthetatheta(t,x)) + kdelta{^a $phi}*kdelta{^b $phi}*1/(x^2*(sin(theta))^2*metthetatheta(t,x))`);\ngrcalc(invmet_s(up,up));\ngrdisplay(invmet_s(up,up));\ngrdef(`rChL{d a b} := 1/2*( met_s{b d ,a} + met_s{a d,b} - met_s{a b,d})`);\ngrdef(`rMCh{^c a b} := invmet_s{^c ^d} * rChL{d a b}`);\ngrdef(`DDL{b c} := Lapse{,c ,b} - rMCh{^d b c}*Lapse{,d}`);\ngrcalc(DDL(dn,dn));\ngrdisplay(DDL(dn,dn));\ngrdef(`rR{u p} := rMCh{^v u p ,v} - rMCh{^v v p ,u} + rMCh{^a u p}*rMCh{^v a v} - rMCh{^a v p}*rMCh{^v a u}`);\ngrdef(`RHO{} := rho(t,x)`);\ngrcalc(RHO);\ngrdef(`TraceS{} := TS(t,x)`);\ngrcalc(TraceS);\ngrdef(`DDL_s{a b} := kdelta{a $x}*kdelta{b $x}*DDLxx(t,x) + kdelta{a $theta}*kdelta{b $theta}*x^2*DDLthetatheta(t,x) + kdelta{a $phi}*kdelta{b $phi}*x^2*DDLthetatheta(t,x)*(sin(theta))^2`);\ngrcalc(DDL_s(dn,dn)); grdisplay(DDL_s(dn,dn));\ngrdef(`TD{} := invmet_s{^i ^j} * DDL_s{i j}`);\ngrcalc(TD);\ngrdisplay(TD);\ngrdef(`DDLTF{i j} := DDL_s{i j} - 1/3*TD*met_s{i j}`);\ngrcalc(DDLTF(dn,dn));\ngrdisplay(DDLTF(dn,dn));\n\ngrdef(`DTK{} := -TD +Lapse*(A{i j}*A{^i ^j} +1/3*Extc^2) +1/2*Lapse*(RHO+TraceS) +Sh{^i}*Extc{,i}`);\ngrcalc(DTK);\ngralter(DTK,simplify,expand);\ngrdisplay(DTK);\ngrdef(`JS{a b} := kdelta{a $x}*kdelta{b $x}*JSxx(t,x) + kdelta{a $theta}*kdelta{b $theta}*x^2*JSthth(t,x) + kdelta{a $phi}*kdelta{b $phi}*x^2*(sin(theta))^2*JSthth(t,x)`);\ngrcalc(JS(dn,dn));\ngrdisplay(JS(dn,dn));\ngrdef(`TJS := invmet_s{^i ^j}*JS{i j}`);\ngrcalc(TJS);\ngralter(TJS,simplify,expand);\ngrdisplay(TJS);\ngrdef(`U{i j} := (Extc*A{i j} - 2*A{i l}*A{^l j})`);\ngrcalc(U(dn,dn));\ngralter(U(dn,dn),simplify,expand);\ngrdisplay(U(dn,dn));\ngrdef(`dg{i j} := -2*Lapse*A{i j} + Q{i j}`);\ngrcalc(dg(dn,dn));\ngralter(dg(dn,dn),simplify,factor);\ngrdisplay(dg(dn,dn));\ngrdef(`dgu{^i ^j} := -g{^i ^l}*dg{l m}*g{^m ^j}`); grcalc(dgu(up,up)); grdisplay(dgu(up,up));\ngrdef(`deltaDGA{^i} := -dgu{^j ^k}*MCh_f{^i j k}`); grcalc(deltaDGA(up)); grdisplay(deltaDGA(up));\ngrdef(`DLAM{^i} := DGA{^i} + deltaDGA{^i}`); grcalc(DLAM(up)); gralter(DLAM(up),simplify,expand); grdisplay(DLAM(up));\ngrdef(`DPH{} := -1/6*Lapse*Extc + Sh{^i}*CF{,i} + 1/6*divbeta(t,x)`);\ngrcalc(DPH); grdisplay(DPH);\ngrdef(`TRB{} := g{^i ^j}*RB{i j}`);\ngrcalc(TRB);\ngralter(TRB,simplify);\ngrdisplay(TRB);\ngrdef(`PSI{} := psi(t,x)`);\ngrcalc(PSI);\ngrdef(`C1 {} := -1/8*TRB`); grcalc(C1); gralter(C1,simplify,expand,factor,expand); grdisplay(C1);\ngrdef(`C5{} := 1/8*A{i j}*A{^i ^j} -1/12*Extc^2 + 1/4*rho(t,x)`);\ngrcalc(C5); gralter(C5,simplify,expand); grdisplay(C5);\ngrdef(`HS3{} := g{^i ^j}*PSI{;j ;i} + C5psi(t,x) + C1s(t,x)*PSI`);\ngrdef(`HS{} := g{^i ^j}*PSI{;j ;i} + C5s(t,x)*PSI^5 + C1s(t,x)*PSI`); grdef(`HSR{} := g{^i ^j}*PSI{;i ;j} - 1/8*TRB*PSI + 1/8*A{i j}*A{^i ^j}*PSI^5 -1/12*PSI^5*Extc^2 + 1/4*rho(t,x)*PSI^5`); grcalc(HSR);gralter(HSR,simplify,expand,factor,expand);grdisplay(HSR);\ngrcalc(HS);\ngralter(HS,simplify,expand,factor,expand);\ngrdisplay(HS);\ngrcalc(HS3); grdisplay(HS3);gralter(HS3,expand);\ngrdef(`RR{i j} := RB{i j} + Rphi{i j}`); \ngrcalc(RR(dn,dn));\ngralter(RR(dn,dn),simplify,expand,factor,expand);\ngrdisplay(RR(dn,dn));\ngrdef(`RR_s{a b} := kdelta{a $x}*kdelta{b $x}*RRxx(t,x) + kdelta{a $theta}*kdelta{b $theta}*x^2*RRthetatheta(t,x) + kdelta{a $phi}*kdelta{b $phi}*x^2*(sin(theta))^2*RRthetatheta(t,x)`);\ngrcalc(RR_s(dn,dn)); grdisplay(RR_s(dn,dn));\ngrdef(`TR{} := invmet_s{^i ^j}*RR_s{i j}`);\ngrcalc(TR);\ngrdisplay(TR);\n\ngrdef(`RRTF{i j} := RR_s{i j} - 1/3*met_s{i j}*TR`); \ngrcalc(RRTF(dn,dn));\ngrdisplay(RRTF(dn,dn));\ngrdef(`P_s{a b} := kdelta{a $x}*kdelta{b $x}*Pxx(t,x) + kdelta{a $theta}*kdelta{b $theta}*x^2*Pthetatheta(t,x) + kdelta{a $phi}*kdelta{b $phi}*x^2*(sin(theta))^2*Pthetatheta(t,x)`);\ngrcalc(P_s(dn,dn)); grdisplay(P_s(dn,dn));\ngrdef(`U_s{a b} := kdelta{a $x}*kdelta{b $x}*Uxx(t,x) + kdelta{a $theta}*kdelta{b $theta}*x^2*Uthetatheta(t,x) + kdelta{a $phi}*kdelta{b $phi}*x^2*(sin(theta))^2*Uthetatheta(t,x)`);\ngrcalc(U_s(dn,dn));\ngrdisplay(U_s(dn,dn));\ngrdef(`DAA{i j} := em4phi(t,x)*(-DDLTF{i j} + Lapse*(RRTF{i j} - ( JS{i j} - 1/3*met_s{i j}*TJS) )) + Lapse*U_s{i j} + P_s{i j}`);\ngrcalc(DAA(dn,dn));\ngralter(DAA(dn,dn),simplify,expand);\ngrdisplay(DAA(dn,dn));\ngrdef(`EMPH{} := exp(-4*CF)`);grcalc(EMPH);grdisplay(EMPH);\ngrdef(`MKTR1{^j ^i} := PSI^6*A{^j ^i}`); \ngrdef(`MK{^i} := MKTR1{^j ^i ;j} - 2/3*PSI^6*g{^i ^j}*Extc{;j} - PSI^6*g{^i ^j}*S{j}`); grcalc(MK(up)); gralter(MK(up),simplify,expand); grdisplay(MK(up));\ngrdef(`DB:= Sh{^i ;i}`); grcalc(DB); grdisplay(DB);gralter(DB,simplify,expand); grdisplay(DB);\n\n\n", "meta": {"hexsha": "70d9c3daa8d4990894874490c072a2ec116cd192", "size": 8442, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "bssn_spher.mpl", "max_stars_repo_name": "rmanak/bssn_spher", "max_stars_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "bssn_spher.mpl", "max_issues_repo_name": "rmanak/bssn_spher", "max_issues_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "bssn_spher.mpl", "max_forks_repo_name": "rmanak/bssn_spher", "max_forks_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 49.3684210526, "max_line_length": 261, "alphanum_fraction": 0.5852878465, "num_tokens": 3990, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9196425311777929, "lm_q2_score": 0.8006920092299293, "lm_q1q2_score": 0.7363504260620449}} |
| {"text": "# Proof by PDF that X <~ rayleigh(1) == X^2 <~ weibull(1,1)\n\nPDF_rayleigh := (a, x) -> 2*x*exp(-x^2/a)/a;\n\nPDF_transform := (x) -> PDF_rayleigh(1,sqrt(x))*diff(sqrt(x),x);\nsimplify(PDF_transform(x));\n\nPDF_weibull := (k, t, x) -> k/t*x^(k-1)*exp(-1*(1/t)*x^k);\nsimplify(PDF_weibull(1, 1, x));\n\nevalb(PDF_weibull(1, 1, x) = PDF_transform(x));", "meta": {"hexsha": "c7577302754077cc9ea7aba3867cc0834023025a", "size": 340, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "tests/RoundTrip2/t_weibull_to_rayleigh.proof.mpl", "max_stars_repo_name": "vmchale/hakaru", "max_stars_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 327, "max_stars_repo_stars_event_min_datetime": "2015-01-03T08:56:51.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-24T12:12:06.000Z", "max_issues_repo_path": "tests/RoundTrip2/t_weibull_to_rayleigh.proof.mpl", "max_issues_repo_name": "vmchale/hakaru", "max_issues_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 155, "max_issues_repo_issues_event_min_datetime": "2015-05-05T17:57:22.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T15:43:39.000Z", "max_forks_repo_path": "tests/RoundTrip2/t_weibull_to_rayleigh.proof.mpl", "max_forks_repo_name": "vmchale/hakaru", "max_forks_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 38, "max_forks_repo_forks_event_min_datetime": "2015-01-23T16:25:37.000Z", "max_forks_repo_forks_event_max_datetime": "2021-03-14T15:09:12.000Z", "avg_line_length": 30.9090909091, "max_line_length": 64, "alphanum_fraction": 0.6, "num_tokens": 146, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9372107931567177, "lm_q2_score": 0.785308580887758, "lm_q1q2_score": 0.7359996779665922}} |
| {"text": "######################################################################\n\n`is_element/equiv` := (A::set) -> proc(R)\n global reason;\n\n if not `is_element/autorel`(A)(R) then\n reason := [convert(procname,string),\"R is not a relation on A\",R,A,reason];\n return false;\n fi;\n\n if not(`is_reflexive/autorel`(A)(R)) then\n reason := [convert(procname,string),\"R is not reflexive\",R];\n return false;\n fi;\n \n if not(`is_symmetric/autorel`(A)(R)) then\n reason := [convert(procname,string),\"R is not symmetric\",R];\n return false;\n fi;\n \n if not(`is_transitive/autorel`(A)(R)) then\n reason := [convert(procname,string),\"R is not transitive\",R];\n return false;\n fi;\n \n return true;\nend;\n\n`is_equal/equiv` := eval(`is_equal/autorel`);\n`is_leq/equiv` := eval(`is_leq/autorel`);\n`is_separated/equiv` := eval(`is_separated/autorel`);\n\n`is_total/equiv` := (A::set) -> proc(R)\n local U,a,b;\n\n U := {seq(seq([a,b],b in A),a in A)} minus R;\n\n return evalb(U = {}); \nend;\n\n`block_partition/equiv` := (A::set) -> proc(R)\n local pi,X,x,B;\n\n pi := NULL;\n X := A;\n\n while X <> {} do\n x := X[1];\n B := map(ab -> ab[2],select(ab -> ab[1] = x,R));\n pi := pi,B;\n X := X minus B;\n od:\n\n pi := {pi};\n\n return pi;\nend:\n\n`block_equiv/partition` := (A::set) -> proc(pi)\n local B,x,y;\n {seq(seq(seq([x,y],y in B),x in B),B in pi)};\nend;\n\n`equiv_is_equiv` := (A::set) -> (R) -> (a,b) ->\n member([a,b],R);\n\n`random_element/equiv` := (A::set) -> proc()\n `block_equiv/partition`(A)(`random_element/partitions`(A)());\nend;\n\n`list_elements/equiv` := proc(A::set)\n map(`block_equiv/partition`(A),\n `list_elements/partitions`(A));\nend:\n\n`count_elements/equiv` := (A::set) -> combinat[bell](nops(A));\n", "meta": {"hexsha": "67e8a32c94eba6be6747eb5f422e9d2bcfdb8e56", "size": 1684, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/equiv.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/equiv.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/equiv.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 21.8701298701, "max_line_length": 77, "alphanum_fraction": 0.575415677, "num_tokens": 549, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8991213772699435, "lm_q2_score": 0.8175744761936437, "lm_q1q2_score": 0.7350986890559815}} |
| {"text": "\r\n\r\nTITLE BetterBreadBakery;\r\n\r\n\r\nMAX\r\n\r\n Profit = 0.05 Sun + 0.08 Moon - 4000/30 ;\r\n\r\nSUBJECT TO\r\n\r\n 1/10 Sun + 1/5 Moon <= 10 * 140 ;\r\n\r\n Sun <= 8000;\r\n Moon <= 5000;\r\nEND\r\n", "meta": {"hexsha": "3db8c9218732f44ddaf8c3b78e6e5351f7a10db0", "size": 190, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Bakery.mpl", "max_stars_repo_name": "BjarniMax/mpl-models", "max_stars_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Bakery.mpl", "max_issues_repo_name": "BjarniMax/mpl-models", "max_issues_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Bakery.mpl", "max_forks_repo_name": "BjarniMax/mpl-models", "max_forks_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 11.1764705882, "max_line_length": 46, "alphanum_fraction": 0.4947368421, "num_tokens": 74, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9481545362802364, "lm_q2_score": 0.7745833737577158, "lm_q1q2_score": 0.734424739555628}} |
| {"text": "#If X ~ Pareto(λ, 1) then log(X) ~ Exp(λ).\n\n# Proof:\nPDF_pareto := (lambda, k, x) -> lambda * k ^ lambda / x ^ (lambda + 1);\n\nPDF_exponential := (alpha, x) -> exp(-x/alpha)/alpha;\n\nsimplify(PDF_pareto(lambda, 1, exp(x))*diff(exp(x),x));\n\nsimplify(PDF_exponential(1/lambda, x));\n\n", "meta": {"hexsha": "c4c75aa9eda343ddd2b1de4eb325e686a1bdcd4b", "size": 279, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "tests/RoundTrip/t_pareto_to_exponential.proof.mpl", "max_stars_repo_name": "vmchale/hakaru", "max_stars_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 327, "max_stars_repo_stars_event_min_datetime": "2015-01-03T08:56:51.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-24T12:12:06.000Z", "max_issues_repo_path": "tests/RoundTrip/t_pareto_to_exponential.proof.mpl", "max_issues_repo_name": "vmchale/hakaru", "max_issues_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 155, "max_issues_repo_issues_event_min_datetime": "2015-05-05T17:57:22.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T15:43:39.000Z", "max_forks_repo_path": "tests/RoundTrip/t_pareto_to_exponential.proof.mpl", "max_forks_repo_name": "vmchale/hakaru", "max_forks_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 38, "max_forks_repo_forks_event_min_datetime": "2015-01-23T16:25:37.000Z", "max_forks_repo_forks_event_max_datetime": "2021-03-14T15:09:12.000Z", "avg_line_length": 23.25, "max_line_length": 71, "alphanum_fraction": 0.6129032258, "num_tokens": 103, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9362849986365572, "lm_q2_score": 0.782662489091802, "lm_q1q2_score": 0.7327951475322023}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: work_gga_x *)\n\ns1 := 0.6:\ns2 := 2.6:\n\n(* The equations to solve in order to obtain the coeficients cc are\n G(s1) = 0\n G(s2) = 1\n G'(s1) = 0\n G'(s2) = 0\nG''(s1) = 0\nG''(s2) = 0\n*)\n\ncc0 := s1^3*(s1^2 - 5*s1*s2 + 10*s2^2)/(s1 - s2)^5:\ncc1 := -30*s1^2*s2^2/(s1 - s2)^5:\ncc2 := 30*s1*s2*(s1 + s2)/(s1 - s2)^5:\ncc3 := -10*(s1^2 + 4*s1*s2 + s2^2)/(s1 - s2)^5:\ncc4 := 15*(s1 + s2)/(s1 - s2)^5:\ncc5 := -6/(s1 - s2)^5:\n\n$define gga_x_rpbe_params\n$include \"gga_x_rpbe.mpl\"\n$include \"gga_x_wc.mpl\"\n\ng := s -> cc0 + cc1*s + cc2*s^2 + cc3*s^3 + cc4*s^4 + cc5*s^5:\n\nf0 := s -> convert(piecewise(\n s < s1, f0_wc(s),\n s > s2, f0_rpbe(s),\n g(s)*f0_rpbe(s) + (1 - g(s))*f0_wc(s)\n), 'Heaviside'):\n\nf := x -> f0(X2S*x):\n", "meta": {"hexsha": "a8ef4764e2464d7c8c4edab666efe1923c571118", "size": 959, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_htbs.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-4.2.3/maple/gga_x_htbs.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-4.2.3/maple/gga_x_htbs.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 22.3023255814, "max_line_length": 68, "alphanum_fraction": 0.5578727842, "num_tokens": 452, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9196425377849806, "lm_q2_score": 0.7956581073313275, "lm_q1q2_score": 0.7317210410353765}} |
| {"text": "`is_element/vector_functions` := (N::posint) -> (A::set) -> proc(x)\n local a;\n global reason;\n\n if not(is_table_on(A)(x)) then\n reason := [convert(procname,string),\"x is not a table on A\",x,A];\n return false; \n fi;\n\n for a in A do\n if not `is_element/R`(N)(x[a]) then\n reason := [convert(procname,string),\"x[a] is not in R^N\",a,x[a],N];\n return false;\n fi;\n od;\n\n return true;\nend;\n\n######################################################################\n\n`is_equal/vector_functions` := (N::posint) -> (A::set) -> proc(x,y) \n local a;\n global reason;\n\n for a in A do\n if not(`is_equal/R`(N)(x[a],y[a])) then\n reason := [convert(procname,string),\"x[a] <> y[a]\",a,x,y];\n return false;\n fi;\n od;\n\n return true;\nend;\n\n######################################################################\n\n`is_nonnegative/vector_functions` := (N::posint) -> (A::set) -> proc(x) \n local a,i;\n\n for a in A do\n for i from 1 to N do\n if x[a][i] < 0 then\n return false;\n fi;\n od;\n od;\n\n return true;\nend:\n\n######################################################################\n\n`is_zero/vector_functions` := (N::posint) -> (A::set) -> proc(x) \n local a,i;\n\n for a in A do\n for i from 1 to N do\n if x[a][i] <> 0 then\n return false;\n fi;\n od;\n od;\n\n return true;\nend:\n\n######################################################################\n\n`is_leq/vector_functions` := (N::posint) -> (A::set) -> proc(x,y)\n local a,i;\n\n for a in A do\n for i from 1 to N do \n if x[a][i] > y[a][i] then\n return false;\n fi;\n od;\n od;\n\n return true;\nend:\n\n######################################################################\n\n`plus/vector_functions` := (N) -> (A::set) -> proc(x,y)\n local z,a;\n\n z := table();\n for a in A do\n z[a] := x[a] +~ y[a];\n od:\n\n return eval(z):\nend:\n\n######################################################################\n\n`times/vector_functions` := (N) -> (A::set) -> proc(t,x)\n local z,a;\n\n z := table();\n for a in A do\n z[a] := t *~ x[a];\n od:\n\n return eval(z):\nend:\n\n######################################################################\n\n`norm/vector_functions` := (N::posint) -> (A::set) -> proc(x)\n local a,n;\n\n n := 0;\n for a in A do n := n + `norm_2/R`(N)(x[a])^2; od;\n \n return sqrt(n);\nend:\n\n######################################################################\n\n`sum/vector_functions` := (N::posint) -> (A::set) -> proc(x)\n local a,u;\n\n u := [0$N];\n for a in A do u := u +~ x[a]; od;\n \n return u;\nend:\n\n######################################################################\n\n`average/vector_functions` := (N::posint) -> (A::set) -> proc(x)\n if A = {} then\n return FAIL;\n fi;\n\n return `sum/vector_functions`(N)(A)(x) /~ nops(A);\nend:\n\n######################################################################\n\n`dist/vector_functions` := (N::posint) -> (A::set) -> proc(x,y)\n local a,n;\n\n n := 0;\n for a in A do n := n + `d_2/R`(N)(x[a],y[a])^2; od;\n \n return sqrt(n);\nend:\n\n######################################################################\n\n`dot/vector_functions` := (N::posint) -> (A::set) -> proc(x,y)\n local a,d;\n\n d := 0;\n for a in A do d := d + `dot/R`(N)(x[a],y[a]); od;\n \n return d;\nend:\n\n######################################################################\n\n`random_element/vector_functions` := (N::posint) -> (A::set) -> proc()\n local x,a;\n\n x := table();\n for a in A do\n x[a] := `random_element/R`(N)();\n od:\n\n return eval(x);\nend;\n\n######################################################################\n\n`list_elements/vector_functions` := NULL;\n`count_elements/vector_functions` := NULL;\n\n", "meta": {"hexsha": "3a20491e84c7541e567990c7806600f15679fcd3", "size": 3544, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/vector_functions.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/vector_functions.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/vector_functions.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 19.4725274725, "max_line_length": 72, "alphanum_fraction": 0.4105530474, "num_tokens": 960, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8824278664544911, "lm_q2_score": 0.8267117898012104, "lm_q1q2_score": 0.7295135208470558}} |
| {"text": "\nTITLE \n Invest3Scen;\n\nINDEX\n invtype := (Stock, Bond) -> (S,B);\n\nSTOCHASTIC\n\nSTAGES\n period := 1..3;\n\nSCENARIOS\n sc := 1..4;\n\nTREE\n BINARY;\n\nPROBABILITIES\n prob[sc] := ALLEQUAL;\n\nRANDOM DATA\n Returns[invtype, period, sc] := \n [Stock, 1, 1, 1.25,\n Stock, 1, 2, 1.25,\n Stock, 1, 3, 1.06,\n Stock, 1, 4, 1.06,\n Stock, 2, 1, 1.25,\n Stock, 2, 2, 1.06,\n Stock, 2, 3, 1.25,\n Stock, 2, 4, 1.06,\n Bond, 1, 1, 1.14,\n Bond, 1, 2, 1.14,\n Bond, 1, 3, 1.12,\n Bond, 1, 4, 1.12,\n Bond, 2, 1, 1.14,\n Bond, 2, 2, 1.12,\n Bond, 2, 3, 1.14,\n Bond, 2, 4, 1.12];\n\nDATA\n InitialWealth = 55;\n Goal := 80;\n SurplusReward := 1;\n ShortPenalty := 4;\n\nVARIABLES\n Invest[period<LAST(period),invtype] -> x;\n\nLASTSTAGE VARIABLES\n Shortage -> Sh;\n Excess -> Ex;\n\nMODEL\n\n MAX obj = SurplusReward*Excess - ShortPenalty*Shortage;\n\nSUBJECT TO\n\n InitInvest[period=1] -> InitInv: \n InitialWealth\n = \n SUM(invtype: Invest);\n\n InvestBal[period=2..LAST(period)-1] -> InvBal: \n SUM(invtype: Invest[period-1] * Returns[period-1])\n = \n SUM(invtype: Invest);\n\n EndInvest[period=LAST(period)] -> EndInv: \n SUM(invtype: Invest[period-1]* Returns[period-1]) + Shortage - Excess \n = \n Goal;\n\nEND", "meta": {"hexsha": "479d388eadbeea36736d7ae6dda8ccf5ab32bb73", "size": 1340, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Stochastic/Invest3Scen.mpl", "max_stars_repo_name": "BjarniMax/mpl-models", "max_stars_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Stochastic/Invest3Scen.mpl", "max_issues_repo_name": "BjarniMax/mpl-models", "max_issues_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Stochastic/Invest3Scen.mpl", "max_forks_repo_name": "BjarniMax/mpl-models", "max_forks_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 17.8666666667, "max_line_length": 78, "alphanum_fraction": 0.5305970149, "num_tokens": 527, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9019206791658465, "lm_q2_score": 0.8080672204860316, "lm_q1q2_score": 0.7288125363124195}} |
| {"text": "`is_element/shuffles` := (n::nonnegint,m::nonnegint) -> proc(s)\n local i;\n\n if not(`is_element/permutations`(n+m)(s)) then\n return false;\n fi;\n\n for i from 1 to n+m-1 do \n if i <> n and s[i+1] < s[i] then\n return false;\n fi;\n od:\n\n return true;\nend:\n\n`is_equal/shuffles` := (n,m) -> (s,t) -> evalb(s = t);\n\n`is_leq/shuffles` := NULL;\n\n`from_subset/shuffles` := (n::nonnegint,m::nonnegint) -> proc(A)\n option remember;\n local X,B,i;\n \n X := {seq(i,i=1..n+m)};\n if A minus X <> {} then return FAIL; fi;\n if nops(A) <> n then return FAIL; fi;\n\n B := X minus A;\n return [op(sort(A)),op(sort(B))];\nend:\n\n`to_subset/shuffles` := (n::nonnegint,m::nonnegint) -> proc(s)\n local i;\n {seq(s[i],i=1..n)};\nend:\n\n`to_grid_path/shuffles` := (n::nonnegint,m::nonnegint) -> proc(s)\n local t,si,i;\n \n t := table():\n t[0] := [0,0];\n si := `inv/permutations`(n+m)(s);\n for i from 1 to n+m do\n t[i] := `if`(si[i] <= n,[1,0],[0,1]) +~ t[i-1];\n od:\n\n return eval(t);\nend:\n\n`from_grid_path/shuffles` := (n::nonnegint,m::nonnegint) -> proc(t)\n local A,i;\n\n A := select(i -> t[i][1] > t[i-1][1],{seq(i,i=1..n+m)});\n return `from_subset/shuffles`(n,m)(A);\nend:\n\n`random_element/shuffles` := (n::nonnegint,m::nonnegint) -> proc()\n local u,A,i;\n u := combinat[randperm](n+m);\n A := {seq(u[i],i=1..n)};\n return `from_subset/shuffles`(n,m)(A);\nend:\n\n`list_elements/shuffles` := proc(n::nonnegint,m::nonnegint)\n local AA;\n AA := map(A -> {op(A)},combinat[choose](n+m,n));\n return map(`from_subset/shuffles`(n,m),AA);\nend:\n\n`list_elements/inverse_shuffles` := proc(n::nonnegint,m::nonnegint)\n option remember;\n\n map(`inv/permutations`(n+m),`list_elements/shuffles`(n,m));\nend:\n\n`count_elements/shuffles` := (n::nonnegint,m::nonnegint) -> binomial(n+m,n);\n\n`sgn/shuffles` := (n::nonnegint,m::nonnegint) -> proc(s)\n local i,j;\n return signum(mul(mul(s[j]-s[i],j=i+1..n+m),i=1..n+m-1));\nend:\n", "meta": {"hexsha": "b425e0555af4e5db8331c34e8fef16d5b28b839e", "size": 1862, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/shuffles.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/shuffles.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/shuffles.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.4337349398, "max_line_length": 76, "alphanum_fraction": 0.6031149302, "num_tokens": 672, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8887587993853655, "lm_q2_score": 0.8198933359135361, "lm_q1q2_score": 0.7286874168505765}} |
| {"text": "read \"../ComputeIdentifiableFunctions.mpl\";\n\ncases := [\n [\n [[\n diff(x1(t), t) - (a * x1(t) - b * x1(t) * x2(t)),\n diff(x2(t), t) - (-c * x2(t) + d * x1(t) * x2(t) + u(t)),\n y(t) = x1(t)\n ],\n [x1, x2], [y], [u], [a, b, c, d]],\n [y(t) * diff(diff(y(t), t), t) - diff(y(t), t)^2 - y(t)^2 * diff(y(t), t) * d + y(t) * diff(y(t), t) * c + a * d * y(t)^3 + u(t) * y(t)^2 * b - a * c * y(t)^2]\n ],\n [\n [[\n diff(xa(t), t) + k1 * xa(t),\n diff(xb(t), t) - k1 * xa(t) + k2 * xb(t),\n diff(xc(t), t) - k2 * xb(t),\n diff(eA(t), t),\n diff(eC(t), t),\n y1(t) - xc(t),\n y2(t) - eA(t) * xa(t) - eB * xb(t) - eC(t) * xc(t),\n y3(t) - eA(t), \n y4(t) - eC(t)\n ],\n [xa, xb, xc, eA, eC], [y2, y1, y3, y4], [], [k1, k2, eB]],\n [\n k1 * k2 * (y2(t) - y1(t) * y4(t)) - eB * k1 * diff(y1(t), t) - k2 * y3(t) * diff(y1(t), t) - y3(t) * diff(diff(y1(t), t), t),\n diff(diff(diff(y1(t), t), t), t) + (k1 + k2) * diff(diff(y1(t), t), t) + k1 * k2 * diff(y1(t), t),\n diff(y3(t), t),\n diff(y4(t), t)\n ]\n ] \n]:\n\nnum_passed := 0:\nnum_failed := 0:\n\nfor case in cases do\n input := case[1]:\n print(input);\n correct := case[2]:\n result := GetIOEquations(op(input), 0):\n passed := true:\n if nops(result) <> nops(correct) then\n passed := false:\n else\n for i from 1 to nops(result) do\n if simplify(result[i] - correct[i]) <> 0 then\n passed := false: \n end if:\n end do:\n end if:\n if passed = true then\n printf(\"PASSED\");\n num_passed := num_passed + 1:\n else\n printf(\"FAILED\");\n print(result);\n print(correct);\n num_failed := num_failed + 1:\n end if:\nend do:\n\nprintf(\"Passed: %a, failed %a \\n\", num_passed, num_failed);\n", "meta": {"hexsha": "91fb692a3b263c1aa67870954c967e52ec50732b", "size": 1957, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "tests/io_eqs.mpl", "max_stars_repo_name": "iliailmer/AllIdentifiableFunctions", "max_stars_repo_head_hexsha": "033d335b6a2e6d53d8d935c627f9724fd2a56ebd", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-03-19T18:42:30.000Z", "max_stars_repo_stars_event_max_datetime": "2021-03-19T18:42:30.000Z", "max_issues_repo_path": "tests/io_eqs.mpl", "max_issues_repo_name": "iliailmer/AllIdentifiableFunctions", "max_issues_repo_head_hexsha": "033d335b6a2e6d53d8d935c627f9724fd2a56ebd", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2021-03-20T15:22:40.000Z", "max_issues_repo_issues_event_max_datetime": "2021-03-21T01:07:04.000Z", "max_forks_repo_path": "tests/io_eqs.mpl", "max_forks_repo_name": "iliailmer/AllIdentifiableFunctions", "max_forks_repo_head_hexsha": "033d335b6a2e6d53d8d935c627f9724fd2a56ebd", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-03-04T20:30:13.000Z", "max_forks_repo_forks_event_max_datetime": "2021-03-04T20:30:13.000Z", "avg_line_length": 30.1076923077, "max_line_length": 167, "alphanum_fraction": 0.399591211, "num_tokens": 702, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8688267660487573, "lm_q2_score": 0.8376199592797929, "lm_q1q2_score": 0.7277466403989543}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: gga_exc *)\n\n$define lda_c_pw_params\n$include \"lda_c_pw.mpl\"\n\npw91_C_c0 := 4.235e-3:\npw91_alpha := 0.09:\npw91_nu := 16/Pi * (3*Pi^2)^(1/3):\npw91_beta := pw91_nu*pw91_C_c0:\n\npw91_c1 := pw91_beta^2/(2*pw91_alpha):\npw91_c2 := 2*pw91_alpha/pw91_beta:\n\n(* Equation (14) *)\nA := (rs, z) -> pw91_c2/(exp(-2*pw91_alpha*f_pw(rs, z)/(mphi(z)^3*pw91_beta^2)) - 1):\n\n(* Equation (13) *)\nH0 := (rs, z, t) -> pw91_c1*mphi(z)^3*log(1\n + pw91_c2*(t^2 + A(rs, z)*t^4) / (1 + A(rs, z)*t^2 + A(rs, z)^2*t^4)\n):\n\n(* Pade parametrized form of C-xc found in\n M Rasolt & DJW Geldart, Phys. Rev. B 34, 1325 (1986)\n*)\nRS_a := [2.568, 23.266, 0.007389]:\nRS_b := [1, 8.723, 0.472]:\nRG_C_xc := rs -> (RS_a[1] + RS_a[2]*rs + RS_a[3]*rs^2)/(1000*(RS_b[1] + RS_b[2]*rs + RS_b[3]*rs^2)):\n\n(* Equation (15) *)\nC_xc0 := 2.568e-3:\nC_x := -0.001667:\nh_a1 := -100 * 4/Pi * (4/(9*Pi))^(1/3):\n\nH1 := (rs, z, t) -> pw91_nu * (RG_C_xc(rs) - C_xc0 - 3*C_x/7)\n * mphi(z)^3*t^2*exp(h_a1*rs*mphi(z)^4*t^2):\n\nf_pw91 := (rs, z, xt, xs0, xs1) ->\n f_pw(rs, z) + H0(rs, z, tt(rs, z, xt)) + H1(rs, z, tt(rs, z, xt)):\nf := (rs, z, xt, xs0, xs1) -> f_pw91(rs, z, xt, xs0, xs1):\n", "meta": {"hexsha": "0ce92ba98fb7aa89d00720a79ee7cd62097ce379", "size": 1389, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_pw91.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_pw91.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_pw91.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 28.9375, "max_line_length": 100, "alphanum_fraction": 0.5752339813, "num_tokens": 641, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9458012747599251, "lm_q2_score": 0.7690802370707281, "lm_q1q2_score": 0.7273970686141601}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: work_lda *)\n\n$define lda_x_params\n$include \"lda_x.mpl\"\n\n(* attenuation function *)\naux1_erf := a -> sqrt(Pi)*erf(1/(2*a)):\naux2_erf := a -> exp(-1/(4*a^2)) - 1:\naux3_erf := a -> 2*a^2*aux2_erf(a) + 1/2:\nattenuation_erf := a -> 1 - 8/3*a*(aux1_erf(a) + 2*a*(aux2_erf(a) - aux3_erf(a))):\n\na_cnst := (4/(9*Pi))^(1/3)*p_a_cam_omega/2:\n\nlda_x_erf_s := (rs, z) -> convert(piecewise(z = -1, 0,\n (1 + z)^(4/3)*attenuation_erf(a_cnst*rs/(1 + z)^(1/3))\n), 'Heaviside'):\n\nf_lda_x_erf := (rs, z) -> lda_x_ax*(\n lda_x_erf_s(rs, z) + lda_x_erf_s(rs, -z)\n)/rs:\n\nf := (rs, z) -> f_lda_x_erf(rs, z):\n", "meta": {"hexsha": "848b695406c4d8201c89d122e5f743edbc5d0ad1", "size": 834, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/lda_x_erf.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-4.2.3/maple/lda_x_erf.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-4.2.3/maple/lda_x_erf.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 26.9032258065, "max_line_length": 82, "alphanum_fraction": 0.6139088729, "num_tokens": 345, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.935346511643776, "lm_q2_score": 0.7745833737577158, "lm_q1q2_score": 0.7245038566215466}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: mgga_exc *)\n\n(* replace: \"BesselI\\(0, \" -> \"xc_bessel_I0(\" *)\n(* replace: \"BesselI\\(1, \" -> \"xc_bessel_I1(\" *)\n\n$define xc_dimensions_2d\n\nprhg07_C := (x, u, t) -> (u - 4*t + x^2/2)/4:\n\n(* This is the solution of solve((y-1)*exp(y) = x/Pi) *)\nprhg07_y := x -> LambertW(m_max(x/Pi, -0.9999999999) * exp(-1)) + 1:\n\nprhg07_v := y -> Pi/X_FACTOR_2D_C * BesselI(0, y/2):\n\nprhg07_f := (x, u, t) ->\n prhg07_v(prhg07_y(prhg07_C(x, u, t)))/2:\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) ->\n mgga_exchange(prhg07_f, rs, z, xs0, xs1, u0, u1, t0, t1):\n", "meta": {"hexsha": "a9ed4b63edf39f656c08e679c1249962ab374684", "size": 789, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_2d_prhg07.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_2d_prhg07.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_2d_prhg07.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 28.1785714286, "max_line_length": 68, "alphanum_fraction": 0.608365019, "num_tokens": 324, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9518632247867715, "lm_q2_score": 0.7606506472514406, "lm_q1q2_score": 0.7240353780289013}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: work_mgga_x *)\n\n(* bottom left column on page 687 of article *)\ne1 := -1.6665:\nc1 := 0.7438:\n\n(* equation 10 *)\nfa := a -> (1 - a) / ((1 + e1*a^2)^2 + c1*a^4)^(1/4):\n\n(* between eqs 8 and 9 *)\nk0 := 0.174:\n(* after eq 11 *)\nb := 0.0233:\n\n(* eq 7 *)\nf := (rs, x, t, u) -> (1 + k0*fa((t-x^2/8)/K_FACTOR_C)) / (1 + b*(X2S*x)^4)^(1/8):\n", "meta": {"hexsha": "080bb7a74247735830faa6692cb11609cfe66cb6", "size": 582, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/mgga_x_mvs.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-4.2.3/maple/mgga_x_mvs.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-4.2.3/maple/mgga_x_mvs.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 23.28, "max_line_length": 82, "alphanum_fraction": 0.5704467354, "num_tokens": 232, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9504109784205502, "lm_q2_score": 0.7606506418255928, "lm_q1q2_score": 0.7229307207336811}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: lda_exc *)\n\na0 := 0.93222*RS_FACTOR:\nkk := 9.47362e-3*RS_FACTOR:\n\nf := (rs, zeta) -> -a0*(1 - kk*log(1 + rs/kk)/rs)/rs:\n", "meta": {"hexsha": "4a3e63d69b81f931474d6941a625e8956c61c7fd", "size": 368, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_xc_zlp.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_xc_zlp.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_xc_zlp.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 24.5333333333, "max_line_length": 68, "alphanum_fraction": 0.652173913, "num_tokens": 129, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9399133531922387, "lm_q2_score": 0.7690802476562641, "lm_q1q2_score": 0.7228687944485166}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: lda_exc *)\n(* prefix:\n lda_c_2d_prm_params *params;\n\n assert(p->params != NULL);\n params = (lda_c_2d_prm_params * )(p->params);\n\n assert(params->N > 1);\n*)\n\n$define xc_dimensions_2d\n\nprm_q := 3.9274: (* 2.258 *)\n\n(* Equation (4) *)\nbeta := rs -> prm_q/(sqrt(Pi)*rs):\n\nphi := rs -> beta(rs)/(beta(rs) + sqrt(Pi)/2):\n\nf0 := rs ->\n + sqrt(Pi)*beta(rs)*(phi(rs) - 1)/(2*sqrt(2 + params_a_c)) (* original version has (phi-1)^2 *)\n + phi(rs)*(phi(rs) - 1)/(2 + params_a_c)\n + sqrt(Pi)*phi(rs)*phi(rs)/(4*beta(rs)*(2 + params_a_c)^1.5)\n + sqrt(Pi)*beta(rs)*(phi(rs) - 1)/sqrt(1 + params_a_c)\n + phi(rs)/(1 + params_a_c):\n\nf := (rs, z) -> f0(rs)*Pi/(2*prm_q*prm_q):\n", "meta": {"hexsha": "787b6cbdec28f864772049d6aead5e55f9e1c783", "size": 917, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_2d_prm.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_2d_prm.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_2d_prm.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 25.4722222222, "max_line_length": 97, "alphanum_fraction": 0.60087241, "num_tokens": 331, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9496693674025231, "lm_q2_score": 0.760650658103136, "lm_q1q2_score": 0.7223666292951181}} |
| {"text": "`is_element/raw_matroids` := proc(M)\n global reason;\n local n,s,t,s1,t1,u,a,b;\n\n if not(type(M,set(set))) then\n reason := [\"not a set of sets\"];\n return false;\n fi;\n \n n := nops(M);\n for s in M do\n for t in M do\n if s <> t then \n s1 := s minus t;\n t1 := t minus s;\n if s1 = {} or t1 = {} then\n reason := [\"s and t are nested\",s,t];\n return false;\n fi;\n for a in s1 do\n u := select(b -> member((s minus {a}) union {b},M),t1);\n if u = {} then\n reason := [\"exchange fails\",s,t];\n return false;\n fi;\n od;\n fi;\n od;\n od;\n \n return true;\nend:\n\n`vertices/raw_matroid` := (M) -> map(op,{op(M)});\n\n`is_basis/raw_matroid` := (M,s) -> member(s,M);\n\n`is_independent/raw_simplicial_complex` := proc(M,s)\n local s0,u;\n \n if not(type(s,{list,set})) then return false; fi;\n \n s0 := {op(s)};\n \n for u in M do\n if s0 minus {op(u)} = {} then\n return true;\n fi;\n od:\n return false;\nend:\n\n`is_dependent/raw_simplicial_complex` := proc(M,s)\n local s0,u;\n \n if not(type(s,{list,set})) then return false; fi;\n \n s0 := {op(s)};\n\n for u in M do\n if s0 minus {op(u)} = {} then\n return false;\n fi;\n od:\n return true;\nend:\n\n`is_element/matroids` := proc(T)\n global reason;\n \n if not(type(T,table)) then\n return false;\n fi;\n\n if not (`is_element/raw_matroids`(T[\"bases\"])) then\n return false;\n fi;\n\n if `vertices/raw_matroid`(T[\"bases\"]) minus T[\"vertices\"] <> {} then\n reason := [\"vertex mismatch\",T[\"vertices\"],`vertices/raw_matroid`(T[\"bases\"])];\n return false;\n fi;\n\n return true;\nend:\n\n`cook/raw_matroid` := proc(M,V_)\n local T;\n\n T := table():\n if nargs > 1 then\n T[\"vertices\"] := V_;\n else\n T[\"vertices\"] := `vertices/raw_matroid`(M);\n fi;\n T[\"bases\"] := M;\n\nend:\n\n`set_rank/matroid` := proc(T)\n local m,r,n,P,A;\n\n m := nops(T[\"vertices\"]);\n r := table():\n n := table():\n P := combinat[powerset](T[\"vertices\"]);\n for A in P do\n r[A] := max(op(map(s -> nops(s intersect A),T[\"bases\"])));\n n[A] := m - r[A];\n od:\n\n T[\"rank\"] := eval(r);\n T[\"nullity\"] := eval(r);\nend:\n\n`set_closure/matroid` := proc(T)\n local r,V,P,c,A,m;\n \n if not(type(T[\"rank\"],table)) then `set_rank/matroid`(T); fi;\n \n r := eval(T[\"rank\"]);\n V := T[\"vertices\"];\n P := combinat[powerset](T[\"vertices\"]);\n c := table():\n for A in P do\n m := r[A];\n c[A] := A union select(b -> r[A union {b}] = m + 1,V minus A);\n od:\n\n T[\"closure\"] := eval(c):\n T[\"flats\"] := select(A -> nops(c[A]) = nops(A),P);\nend:\n\n`res/matroid` := proc(T,A)\n local U,B,m;\n \n if not(type(A,set) and A minus T[\"vertices\"] = {}) then\n error(\"A is not a subset of the vertices of T\");\n fi;\n\n U := table():\n U[\"vertices\"] := A;\n B := map(s -> s intersect A,T[\"bases\"]);\n m := max(map(nops,B));\n U[\"bases\"] := select(s -> nops(s) = m,T[\"bases\"]);\nend:\n\nuniform_matroid := proc(A_::{nonnegint,set},k)\n local T,A;\n \n if type(A_,nonnegint) then\n A := {seq(i,i=1..A_)};\n else\n A := A_;\n fi;\n\n T := table():\n T[\"vertices\"] := A;\n T[\"bases\"] := combinat[choose](A,k);\n\n return eval(T);\nend:\n\nlinear_matroid := proc(p,d)\n local T,V,i,j,B,f;\n \n V := [[]];\n\n for i from 1 to d do\n V := [seq(seq([op(v),j],j=0..p-1),v in V)];\n od:\n\n B := [seq([j],j=2..p^d)];\n for i from 2 to d do\n B := [seq(seq([op(b),j],j=b[-1]+1..p^d),b in B)];\n od:\n\n f := b -> modp(Determinant(Matrix(map(i -> V[i],b))),p);\n B := select(b -> f(b) <> 0,B);\n\n T := table():\n T[\"vectors\"] := V;\n T[\"vertices\"] := {seq(i,i=1..p^d)};\n T[\"bases\"] := map(b -> {op(b)},{op(B)});\n\n return eval(T);\nend:\n\n", "meta": {"hexsha": "861355dab78787c487169ec062987700aefb9b70", "size": 3444, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/simplicial_complexes/matroid.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/simplicial_complexes/matroid.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/simplicial_complexes/matroid.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 18.2222222222, "max_line_length": 81, "alphanum_fraction": 0.5461672474, "num_tokens": 1169, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8933094117351309, "lm_q2_score": 0.8080672204860316, "lm_q1q2_score": 0.7218540533748192}} |
| {"text": "# Proof by PDF that \n#\tif X <~ standardChiSq(n) then cX <~ gamma(k = n/2, t = 2*c)\t\t\n\nPDF_chisq := (n, x) -> x^(n/2-1)*exp(-x/2)/(2^(n/2)*GAMMA(n/2)); \nPDF_cX := (n, c, x) -> PDF_chisq(n, x/c)/c;\nPDF_sub := (k, t, x) -> PDF_cX(2*k, t/2, x);\nsimplify(PDF_sub(k, t, x));\n\n\nPDF_gamma := (k, t, x) -> x^(k-1)*exp(-x/t)/(GAMMA(k)*t^k);\nsimplify(PDF_gamma(k, t, x));\n\n# NOTE: Doesn't evaluate true, but inspection of forms given by\n#\t\tthe 2 calls to simplify prove it so\nevalb(PDF_sub(k, t, x) = PDF_gamma(k, t, x));\n", "meta": {"hexsha": "529d99aa8d6bf6c8d34f8cbec8aadba8d2920c8c", "size": 511, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "tests/RoundTrip/t_stdChiSq_to_gamma.proof.mpl", "max_stars_repo_name": "vmchale/hakaru", "max_stars_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 327, "max_stars_repo_stars_event_min_datetime": "2015-01-03T08:56:51.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-24T12:12:06.000Z", "max_issues_repo_path": "tests/RoundTrip/t_stdChiSq_to_gamma.proof.mpl", "max_issues_repo_name": "vmchale/hakaru", "max_issues_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 155, "max_issues_repo_issues_event_min_datetime": "2015-05-05T17:57:22.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T15:43:39.000Z", "max_forks_repo_path": "tests/RoundTrip/t_stdChiSq_to_gamma.proof.mpl", "max_forks_repo_name": "vmchale/hakaru", "max_forks_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 38, "max_forks_repo_forks_event_min_datetime": "2015-01-23T16:25:37.000Z", "max_forks_repo_forks_event_max_datetime": "2021-03-14T15:09:12.000Z", "avg_line_length": 31.9375, "max_line_length": 65, "alphanum_fraction": 0.5694716243, "num_tokens": 221, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9314625012602594, "lm_q2_score": 0.7718434873426302, "lm_q1q2_score": 0.7189432653016077}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: work_lda *)\n(* prefix:\n lda_c_ml1_params *params;\n\n assert(p->params != NULL);\n params = (lda_c_ml1_params * )(p->params);\n*)\n\nC := 6.187335:\nb := [2.763169, 1.757515, 1.741397, 0.568985, 1.572202, 1.885389]:\n\nmalpha := z -> params_a_fc*((1 + z)^params_a_q + (1 - z)^params_a_q):\nmbeta := z -> (1 + z)^(1/3)*(1 - z)^(1/3)/((1 + z)^(1/3) + (1 - z)^(1/3)):\n\nk := (rs, z) -> C*malpha(z)*mbeta(z)*RS_FACTOR/rs:\nQ := (rs, z) -> \n - b[1]/(1 + b[2]*k(rs, z)) \n + b[3]*log(1 + b[4]/k(rs, z))/k(rs, z)\n + b[5]/k(rs, z)\n - b[6]/k(rs, z)^2:\n\nf := (rs, zeta) -> 1/2*(RS_FACTOR/rs)^3 * (1 - zeta^2)/4 * Q(rs, zeta):", "meta": {"hexsha": "807d9322dfd489616dc35040e17191979fcc244d", "size": 858, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/lda_c_ml1.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-4.2.3/maple/lda_c_ml1.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-4.2.3/maple/lda_c_ml1.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 28.6, "max_line_length": 75, "alphanum_fraction": 0.5547785548, "num_tokens": 364, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9433475778774728, "lm_q2_score": 0.7606506635289836, "lm_q1q2_score": 0.7175579610509593}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: gga_exc *)\n\npbea_mu := 0.00361218645365094697:\npbea_alpha := 0.52:\n\npbea_f := x -> 1 + KAPPA_PBE*(1 - (1 + pbea_mu*x^2/(pbea_alpha*KAPPA_PBE))^(-pbea_alpha)):\n\n\nf := (rs, z, xt, xs0, xs1) -> gga_exchange(pbea_f, rs, z, xs0, xs1):\n", "meta": {"hexsha": "961ce7bb318f5d5829f397e214a3cccf99ccc36d", "size": 482, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_pbea.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_pbea.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_pbea.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 26.7777777778, "max_line_length": 91, "alphanum_fraction": 0.6576763485, "num_tokens": 184, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9532750400464604, "lm_q2_score": 0.7520125682019722, "lm_q1q2_score": 0.7168748110681765}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: work_mgga_x *)\n\nmlambda := 0.6866:\nmbeta := 79.873:\n\n(* below Equation (6) *)\ny := p -> (2*mlambda - 1)^2 * p:\n\n(* Equation (7) *)\nf0 := x -> (1 + 10*70*y(X2S^2*x^2)/27 + mbeta*y(X2S^2*x^2)^2)^(1/10):\n\nR := (x, t) -> 1 + 595*(2*mlambda - 1)^2 * X2S^2*x^2/54 \\\n - (t - 3*(mlambda^2 - mlambda + 1/2)*(t - K_FACTOR_C - x^2/72))/K_FACTOR_C:\n\nfx_DME := (x, t) -> 1/f0(x)^2 + 7*R(x, t)/(9*f0(x)^4):\n\nmalpha := (x, t) -> (t - x^2/8)/K_FACTOR_C:\nqtilde := (x, t) -> 9/20*(malpha(x, t) - 1) + 2*X2S^2*x^2/3:\n\nfx_SC_aux := (x, t) -> (1 + 10*( \\\n + (MU_GE + 50*X2S^2*x^2/729)*X2S^2*x^2 \\\n + 146*qtilde(x, t)^2/2025 \\\n - 73*qtilde(x,t)/405*(3*K_FACTOR_C/(5*t))*(1 - K_FACTOR_C/t))\n ):\n\n(* It turns out that the quantity fx_SC_aux can become negative, leading to NaN.\n this appears, for example, for the following densities\n\n ./xc-get_data 540 1 729.292719352103 0 365940004.708665 0 0 -970050.160877395 0 64600.7149099035 0\n\n As a turn around, I demand that the function is always larger than 1e-16\n*)\nfx_SC := (x, t) -> m_max(fx_SC_aux(x,t), 1e-16)^(0.1):\n\nw := t-> (K_FACTOR_C^2/t^2 + 3*K_FACTOR_C^3/t^3)/(1 + K_FACTOR_C^3/t^3)^2:\n\nf := (rs, x, t, u) -> w(t)*fx_DME(x, t) + (1 - w(t))*fx_SC(x, t):\n", "meta": {"hexsha": "cd3881b5db1299083c562d3af39302cc036dafde", "size": 1473, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/mgga_x_tm.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-4.2.3/maple/mgga_x_tm.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-4.2.3/maple/mgga_x_tm.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 32.0217391304, "max_line_length": 101, "alphanum_fraction": 0.5763747454, "num_tokens": 630, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9207896737173119, "lm_q2_score": 0.7772998560157665, "lm_q1q2_score": 0.7157296808012711}} |
| {"text": "# Euler found rational curves on the surface given by\n# w+x+y+z = wxyz + a = 0. The formula here is similar to Euler's\n# but simpler, and is taken from slides of Elkies\n\n`f/euler_quartic` := proc(a,x) local i; [add(x[i],i=1..4),mul(x[i],i=1..4)+a]; end:\n\n`g/euler_quartic` := (a,s) -> [\n 1/2*s^(-3)*(s^4-4*a)^( 2)*(s^4+12*a)^(-1),\n 2*a*s^(-3)*(s^4-4*a)^(-1)*(s^4+12*a)^(-1)*(3*s^4+4*a)^2,\n 1/2*s * (s^4+12*a) *(3*s^4+4*a)^(-1),\n -2*s^5 *(s^4-4*a)^(-1)*(s^4+12*a) *(3*s^4+4*a)^(-1)\n];\n\ncheck_euler_quartic := proc()\n local a,s;\n\n _ASSERT(\n simplify(`f/euler_quartic`(a,`g/euler_quartic`(a,s))) = [0,0],\n \"Euler quartic relation\"\n );\nend:\n\n", "meta": {"hexsha": "4d1b599d5cad3eca35ee64fae8db34b0155dabbe", "size": 670, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/euler_quartic.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/euler_quartic.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/euler_quartic.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 29.1304347826, "max_line_length": 83, "alphanum_fraction": 0.528358209, "num_tokens": 291, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9196425377849806, "lm_q2_score": 0.7772998560157665, "lm_q1q2_score": 0.7148380122062395}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: work_gga_x *)\n\na5 := 133.983631:\na6 := 3.217063:\na7 := 136.707378:\na8 := 3.223476:\na9 := 2.675484:\na10 := 3.473804:\n\nf1 := s -> (1 - a5*s^a6 + a7*s^a8)/(1 + a9*s^a10):\n\n$include \"gga_x_lag.mpl\"\nunassign('f'):\n\nf := x -> f0(X2S*x) + f1(X2S*x):\n", "meta": {"hexsha": "7433517b3948b2a9a89ca3b8254214c3b7270538", "size": 504, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_airy.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-4.2.3/maple/gga_x_airy.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-4.2.3/maple/gga_x_airy.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 21.0, "max_line_length": 68, "alphanum_fraction": 0.6051587302, "num_tokens": 207, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9425067211996142, "lm_q2_score": 0.7577943712746406, "lm_q1q2_score": 0.7142262882135846}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: work_mgga_x *)\n\na := 0.5389:\nb := 3:\n\np := x -> X2S^2*x^2:\nq := u -> X2S^2*u:\n\n(* Equation (15) *)\nfab := z -> piecewise( \\\n z<=0, 0, \\\n z>=a, 1, \\\n (1 + exp(a/(a-z)))^b/(exp(a/z) + exp(a/(a-z)))^b \\\n):\n\n(* Equation (7) *)\nmDelta := (x, u) -> 8*q(u)^2/81 - p(x)*q(u)/9 + 8*p(x)^2/243:\n\nf_W := x -> 5*p(x)/3:\n\n(* Equation (8) *)\nf_GE4 := (x, u) -> 1 + 5*p(x)/27 + 20*q(u)/9 + mDelta(x, u):\n\n(* Equation (11) *)\nf_GE4_M := (x, u) -> f_GE4(x, u)/sqrt(1 + mDelta(x, u)^2/(1 + f_W(x))^2):\n\n(* Equation (17) *)\nf := (rs, x, t, u) -> f_W(x) + (f_GE4_M(x, u) - f_W(x))*fab(f_GE4_M(x, u) - f_W(x)):\n", "meta": {"hexsha": "1cca8ba4910687599481115a6b7c838befe85e3d", "size": 853, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/mgga_k_pc07.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-4.2.3/maple/mgga_k_pc07.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-4.2.3/maple/mgga_k_pc07.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 23.0540540541, "max_line_length": 86, "alphanum_fraction": 0.5029308324, "num_tokens": 365, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9532750360641185, "lm_q2_score": 0.7490872075132152, "lm_q1q2_score": 0.7140861347573301}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: gga_exc *)\n\n(* eqn (5) *)\nmeyer_feta := y -> 1/2*(1 + (1 - y^2)*log((1 + y)/abs(1 - y))/(2*y)):\n\n(* eqn (7) *)\nmeyer_lambda := y -> (1 - meyer_feta(y)) / (3 * y^2 * meyer_feta(y)):\n\n(* enhancement factor from eqn (1) *)\nmeyer_f := x -> 1 + meyer_lambda(X2S*x/6)*x^2/(8*K_FACTOR_C):\n\nf := (rs, zeta, xt, xs0, xs1) -> gga_kinetic(meyer_f, rs, zeta, xs0, xs1):\n", "meta": {"hexsha": "3304c556f6e51a5b26eb5b797f96b26ceeef256e", "size": 606, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_k_meyer.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/gga_exc/gga_k_meyer.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/gga_exc/gga_k_meyer.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 28.8571428571, "max_line_length": 74, "alphanum_fraction": 0.602310231, "num_tokens": 232, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9449947055100817, "lm_q2_score": 0.7549149868676284, "lm_q1q2_score": 0.7133906657001217}} |
| {"text": "######################################################################\n# epi(A,B) is the set of surjective maps from A to B\n\n`is_element/epi` := (A::set,B::set) -> proc(p)\n local a,b,hit;\n global reason;\n\n if not `is_element/maps`(A,B)(p) then\n reason := [convert(procname,string),\"p is not a map from A to B\",p,A,B,reason];\n return false;\n fi;\n\n hit := table();\n for b in B do hit[b] := false; od;\n for a in A do hit[p[a]] := true; od;\n for b in B do if not hit[b] then\n reason := [convert(procname,string),\"b is not hit\",b];\n return false;\n fi; od;\n return true;\nend;\n\n`is_equal/epi` := (A::set,B::set) -> proc(p,q)\n local a;\n global reason;\n\n for a in A do \n if p[a] <> q[a] then\n reason := [convert(procname,string),\"p[a] <> q[a]\",a,p[a],q[a]];\n return false;\n fi; \n od;\n\n return true;\nend;\n\n`is_leq/epi` := NULL;\n\n`random_element/epi` := (A::set,B::set) -> proc()\n local p,m,n,A0,r,i;\n\n n := nops(A);\n m := nops(B);\n if m > n then return FAIL; fi;\n\n p := table();\n A0 := combinat[randperm]([op(A)]);\n\n for i from 1 to m do p[A0[i]] := B[i]; od;\n\n r := rand(1..m);\n\n for i from m+1 to n do p[A0[i]] := B[r()]; od;\n\n return eval(p);\nend;\n\n`list_elements/epi` := proc(A::set,B::set)\n local n,m,B0,b,E,E0,k,CC,C,c,p0,p;\n\n n := nops(A);\n m := nops(B);\n\n if n < m then return []; fi;\n if m = 0 then\n if n = 0 then \n return [table()];\n else \n return [];\n fi;\n fi;\n\n B0 := sort(B);\n b := B0[1];\n B0 := {op(2..-1,B0)};\n\n E := [];\n\n for k from 1 to n-m+1 do\n CC := combinat[choose](A,k);\n for C in CC do\n E0 := `list_elements/epi`(A minus C,B0);\n for p0 in E0 do\n p := copy(p0);\n for c in C do p[c] := b; od;\n E := [op(E),eval(p)];\n od;\n od;\n od;\n\n return E;\nend;\n\n`count_elements/epi` := (A::set,B::set) -> Stirling2(nops(A),nops(B)) * nops(B)!;", "meta": {"hexsha": "5bceaedb05d3ce10d574186a7d011f6eebe52572", "size": 1776, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/epi.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/epi.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/epi.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 18.8936170213, "max_line_length": 81, "alphanum_fraction": 0.5253378378, "num_tokens": 630, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8670357598021707, "lm_q2_score": 0.8221891261650248, "lm_q1q2_score": 0.7128673737055751}} |
| {"text": "`is_element/young_partitions` := (k,n) -> proc(lambda)\n local i;\n\n if not(type(lambda,list(nonnegint))) then\n return false;\n fi;\n\n if nops(lambda) <> k then\n return false;\n fi;\n\n if k > 0 and lambda[1] > n-k then\n return false;\n fi;\n\n for i from 1 to k-1 do \n if lambda[i] < lambda[i+1] then\n return false;\n fi;\n od;\n\n return true;\nend:\n\n`young_partition/from_set` := (n,k) -> proc(P)\n local i;\n return [seq(n-k+i-P[i],i=1..k)];\nend:\n\n`list_elements/young_partitions` := proc(n,k)\n map(`young_partition/from_set`(n,k),combinat[choose](n,k));\nend:\n\n`random_element/young_partitions` := (n,k) -> proc()\n if k > n then return FAIL; fi;\n `young_partition/from_set`(n,k)(combinat[randcomb](n,k));\nend:\n\n`count_elements/young_partitions` := (n,k) -> binomial(n,k);\n\n`weight/young_partitions` := (lambda) -> `+`(op(lambda)):\n\n`length/young_partitions` := (lambda) -> nops(lambda):\n\n`cell_dim/young_partitions` := (n,k) -> \n k * (n - k) - `weight/young_partitions`(lambda):\n\n`matrix/young_partitions` := (n,k) -> (lambda) -> proc(a)\n local A,P,S,u,i,j;\n A := Matrix(k,n);\n P := [seq(n-k+i-lambda[i],i=1..k)];\n S := {op(P)};\n u := 1;\n for i from 1 to k do\n for j from 1 to P[i] - 1 do\n if not(member(j,S)) then\n A[i,j] := a[u];\n u := u+1;\n fi;\n od:\n A[i,P[i]] := 1;\n od:\n return A;\nend:\n\n`giambelli_matrix/young_partitions` := proc(lambda)\n local i,j,k,f;\n k := nops(lambda);\n f := (i) -> `if`(i < 0,0,`if`(i = 0,1,c[i]));\n Matrix([seq([seq(f(lambda[i]-i+j),j=1..k)],i=1..k)]);\nend:\n\n`schur_function/young_partitions` := (lambda) ->\n Determinant(`giambelli_matrix/young_partitions`(lambda)):\n\n", "meta": {"hexsha": "86226763f1a2f053faba56ccba9820910e51e047", "size": 1604, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/young.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/young.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/young.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 21.1052631579, "max_line_length": 60, "alphanum_fraction": 0.6078553616, "num_tokens": 544, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.897695283896349, "lm_q2_score": 0.7931059560743422, "lm_q1q2_score": 0.7119674763980419}} |
| {"text": "`mu/BA` := proc()\n apply_bilinear_assoc(`mu_aux0/BA`,`bar/BA`())(args);\n local xx,ca,cb,pa,pb;\n if nargs > 2 then\n return `mu/BA`(`mu/BA`(a,b),args[3..-1]);\n fi;\n if type(a,numeric) or type(b,numeric) then\n return expand(a*b);\n elif type(a,`+`) then\n return map(`mu/BA`,a,b);\n elif type(b,`+`) then\n return map2(`mu/BA`,a,b);\n fi;\n if type(a,`*`) then \n xx := selectremove(type,a,numeric);\n ca := xx[1];\n pa := xx[2];\n else\n ca := 1;\n pa := a;\n fi;\n if type(b,`*`) then \n xx := selectremove(type,b,numeric);\n cb := xx[1];\n pb := xx[2];\n else\n cb := 1;\n pb := b;\n fi;\n if type(pa,specfunc(anything,`bar/BA`)) and\n type(pb,specfunc(anything,`bar/BA`)) then\n return expand(ca*cb*`mu_aux0/BA`(pa,pb));\n else\n return('`mu/BA`'(args))\n fi;\nend:\n\n\n`mu/EA` := proc()\n apply_linear_assoc(`mu0/EA`,`bar/EA`())(args);\nend:\n\n\n`mu/EC` := proc(a,b)\n local xx,ca,cb,pa,pb,na,nb,ka,kb,la,lb,ia,ib;\n if nargs > 2 then\n return `mu/EC`(`mu/EC`(a,b),args[3..-1]);\n fi;\n if type(a,numeric) or type(b,numeric) then\n return expand(a*b);\n elif type(a,`+`) then\n return map(`mu/EC`,a,b);\n elif type(b,`+`) then\n return map2(`mu/EC`,a,b);\n fi;\n if type(a,`*`) then \n xx := selectremove(type,a,numeric);\n ca := xx[1];\n pa := xx[2];\n else\n ca := 1;\n pa := a;\n fi;\n if type(b,`*`) then \n xx := selectremove(type,b,numeric);\n cb := xx[1];\n pb := xx[2];\n else\n cb := 1;\n pb := b;\n fi;\n if type(pa,specfunc(anything,`e/EC`)) and\n type(pb,specfunc(anything,`e/EC`)) then\n na,ka,ia := op(pa);\n nb,kb,ib := op(pb);\n if nb <> na then return FAIL; fi;\n if modp(ka,2) = 1 and modp(kb,2) = 1 then\n return 0;\n fi;\n la := floor(ka/2);\n lb := floor(kb/2);\n return ca * cb * binomial(la+lb,la) * `e/EC`(na,ka+kb,modp(ia+ib,na));\n else\n return('`mu/EC`'(args))\n fi;\nend:\n", "meta": {"hexsha": "c3afa20f67945b3903683bf7d6e4c012c6ec8372", "size": 1774, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/scratch.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/scratch.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/scratch.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 20.3908045977, "max_line_length": 72, "alphanum_fraction": 0.5631341601, "num_tokens": 720, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.894789468908171, "lm_q2_score": 0.7956580976404296, "lm_q1q2_score": 0.7119464866201657}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: gga_exc *)\n(* prefix:\n gga_x_ak13_params *params;\n\n assert(p->params != NULL);\n params = (gga_x_ak13_params * )(p->params);\n*)\n\nak13_f0 := s -> 1 + params_a_B1*s*log(1 + s) + params_a_B2*s*log(1 + log(1 + s)):\nak13_f := x -> ak13_f0(X2S*x):\n\nf := (rs, zeta, xt, xs0, xs1) -> gga_exchange(ak13_f, rs, zeta, xs0, xs1):\n", "meta": {"hexsha": "bf73f3a71095fdbc9cecf571b12c28b5e791a324", "size": 569, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_ak13.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_ak13.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_ak13.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 27.0952380952, "max_line_length": 81, "alphanum_fraction": 0.6432337434, "num_tokens": 203, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9504109784205503, "lm_q2_score": 0.7490872187162397, "lm_q1q2_score": 0.7119407164624302}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: lda_exc *)\n(* prefix:\n lda_c_ml1_params *params;\n\n assert(p->params != NULL);\n params = (lda_c_ml1_params * )(p->params);\n*)\n\nml1_C := 6.187335:\nml1_b := [2.763169, 1.757515, 1.741397, 0.568985, 1.572202, 1.885389]:\n\nml1_alpha := z -> params_a_fc*((1 + z)^params_a_q + (1 - z)^params_a_q):\nml1_beta := z -> (1 - z^2)^(1/3)/((1 + z)^(1/3) + (1 - z)^(1/3)):\n\n(* From the paper: \"Note that the antiparailel-spin correlation length\n diverges when the spin-polarization parameter tends to 1\", which means\n that Q diverges for a ferromagnetic density *)\nml1_k := (rs, z) -> ml1_C*n_total(rs)^(1/3) * ml1_alpha(z)*ml1_beta(z):\n\n(* Eq. 32 *)\nml1_Q := (rs, z) ->\n - ml1_b[1]/(1 + ml1_b[2]*ml1_k(rs, z))\n + ml1_b[3]*log(1 + ml1_b[4]/ml1_k(rs, z))/ml1_k(rs, z)\n + ml1_b[5]/ml1_k(rs, z)\n - ml1_b[6]/ml1_k(rs, z)^2:\n\n(* screen for small spin densities to avoid divergences in the\n potentials. Note that beta is zero for any polarized density and\n the whole expression for alpha*beta is symmetric in z. Note also\n that in the expression for Q one divides by k that is zero for\n ferromagnetic densities. *)\n\n(* there is a factor of 1/2 wrong in Eq. 31 as explained in the Erratum *)\n(* With the formula below we can reproduce exactly the values of Table I.\n Note that in the Erratum the authors afirm that all the results are correct,\n and only the formulas had misspells. *)\nml1_f := (rs, z) -> n_total(rs) *\n my_piecewise3(1 - abs(z) <= p_a_zeta_threshold, 0, (1 - z^2)/4 * ml1_Q(rs, z_thr(z))):\n\nf := (rs, z) -> ml1_f(rs, z):\n", "meta": {"hexsha": "3e1080d6e0812af9d5310e89b7730467d8a13dbe", "size": 1785, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_ml1.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_ml1.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_ml1.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 36.4285714286, "max_line_length": 88, "alphanum_fraction": 0.6599439776, "num_tokens": 620, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9465966702001758, "lm_q2_score": 0.7520125737597972, "lm_q1q2_score": 0.7118525982696882}} |
| {"text": "# Generated using bssn_4d_spher_matter.mw\neq_evol_rPIb2:= \ndiff(rPIb2(t,x) ,t) = \nexpand( simplify (\n(-mass*rpsi(t,x) + 2*(diff(rpsi(t, x), x))/(a1(t, x)^2*x)+(diff(diff(rpsi(t, x), x), x))/a1(t, x)^2-(diff(rpsi(t, x), x))*(diff(a1(t, x), x))/a1(t, x)^3+2*rPIb2(t, x)*beta(t, x)/(alpha(t, x)*b1(t, x)^2*a1(t, x)*x)+beta(t, x)*(diff(rPIb2(t, x), x))/(alpha(t, x)*b1(t, x)^2*a1(t, x))+rPIb2(t, x)*(diff(beta(t, x), x))/(alpha(t, x)*b1(t, x)^2*a1(t, x))+2*(diff(rpsi(t, x), x))*(diff(b1(t, x), x))/(b1(t, x)*a1(t, x)^2)+(diff(rpsi(t, x), x))*(diff(alpha(t, x), x))/(alpha(t, x)*a1(t, x)^2) ) * (alpha(t,x)*b1(t,x)^2*a1(t,x))\n) );\n\neq_evol_iPIb2:=\n(diff(iPIb2(t, x), t)) = expand( simplify (\n\n( -mass*ipsi(t,x) + 2*(diff(ipsi(t, x), x))/(a1(t, x)^2*x)+(diff(diff(ipsi(t, x), x), x))/a1(t, x)^2-(diff(ipsi(t, x), x))*(diff(a1(t, x), x))/a1(t, x)^3+2*iPIb2(t, x)*beta(t, x)/(alpha(t, x)*b1(t, x)^2*a1(t, x)*x)+iPIb2(t, x)*(diff(beta(t, x), x))/(alpha(t, x)*b1(t, x)^2*a1(t, x))+2*(diff(ipsi(t, x), x))*(diff(b1(t, x), x))/(b1(t, x)*a1(t, x)^2)+(diff(ipsi(t, x), x))*(diff(alpha(t, x), x))/(alpha(t, x)*a1(t, x)^2)+beta(t, x)*(diff(iPIb2(t, x), x))/(alpha(t, x)*b1(t, x)^2*a1(t, x))) * (alpha(t,x)*b1(t,x)^2*a1(t,x))\n) );\n\n\neq_evol_rpsi := diff(rpsi(t,x),t) = alpha(t,x)/a1(t,x)*rPI(t,x)+beta(t,x)*rPHI(t,x);\n\neq_evol_ipsi := diff(ipsi(t,x),t) = alpha(t,x)/a1(t,x)*iPI(t,x)+beta(t,x)*iPHI(t,x);\n", "meta": {"hexsha": "fab472dec646fc92223ec26af4c6c4f33b01182f", "size": 1388, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "eq_evol_matter.mpl", "max_stars_repo_name": "rmanak/bssn_spher", "max_stars_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "eq_evol_matter.mpl", "max_issues_repo_name": "rmanak/bssn_spher", "max_issues_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "eq_evol_matter.mpl", "max_forks_repo_name": "rmanak/bssn_spher", "max_forks_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 77.1111111111, "max_line_length": 520, "alphanum_fraction": 0.5216138329, "num_tokens": 674, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9314625069680098, "lm_q2_score": 0.7634837689358857, "lm_q1q2_score": 0.7111565054424048}} |
| {"text": "input := FileTools:-Text:-ReadFile(\"AoC-2021-9-input.txt\" ):\n\nogrid := ((parse~)@StringTools:-Explode)~(subs(\"\"=NULL,StringTools:-Split(input))):\ngridw := nops(ogrid[1]);\ngridl := nops(ogrid);\ngrid := [ [ 9 $ (gridw+2) ], map(l->[9,l[],9], ogrid)[], [ 9 $ (gridw+2) ] ]:\n\nlowpoints := NULL:\nrisklevel := 0:\nfor i from 2 to gridl+1 do\n for j from 2 to gridw+1 do\n if grid[i][j] < grid[i-1][j]\n and grid[i][j] < grid[i+1][j]\n and grid[i][j] < grid[i][j-1]\n and grid[i][j] < grid[i][j+1]\n then\n lowpoints := lowpoints, [i,j];\n risklevel := risklevel + grid[i][j]+1;\n end if;\n end do;\nend do:\n\nanswer1 := risklevel;\n\ncounted := table(sparse=0):\nbasinsize := proc( input )\nglobal grid, counted;\nlocal nb, x, y, v;\n\n x, y, v := op(input);\n\n if v = 9 or counted[input] <> 0 then\n return 0;\n end if;\n\n nb := [[x, y-1], [x, y+1], [x-1, y], [x+1,y]];\n nb := remove( n->(min(n)<2 or n[1]>gridl+2 or n[2]>gridw+2), nb);\n nb := map(n->[n[1], n[2], grid[n[1]][n[2]]], nb);\n #nb := remove(n->n[3]=9 or n[3] < v, nb); # for non-9 bounded basins\n\n counted[ input ] := 1;\n\n if nb = [] then\n return 1;\n else\n return add(map(thisproc, nb))+1;\n end if;\nend proc:\n\nbs := map(l->basinsize([l[], grid[l[1]][l[2]]]), [lowpoints]):\nanswer2 := mul( sort(bs)[-3..-1] );\n", "meta": {"hexsha": "9fcf53d1a03ddc65556ad99528fb876abf27c6fc", "size": 1384, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Day9/AoC9-Maple.mpl", "max_stars_repo_name": "johnpmay/AdventOfCode2021", "max_stars_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-12-04T18:24:03.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-04T18:24:03.000Z", "max_issues_repo_path": "Day9/AoC9-Maple.mpl", "max_issues_repo_name": "johnpmay/AdventOfCode2021", "max_issues_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Day9/AoC9-Maple.mpl", "max_forks_repo_name": "johnpmay/AdventOfCode2021", "max_forks_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 26.6153846154, "max_line_length": 83, "alphanum_fraction": 0.5043352601, "num_tokens": 515, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8519527869325345, "lm_q2_score": 0.8333245911726382, "lm_q1q2_score": 0.7099532078689441}} |
| {"text": "# Proof by PDF that X <~ rayleigh(1) == X^2 <~ gamma(1,2)\n\nPDF_rayleigh := (a, x) -> 2*x*exp(-x^2/a)/a;\n\nPDF_gamma := (k, t, x) -> x^(k-1)*exp(-x/t)/(GAMMA(k)*t^k);\nsimplify(PDF_gamma(1, 2, x));\n\nPDF_transform := (x) -> PDF_rayleigh(2,sqrt(x))*diff(sqrt(x),x);\nsimplify(PDF_transform(x));\n\nevalb(PDF_gamma(1, 2, x) = PDF_transform(x));", "meta": {"hexsha": "48c144d085da7eb8070a2f9fd4e13c341e60e214", "size": 335, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "tests/RoundTrip2/t_gamma_to_rayleigh.proof.mpl", "max_stars_repo_name": "vmchale/hakaru", "max_stars_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 327, "max_stars_repo_stars_event_min_datetime": "2015-01-03T08:56:51.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-24T12:12:06.000Z", "max_issues_repo_path": "tests/RoundTrip2/t_gamma_to_rayleigh.proof.mpl", "max_issues_repo_name": "vmchale/hakaru", "max_issues_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 155, "max_issues_repo_issues_event_min_datetime": "2015-05-05T17:57:22.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T15:43:39.000Z", "max_forks_repo_path": "tests/RoundTrip2/t_gamma_to_rayleigh.proof.mpl", "max_forks_repo_name": "vmchale/hakaru", "max_forks_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 38, "max_forks_repo_forks_event_min_datetime": "2015-01-23T16:25:37.000Z", "max_forks_repo_forks_event_max_datetime": "2021-03-14T15:09:12.000Z", "avg_line_length": 30.4545454545, "max_line_length": 64, "alphanum_fraction": 0.5940298507, "num_tokens": 139, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9230391706552536, "lm_q2_score": 0.7690802423634961, "lm_q1q2_score": 0.709891189078543}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n 2020 Susi Lehtola\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* error function:\n Toulouse et al, Int. J. of Quant. Chem. 100, 1047 (2004); doi:10.1002/qua.20259\n Tawada et al, J. Chem. Phys. 120, 8425 (2004); doi:10.1063/1.1688752\n*)\natt_erf_aux1 := a -> sqrt(Pi)*erf(1/(2*a)):\natt_erf_aux2 := a -> exp(-1/(4*a^2)) - 1:\natt_erf_aux3 := a -> 2*a^2*att_erf_aux2(a) + 1/2:\n(* This is the full function, which is numerically unstable for large a *)\nattenuation_erf0 := a ->\n 1 - 8/3*a*(att_erf_aux1(a) + 2*a*(att_erf_aux2(a) - att_erf_aux3(a))):\n(* The cutoff and order are determined by check_attenuation.mpl *)\nattenuation_erf := a -> enforce_smooth_lr(attenuation_erf0, a, 1.35, 16):\n\n(* These are for hyb_mgga_x_js18 and hyb_mgga_x_pjs18. This is the\nbracket in eqn (10) in Patra et al, 2018 *)\nattenuation_erf_f20 := a ->\n 1 + 24*a^2*( (20*a^2 - 64*a^4)*exp(-1/(4*a^2))\n - 3 - 36*a^2 + 64*a^4\n + 10*a*sqrt(Pi)*erf(1/(2*a))):\n(* The cutoff and order are determined by check_attenuation.mpl *)\nattenuation_erf_f2 := a -> enforce_smooth_lr(attenuation_erf_f20, a, 0.27, 46):\n\n(* This is eqn (11) in Patra et al, 2018 *)\nattenuation_erf_f30 := a ->\n 1 + 8/7*a*(\n (-8*a + 256*a^3 - 576*a^5 + 3840*a^7 - 122880*a^9)*exp(-1/(4*a^2))\n + 24*a^3*(-35 + 224*a^2 - 1440*a^4 + 5120*a^6)\n + 2*sqrt(Pi)*(-2 + 60*a^2)*erf(1/(2*a))):\n(* The cutoff and order are determined by check_attenuation.mpl *)\nattenuation_erf_f3 := a -> enforce_smooth_lr(attenuation_erf_f30, a, 0.32, 38):\n\n(* erf_gau - screening function = + 2 mu/sqrt(pi) exp(-mu^2 r^2)\n Song et al, J. Chem. Phys. 127, 154109 (2007); doi:10.1063/1.2790017\n You can recover the result in Int. J. of Quant. Chem. 100, 1047 (2004)\n by putting a = a/sqrt(3) and multiplying the whole attenuation function by -sqrt(3)\n*)\nattenuation_gau0 := a -> -8/3*a*(att_erf_aux1(a) + 2*a*att_erf_aux2(a)*(1 - 8*a^2) - 4*a):\n(* The cutoff and order are determined by check_attenuation.mpl *)\nattenuation_gau := a -> enforce_smooth_lr(attenuation_gau0, a, 2.07, 14):\n\n(* yukawa\n Akinaga and Ten-no, Chem. Phys. Lett. 462, 348 (2008); doi:10.1016/j.cplett.2008.07.103\n*)\natt_yuk_aux1 := a -> arctan(1, a):\natt_yuk_aux2 := a -> log(1 + 1/a^2):\natt_yuk_aux3 := a -> a^2 + 1:\nattenuation_yukawa0 := a -> 1 - 8/3*a*(att_yuk_aux1(a) + a/4*(1 - (att_yuk_aux3(a) + 2)*att_yuk_aux2(a))):\n(* The cutoff and order are determined by check_attenuation.mpl *)\nattenuation_yukawa := a -> enforce_smooth_lr(attenuation_yukawa0, a, 1.92, 36):\n", "meta": {"hexsha": "169d0c9227d8171115814235cebd03b2d9024e23", "size": 2708, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/attenuation.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/attenuation.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/attenuation.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 45.8983050847, "max_line_length": 106, "alphanum_fraction": 0.6521418021, "num_tokens": 1072, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.950410972802222, "lm_q2_score": 0.7461389986757757, "lm_q1q2_score": 0.7091386915771198}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: lda_exc *)\n\na := 0.0311:\nb := -0.048:\nc := 0.009:\nd := -0.017:\n\nf := (rs, zeta) -> a*log(rs) + b + c*rs*log(rs) + d*rs:\n", "meta": {"hexsha": "9d626f472353264b42db38b12efe9cb3548675fc", "size": 370, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_rpa.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_rpa.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_rpa.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 21.7647058824, "max_line_length": 68, "alphanum_fraction": 0.6108108108, "num_tokens": 133, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9353465116437761, "lm_q2_score": 0.7577943712746406, "lm_q1q2_score": 0.7088003217150236}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: gga_exc *)\n\n(* constants from text in section 2 *)\npbetrans_kappa_pbe := 0.814: (* This is probably a misprint in the manuscript as KAPPA_PBE is 0.8040 *)\npbetrans_kappa_revpbe := 1.227:\npbetrans_mu := 0.219:\n\n(* parameters from section 4 *)\npbetrans_alpha := 2*(3*Pi^2)^(1/3):\npbetrans_beta := 3:\n\n(* eq 3 *)\npbetrans_fermi := s -> 1/(1+exp(-pbetrans_alpha*(s-pbetrans_beta))):\n(* eq 5 *)\npbetrans_kappa := s -> (1-pbetrans_fermi(s))*pbetrans_kappa_revpbe + pbetrans_fermi(s)*pbetrans_kappa_pbe:\n(* eq 4 *)\npbetrans_f0 := s -> 1 + pbetrans_kappa(s)*(1 - pbetrans_kappa(s)/(pbetrans_kappa(s) + pbetrans_mu*s^2)):\n\npbetrans_f := x -> pbetrans_f0(X2S*x):\n\nf := (rs, z, xt, xs0, xs1) -> gga_exchange(pbetrans_f, rs, z, xs0, xs1):\n\n\n", "meta": {"hexsha": "86bdb54226d6549464ec6db731b9cad95fb3a2ad", "size": 978, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_pbetrans.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_pbetrans.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/gga_exc/gga_x_pbetrans.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 30.5625, "max_line_length": 106, "alphanum_fraction": 0.6799591002, "num_tokens": 363, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9609517050371973, "lm_q2_score": 0.7371581510799252, "lm_q1q2_score": 0.708373382162322}} |
| {"text": "Fun2 := module()\n\n description \"fun2\";\n\n # Module defined as a package (i.e.) collection of procedures\n option package, load = ModuleLoad, unload = ModuleUnLoad;\n\n export fun, grad, hess, F, JF;\n \n local ModuleLoad,\n ModuleUnLoad,\n f1, f2, f12,\n CST;\n\n uses LinearAlgebra;\n\n ModuleLoad := proc()\n CST := 53/27;\n NULL;\n end proc;\n\n ModuleUnLoad := proc()\n NULL;\n end proc:\n \n # Explicitly call ModuleLoad here so the type is registered when this\n # code is cut&pasted in. ModuleLoad gets called when the module is\n # read from the repository, but the code used to define a module\n # (like the command below) is not called at library read time.\n ModuleLoad();\n\n f1 := unapply( sin(3*x+5*y)+x+exp(3*(x-y))-1, (x,y) );\n f2 := unapply( (CST*x^2+2*y^2+cos(x-y)^2), (x,y) );\n f12 := unapply( f1(x,y)^2+f2(x,y)^2, (x,y) );\n\n fun := proc( X::Vector )\n local x, y;\n x := X[1];\n y := X[2];\n f12(x,y);\n end proc;\n\n grad := proc( X::Vector )\n local x, y;\n x := X[1];\n y := X[2];\n eval(<D[1](f12)(x,y),D[2](f12)(x,y)>);\n end proc;\n\n hess := proc( X::Vector )\n local x, y, d11, d12, d22;\n x := X[1];\n y := X[2];\n d11 := eval(D[1,1](f12)(x,y));\n d12 := eval(D[1,2](f12)(x,y));\n d22 := eval(D[2,2](f12)(x,y));\n <<d11,d12>|<d12,d22>>;\n end proc;\n\n F := proc( X::Vector )\n local x, y;\n x := X[1];\n y := X[2];\n <f1(x,y),f2(x,y)>;\n end proc;\n\n JF := proc( X::Vector )\n local x, y;\n x := X[1];\n y := X[2];\n <<D[1](f1)(x,y),D[1](f2)(x,y)>|\n <D[2](f1)(x,y),D[2](f2)(x,y)>>;\n end proc;\n\nend module:\n", "meta": {"hexsha": "2183a56068cc84ccf71d7b3828fd542347287e79", "size": 1614, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple/NL-Fun2.mpl", "max_stars_repo_name": "ebertolazzi/NLtoolbox", "max_stars_repo_head_hexsha": "99e47bdc346f3ac7b4834f2a6b431327d00e5ab1", "max_stars_repo_licenses": ["BSD-2-Clause", "Unlicense"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-06-28T09:12:53.000Z", "max_stars_repo_stars_event_max_datetime": "2021-06-28T09:12:53.000Z", "max_issues_repo_path": "maple/NL-Fun2.mpl", "max_issues_repo_name": "ebertolazzi/NLtoolbox", "max_issues_repo_head_hexsha": "99e47bdc346f3ac7b4834f2a6b431327d00e5ab1", "max_issues_repo_licenses": ["BSD-2-Clause", "Unlicense"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "maple/NL-Fun2.mpl", "max_forks_repo_name": "ebertolazzi/NLtoolbox", "max_forks_repo_head_hexsha": "99e47bdc346f3ac7b4834f2a6b431327d00e5ab1", "max_forks_repo_licenses": ["BSD-2-Clause", "Unlicense"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 21.2368421053, "max_line_length": 71, "alphanum_fraction": 0.5192069393, "num_tokens": 614, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8519527869325346, "lm_q2_score": 0.8311430436757312, "lm_q1q2_score": 0.7080946323991285}} |
| {"text": "moore_net_complex := proc(n::posint)\n local T,m,i;\n\n m := 3*n;\n\n T[\"vertices\"] := {seq(i,i=1..2*m+1)};\n T[\"faces\"] := {\n seq({1,2+i,2+modp(i+1,m)},i=0..m-1),\n seq({2+i,2+modp(i+1,m),m+2+modp(i+1,m)},i=0..m-1),\n seq({2+i,m+2+i,m+2+modp(i+1,m)},i=0..m-1)\n };\n\n T[\"max_simplices\"] := T[\"faces\"];\n \n T[\"embedding_dim\"] := 2;\n T[\"embedding\"] := table([\n 1 = [0,0],\n seq(i = [2*cos(2*Pi*(i-2)/m),2*sin(2*Pi*(i-2)/m)],i=2..m+1),\n seq(i = [3*cos(2*Pi*(i-m-2)/m),3*sin(2*Pi*(i-m-2)/m)],i=m+2..2*m+1)\n ]);\n\n T[\"plot\"] :=\n `plot/simplicial_complex`(T[\"vertices\"])(T[\"faces\"],2,T[\"embedding\"]);\n\n return eval(T);\nend:\n\nmoore_complex := proc(n::posint)\n local T0,T,m,i;\n\n m := 3*n;\n\n T[\"vertices\"] := {seq(i,i=1..m+4)};\n T[\"faces\"] := {\n seq({1,2+i,2+modp(i+1,m)},i=0..m-1),\n seq({2+i,2+modp(i+1,m),m+2+modp(i+1,3)},i=0..m-1),\n seq({2+i,m+2+modp(i,3),m+2+modp(i+1,3)},i=0..m-1)\n };\n T[\"max_simplices\"] := T[\"faces\"];\n\n return eval(T);\nend:\n\npunctured_moore_complex := proc(n::posint)\n local T,E,F,m,a,R0,R1,tor,tor_arc,i,v;\n\n m := 3*n;\n\n T[\"vertices\"] := {seq(i,i=2..m+4)};\n F := {\n seq({2+i,2+modp(i+1,m),m+2+modp(i+1,3)},i=0..m-1),\n seq({2+i,m+2+modp(i,3),m+2+modp(i+1,3)},i=0..m-1)\n };\n T[\"faces\"] := F;\n T[\"max_simplices\"] := T[\"faces\"];\n E := map(op,map(f -> {{f[1],f[2]},{f[1],f[3]},{f[2],f[3]}},F));\n T[\"edges\"] := E;\n \n R0 := 3;\n R1 := 1;\n\n tor := u -> \n (R0+R1*u[3]*cos(2*Pi*u[2])) *~ [cos(2*Pi*u[1]),sin(2*Pi*u[1]),0] +~\n [0,0,R1*u[3]*sin(2*Pi*u[2])];\n\n a := table([\n seq( 2+i = evalf([i/3,i/m,1]),i=0..m-1),\n seq(m+2+i = evalf([i/3,i/m,0]),i=0..2)\n ]);\n\n T[\"tor_embedding\"] := eval(a);\n\n T[\"embedding_dim\"] := 2;\n T[\"embedding\"] := table([\n seq(v = tor(a[v]),v in T[\"vertices\"])\n ]);\n\n T[\"plot\"] :=\n `plot/simplicial_complex`(T[\"vertices\"])(T[\"faces\"],2,T[\"embedding\"]);\n\n tor_arc := proc(u,v)\n local w;\n w := v -~ u;\n w := [w[1] - round(w[1]),w[2] - round(w[2]),w[3]];\n spacecurve(tor(u +~ t *~ w),t=0..1);\n end:\n\n T[\"curved_plot\"] :=\n display(map(e -> tor_arc(a[e[1]],a[e[2]]),E),\n axes=none,scaling=constrained);\n\n return eval(T);\nend:\n\n", "meta": {"hexsha": "17167f492282cb48cdf54036e1b8a7c95ec156ad", "size": 2067, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/simplicial_complexes/moore_complex.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/simplicial_complexes/moore_complex.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/simplicial_complexes/moore_complex.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 21.7578947368, "max_line_length": 73, "alphanum_fraction": 0.496371553, "num_tokens": 956, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8807970842359877, "lm_q2_score": 0.8031737963569016, "lm_q1q2_score": 0.7074331379659078}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: gga_exc *)\n\n$define gga_c_pbe_params\n$include \"gga_c_pbe.mpl\"\n\n(* in the paper we have beta_a = 0.066725 *)\nbeta_a := 0.066724550603149220:\nbeta_b := 0.1:\nbeta_c := 0.1778:\n\n(* we redefine beta here *)\n(* this is the Hu and Langreth expression *)\nmbeta := (rs, t) -> beta_a*(1 + beta_b*rs)/(1 + beta_c*rs):\n", "meta": {"hexsha": "0ded8c0b9737b5de877d86ab80bb2fa785b55a47", "size": 555, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_regtpss.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_regtpss.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_regtpss.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 25.2272727273, "max_line_length": 68, "alphanum_fraction": 0.6774774775, "num_tokens": 184, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9230391579526934, "lm_q2_score": 0.7662936377487304, "lm_q1q2_score": 0.7073190341320944}} |
| {"text": "# Differential geometry of curves in R^3\n\nanalyse_curve := proc(x,t)\n local T;\n T := table():\n T[\"x\"] := x;\n T[\"t\"] := t;\n T[\"v\"] := map(diff,x,t);\n T[\"speed\"] := simplify(`norm_2/R`(3)(T[\"v\"]));\n T[\"s\"] := int(T[\"speed\"],t);\n T[\"v_hat\"] := simplify(T[\"v\"] /~ T[\"speed\"]);\n T[\"T\"] := T[\"v_hat\"];\n T[\"a\"] := map(diff,T[\"v\"],t);\n T[\"v_hat_dot\"] := simplify(map(diff,T[\"v_hat\"],t));\n T[\"curvature\"] := simplify(`norm_2/R`(3)(T[\"v_hat_dot\"]));\n T[\"N\"] := simplify(T[\"v_hat_dot\"] /~ T[\"curvature\"]);\n T[\"radius_of_curvature\"] := simplify(1/T[\"curvature\"]);\n T[\"B\"] := `cross_product`(T[\"T\"],T[\"N\"]);\n \n return eval(T);\nend:", "meta": {"hexsha": "53cf329261a05095cfffb4c439a67f6abaa436b6", "size": 618, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/space_curves.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/space_curves.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/space_curves.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 29.4285714286, "max_line_length": 59, "alphanum_fraction": 0.5307443366, "num_tokens": 216, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.9591542817548989, "lm_q2_score": 0.7371581741774411, "lm_q1q2_score": 0.7070484190929162}} |
| {"text": "program primefactor;\t{ program18 }\r\nvar factor : array[200] of integer;\r\n\ti, n, can : integer;\r\nbegin\r\n\ti := 0;\r\n\twhile i < 200 do begin\r\n\t\tfactor[i] := 0;\r\n\t\ti := i + 1\r\n\tend;\r\n\twriteln('Input positive integer');\r\n\treadln(n);\r\n\tcan := 2;\r\n\twhile (can <= n div 2) and (can < 200) do begin\r\n\t\tif (n - (n div can) * can) <> 0 then can := can + 1\r\n\t\telse begin\r\n\t\t\tfactor[can] := factor[can] + 1;\r\n\t\t\tn := n div can\r\n\t\tend\r\n\tend;\r\n\ti := 0;\r\n\tif n < 200 then begin\r\n\t\tfactor[n] := factor[n]+1;\r\n\t\tn := 1\r\n\tend;\r\n\twhile i < 200 do begin\r\n\t\tif factor[i] <> 0 then begin\r\n\t\t\twriteln(' ', i, ' ** ', factor[i]);\r\n\t\tend;\r\n\t\ti := i + 1\r\n\tend;\r\n\tif n > 1 then writeln(' ', n, ' ** ', 1)\r\nend.\r\n", "meta": {"hexsha": "7d943fd38e4beb2f324c2a715cf7379591c752a3", "size": 689, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "data/sample18.mpl", "max_stars_repo_name": "naru380/SoftwareExperience5", "max_stars_repo_head_hexsha": "89020bf73d9fc6b58f8d564c7aaed52a0e02f371", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2022-02-10T01:27:36.000Z", "max_stars_repo_stars_event_max_datetime": "2022-02-10T01:27:36.000Z", "max_issues_repo_path": "task1_sample/sample18.mpl", "max_issues_repo_name": "shouth/LanguageProcessing", "max_issues_repo_head_hexsha": "7d4f751b5babb97857310990e746740f884fa5e5", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 14, "max_issues_repo_issues_event_min_datetime": "2020-10-04T11:15:32.000Z", "max_issues_repo_issues_event_max_datetime": "2021-01-20T02:11:14.000Z", "max_forks_repo_path": "samples/program1/sample18.mpl", "max_forks_repo_name": "Hiroya-W/lang-processing", "max_forks_repo_head_hexsha": "c93ef2d5757e560c4df2335f07ac25552750140c", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 20.8787878788, "max_line_length": 54, "alphanum_fraction": 0.5108853411, "num_tokens": 249, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8774767810736693, "lm_q2_score": 0.8056321866478979, "lm_q1q2_score": 0.7069235378691391}} |
| {"text": "function [x,f,exitflag,output] = minFunc(funObj,x0,options,varargin)\n% minFunc(funObj,x0,options,varargin)\n%\n% Unconstrained optimizer using a line search strategy\n%\n% Uses an interface very similar to fminunc\n% (it doesn't support all of the optimization toolbox options,\n% but supports many other options).\n%\n% It computes descent directions using one of ('Method'):\n% - 'sd': Steepest Descent\n% (no previous information used, not recommended)\n% - 'csd': Cyclic Steepest Descent\n% (uses previous step length for a fixed length cycle)\n% - 'bb': Barzilai and Borwein Gradient\n% (uses only previous step)\n% - 'cg': Non-Linear Conjugate Gradient\n% (uses only previous step and a vector beta)\n% - 'scg': Scaled Non-Linear Conjugate Gradient\n% (uses previous step and a vector beta, \n% and Hessian-vector products to initialize line search)\n% - 'pcg': Preconditionined Non-Linear Conjugate Gradient\n% (uses only previous step and a vector beta, preconditioned version)\n% - 'lbfgs': Quasi-Newton with Limited-Memory BFGS Updating\n% (default: uses a predetermined nunber of previous steps to form a \n% low-rank Hessian approximation)\n% - 'newton0': Hessian-Free Newton\n% (numerically computes Hessian-Vector products)\n% - 'pnewton0': Preconditioned Hessian-Free Newton \n% (numerically computes Hessian-Vector products, preconditioned\n% version)\n% - 'qnewton': Quasi-Newton Hessian approximation\n% (uses dense Hessian approximation)\n% - 'mnewton': Newton's method with Hessian calculation after every\n% user-specified number of iterations\n% (needs user-supplied Hessian matrix)\n% - 'newton': Newton's method with Hessian calculation every iteration\n% (needs user-supplied Hessian matrix)\n% - 'tensor': Tensor\n% (needs user-supplied Hessian matrix and Tensor of 3rd partial derivatives)\n%\n% Several line search strategies are available for finding a step length satisfying\n% the termination criteria ('LS'):\n% - 0: Backtrack w/ Step Size Halving\n% - 1: Backtrack w/ Quadratic/Cubic Interpolation from new function values\n% - 2: Backtrack w/ Cubic Interpolation from new function + gradient\n% values (default for 'bb' and 'sd')\n% - 3: Bracketing w/ Step Size Doubling and Bisection\n% - 4: Bracketing w/ Cubic Interpolation/Extrapolation with function +\n% gradient values (default for all except 'bb' and 'sd')\n% - 5: Bracketing w/ Mixed Quadratic/Cubic Interpolation/Extrapolation\n% - 6: Use Matlab Optimization Toolbox's line search\n% (requires Matlab's linesearch.m to be added to the path)\n%\n% Above, the first three find a point satisfying the Armijo conditions,\n% while the last four search for find a point satisfying the Wolfe\n% conditions. If the objective function overflows, it is recommended\n% to use one of the first 3.\n% The first three can be used to perform a non-monotone\n% linesearch by changing the option 'Fref'.\n%\n% Several strategies for choosing the initial step size are avaiable ('LS_init'):\n% - 0: Always try an initial step length of 1 (default for all except 'cg' and 'sd')\n% (t = 1)\n% - 1: Use a step similar to the previous step (default for 'cg' and 'sd')\n% (t = t_old*min(2,g'd/g_old'd_old))\n% - 2: Quadratic Initialization using previous function value and new\n% function value/gradient (use this if steps tend to be very long)\n% (t = min(1,2*(f-f_old)/g))\n% - 3: The minimum between 1 and twice the previous step length\n% (t = min(1,2*t)\n% - 4: The scaled conjugate gradient step length (may accelerate\n% conjugate gradient methods, but requires a Hessian-vector product)\n% (t = g'd/d'Hd)\n%\n% Inputs:\n% funObj is a function handle\n% x0 is a starting vector;\n% options is a struct containing parameters\n% (defaults are used for non-existent or blank fields)\n% all other arguments are passed to funObj\n%\n% Outputs:\n% x is the minimum value found\n% f is the function value at the minimum found\n% exitflag returns an exit condition\n% output returns a structure with other information\n%\n% Supported Input Options\n% Display - Level of display [ off | final | (iter) | full | excessive ]\n% MaxFunEvals - Maximum number of function evaluations allowed (1000)\n% MaxIter - Maximum number of iterations allowed (500)\n% TolFun - Termination tolerance on the first-order optimality (1e-5)\n% TolX - Termination tolerance on progress in terms of function/parameter changes (1e-9)\n% Method - [ sd | csd | bb | cg | scg | pcg | {lbfgs} | newton0 | pnewton0 |\n% qnewton | mnewton | newton | tensor ]\n% c1 - Sufficient Decrease for Armijo condition (1e-4)\n% c2 - Curvature Decrease for Wolfe conditions (.2 for cg methods, .9 otherwise)\n% LS_init - Line Search Initialization -see above (2 for cg/sd, 4 for scg, 0 otherwise)\n% LS - Line Search type -see above (2 for bb, 4 otherwise)\n% Fref - Setting this to a positive integer greater than 1\n% will use non-monotone Armijo objective in the line search.\n% (20 for bb, 10 for csd, 1 for all others)\n% numDiff - compute derivative numerically\n% (default: 0) (this option has a different effect for 'newton', see below)\n% useComplex - if 1, use complex differentials when computing numerical derivatives\n% to get very accurate values (default: 0)\n% DerivativeCheck - if 'on', computes derivatives numerically at initial\n% point and compares to user-supplied derivative (default: 'off')\n% outputFcn - function to run after each iteration (default: []). It\n% should have the following interface:\n% outputFcn(x,infoStruct,state,varargin{:})\n% useMex - where applicable, use mex files to speed things up (default: 1)\n%\n% Method-specific input options:\n% newton:\n% HessianModify - type of Hessian modification for direct solvers to\n% use if the Hessian is not positive definite (default: 0)\n% 0: Minimum Euclidean norm s.t. eigenvalues sufficiently large\n% (requires eigenvalues on iterations where matrix is not pd)\n% 1: Start with (1/2)*||A||_F and increment until Cholesky succeeds\n% (an approximation to method 0, does not require eigenvalues)\n% 2: Modified LDL factorization\n% (only 1 generalized Cholesky factorization done and no eigenvalues required)\n% 3: Modified Spectral Decomposition\n% (requires eigenvalues)\n% 4: Modified Symmetric Indefinite Factorization\n% 5: Uses the eigenvector of the smallest eigenvalue as negative\n% curvature direction\n% cgSolve - use conjugate gradient instead of direct solver (default: 0)\n% 0: Direct Solver\n% 1: Conjugate Gradient\n% 2: Conjugate Gradient with Diagonal Preconditioner\n% 3: Conjugate Gradient with LBFGS Preconditioner\n% x: Conjugate Graident with Symmetric Successive Over Relaxation\n% Preconditioner with parameter x\n% (where x is a real number in the range [0,2])\n% x: Conjugate Gradient with Incomplete Cholesky Preconditioner\n% with drop tolerance -x\n% (where x is a real negative number)\n% numDiff - compute Hessian numerically\n% (default: 0, done with complex differentials if useComplex = 1)\n% LS_saveHessiancomp - when on, only computes the Hessian at the\n% first and last iteration of the line search (default: 1)\n% mnewton:\n% HessianIter - number of iterations to use same Hessian (default: 5)\n% qnewton:\n% initialHessType - scale initial Hessian approximation (default: 1)\n% qnUpdate - type of quasi-Newton update (default: 3):\n% 0: BFGS\n% 1: SR1 (when it is positive-definite, otherwise BFGS)\n% 2: Hoshino\n% 3: Self-Scaling BFGS\n% 4: Oren's Self-Scaling Variable Metric method \n% 5: McCormick-Huang asymmetric update\n% Damped - use damped BFGS update (default: 1)\n% newton0/pnewton0:\n% HvFunc - user-supplied function that returns Hessian-vector products\n% (by default, these are computed numerically using autoHv)\n% HvFunc should have the following interface: HvFunc(v,x,varargin{:})\n% useComplex - use a complex perturbation to get high accuracy\n% Hessian-vector products (default: 0)\n% (the increased accuracy can make the method much more efficient,\n% but gradient code must properly support complex inputs)\n% useNegCurv - a negative curvature direction is used as the descent\n% direction if one is encountered during the cg iterations\n% (default: 1)\n% precFunc (for pnewton0 only) - user-supplied preconditioner\n% (by default, an L-BFGS preconditioner is used)\n% precFunc should have the following interfact:\n% precFunc(v,x,varargin{:})\n% lbfgs:\n% Corr - number of corrections to store in memory (default: 100)\n% (higher numbers converge faster but use more memory)\n% Damped - use damped update (default: 0)\n% pcg:\n% cgUpdate - type of update (default: 2)\n% cg/scg/pcg:\n% cgUpdate - type of update (default for cg/scg: 2, default for pcg: 1)\n% 0: Fletcher Reeves\n% 1: Polak-Ribiere\n% 2: Hestenes-Stiefel (not supported for pcg)\n% 3: Gilbert-Nocedal\n% HvFunc (for scg only)- user-supplied function that returns Hessian-vector \n% products\n% (by default, these are computed numerically using autoHv)\n% HvFunc should have the following interface:\n% HvFunc(v,x,varargin{:})\n% precFunc (for pcg only) - user-supplied preconditioner\n% (by default, an L-BFGS preconditioner is used)\n% precFunc should have the following interfact:\n% precFunc(v,x,varargin{:})\n% bb:\n% bbType - type of bb step (default: 1)\n% 0: min_alpha ||delta_x - alpha delta_g||_2\n% 1: min_alpha ||alpha delta_x - delta_g||_2\n% 2: Conic BB\n% 3: Gradient method with retards\n% csd:\n% cycle - length of cycle (default: 3)\n%\n% Supported Output Options\n% iterations - number of iterations taken\n% funcCount - number of function evaluations\n% algorithm - algorithm used\n% firstorderopt - first-order optimality\n% message - exit message\n% trace.funccount - function evaluations after each iteration\n% trace.fval - function value after each iteration\n%\n% Author: Mark Schmidt (2006)\n% Web: http://www.cs.ubc.ca/~schmidtm\n%\n% Sources (in order of how much the source material contributes):\n% J. Nocedal and S.J. Wright. 1999. \"Numerical Optimization\". Springer Verlag.\n% R. Fletcher. 1987. \"Practical Methods of Optimization\". Wiley.\n% J. Demmel. 1997. \"Applied Linear Algebra. SIAM.\n% R. Barret, M. Berry, T. Chan, J. Demmel, J. Dongarra, V. Eijkhout, R.\n% Pozo, C. Romine, and H. Van der Vost. 1994. \"Templates for the Solution of\n% Linear Systems: Building Blocks for Iterative Methods\". SIAM.\n% J. More and D. Thuente. \"Line search algorithms with guaranteed\n% sufficient decrease\". ACM Trans. Math. Softw. vol 20, 286-307, 1994.\n% M. Raydan. \"The Barzilai and Borwein gradient method for the large\n% scale unconstrained minimization problem\". SIAM J. Optim., 7, 26-33,\n% (1997).\n% \"Mathematical Optimization\". The Computational Science Education\n% Project. 1995.\n% C. Kelley. 1999. \"Iterative Methods for Optimization\". Frontiers in\n% Applied Mathematics. SIAM.\n\nif nargin < 3\n options = [];\nend\n\n% Get Parameters\n[verbose,verboseI,debug,doPlot,maxFunEvals,maxIter,tolFun,tolX,method,...\n corrections,c1,c2,LS_init,LS,cgSolve,qnUpdate,cgUpdate,initialHessType,...\n HessianModify,Fref,useComplex,numDiff,LS_saveHessianComp,...\n DerivativeCheck,Damped,HvFunc,bbType,cycle,...\n HessianIter,outputFcn,useMex,useNegCurv,precFunc] = ...\n minFunc_processInputOptions(options);\n\nif isfield(options, 'logfile')\n logfile = options.logfile;\nelse\n logfile = [];\nend\n\n% Constants\nSD = 0;\nCSD = 1;\nBB = 2;\nCG = 3;\nPCG = 4;\nLBFGS = 5;\nQNEWTON = 6;\nNEWTON0 = 7;\nNEWTON = 8;\nTENSOR = 9;\n\n% Initialize\np = length(x0);\nd = zeros(p,1);\nx = x0;\nt = 1;\n\n% If necessary, form numerical differentiation functions\nfunEvalMultiplier = 1;\nif numDiff && method ~= TENSOR\n varargin(3:end+2) = varargin(1:end);\n varargin{1} = useComplex;\n varargin{2} = funObj;\n if method ~= NEWTON\n if debug\n if useComplex\n fprintf('Using complex differentials for gradient computation\\n');\n else\n fprintf('Using finite differences for gradient computation\\n');\n end\n end\n funObj = @autoGrad;\n else\n if debug\n if useComplex\n fprintf('Using complex differentials for gradient computation\\n');\n else\n fprintf('Using finite differences for gradient computation\\n');\n end\n end\n funObj = @autoHess;\n end\n\n if method == NEWTON0 && useComplex == 1\n if debug\n fprintf('Turning off the use of complex differentials\\n');\n end\n useComplex = 0;\n end\n\n if useComplex\n funEvalMultiplier = p;\n else\n funEvalMultiplier = p+1;\n end\nend\n\n% Evaluate Initial Point\nif method < NEWTON\n [f,g] = feval(funObj, x, varargin{:});\nelse\n [f,g,H] = feval(funObj, x, varargin{:});\n computeHessian = 1;\nend\nfunEvals = 1;\n\nif strcmp(DerivativeCheck,'on')\n if numDiff\n fprintf('Can not do derivative checking when numDiff is 1\\n');\n end\n % Check provided gradient/hessian function using numerical derivatives\n fprintf('Checking Gradient:\\n');\n [f2,g2] = autoGrad(x,useComplex,funObj,varargin{:});\n\n fprintf('Max difference between user and numerical gradient: %f\\n',max(abs(g-g2)));\n if max(abs(g-g2)) > 1e-4\n fprintf('User NumDif:\\n');\n [g g2]\n diff = abs(g-g2)\n pause;\n end\n\n if method >= NEWTON\n fprintf('Check Hessian:\\n');\n [f2,g2,H2] = autoHess(x,useComplex,funObj,varargin{:});\n\n fprintf('Max difference between user and numerical hessian: %f\\n',max(abs(H(:)-H2(:))));\n if max(abs(H(:)-H2(:))) > 1e-4\n H\n H2\n diff = abs(H-H2)\n pause;\n end\n end\nend\n\n% Output Log\nif verboseI\n fprintf('%10s %10s %15s %15s %15s\\n','Iteration','FunEvals','Step Length','Function Val','Opt Cond');\nend\n\nif logfile\n fid = fopen(logfile, 'a');\n if (fid > 0)\n fprintf(fid, '-- %10s %10s %15s %15s %15s\\n','Iteration','FunEvals','Step Length','Function Val','Opt Cond');\n fclose(fid);\n end\nend\n\n% Output Function\nif ~isempty(outputFcn)\n callOutput(outputFcn,x,'init',0,funEvals,f,[],[],g,[],sum(abs(g)),varargin{:});\nend\n\n% Initialize Trace\ntrace.fval = f;\ntrace.funcCount = funEvals;\n\n% Check optimality of initial point\nif sum(abs(g)) <= tolFun\n exitflag=1;\n msg = 'Optimality Condition below TolFun';\n if verbose\n fprintf('%s\\n',msg);\n end\n if nargout > 3\n output = struct('iterations',0,'funcCount',1,...\n 'algorithm',method,'firstorderopt',sum(abs(g)),'message',msg,'trace',trace);\n end\n return;\nend\n\n% Perform up to a maximum of 'maxIter' descent steps:\nfor i = 1:maxIter\n\n % ****************** COMPUTE DESCENT DIRECTION *****************\n\n switch method\n case SD % Steepest Descent\n d = -g;\n\n case CSD % Cyclic Steepest Descent\n\n if mod(i,cycle) == 1 % Use Steepest Descent\n alpha = 1;\n LS_init = 2;\n LS = 4; % Precise Line Search\n elseif mod(i,cycle) == mod(1+1,cycle) % Use Previous Step\n alpha = t;\n LS_init = 0;\n LS = 2; % Non-monotonic line search\n end\n d = -alpha*g;\n\n case BB % Steepest Descent with Barzilai and Borwein Step Length\n\n if i == 1\n d = -g;\n else\n y = g-g_old;\n s = t*d;\n if bbType == 0\n yy = y'*y;\n alpha = (s'*y)/(yy);\n if alpha <= 1e-10 || alpha > 1e10\n alpha = 1;\n end\n elseif bbType == 1\n sy = s'*y;\n alpha = (s'*s)/sy;\n if alpha <= 1e-10 || alpha > 1e10\n alpha = 1;\n end\n elseif bbType == 2 % Conic Interpolation ('Modified BB')\n sy = s'*y;\n ss = s'*s;\n alpha = ss/sy;\n if alpha <= 1e-10 || alpha > 1e10\n alpha = 1;\n end\n alphaConic = ss/(6*(myF_old - f) + 4*g'*s + 2*g_old'*s);\n if alphaConic > .001*alpha && alphaConic < 1000*alpha\n alpha = alphaConic;\n end\n elseif bbType == 3 % Gradient Method with retards (bb type 1, random selection of previous step)\n sy = s'*y;\n alpha = (s'*s)/sy;\n if alpha <= 1e-10 || alpha > 1e10\n alpha = 1;\n end\n v(1+mod(i-2,5)) = alpha;\n alpha = v(ceil(rand*length(v)));\n end\n d = -alpha*g;\n end\n g_old = g;\n myF_old = f;\n\n\n case CG % Non-Linear Conjugate Gradient\n\n if i == 1\n d = -g; % Initially use steepest descent direction\n else\n gtgo = g'*g_old;\n gotgo = g_old'*g_old;\n\n if cgUpdate == 0\n % Fletcher-Reeves\n beta = (g'*g)/(gotgo);\n elseif cgUpdate == 1\n % Polak-Ribiere\n beta = (g'*(g-g_old)) /(gotgo);\n elseif cgUpdate == 2\n % Hestenes-Stiefel\n beta = (g'*(g-g_old))/((g-g_old)'*d);\n else\n % Gilbert-Nocedal\n beta_FR = (g'*(g-g_old)) /(gotgo);\n beta_PR = (g'*g-gtgo)/(gotgo);\n beta = max(-beta_FR,min(beta_PR,beta_FR));\n end\n\n d = -g + beta*d;\n\n % Restart if not a direction of sufficient descent\n if g'*d > -tolX\n if debug\n fprintf('Restarting CG\\n');\n end\n beta = 0;\n d = -g;\n end\n\n % Old restart rule:\n %if beta < 0 || abs(gtgo)/(gotgo) >= 0.1 || g'*d >= 0\n\n end\n g_old = g;\n\n case PCG % Preconditioned Non-Linear Conjugate Gradient\n\n % Apply preconditioner to negative gradient\n if isempty(precFunc)\n % Use L-BFGS Preconditioner\n if i == 1\n old_dirs = zeros(length(g),0);\n old_stps = zeros(length(g),0);\n Hdiag = 1;\n s = -g;\n else\n [old_dirs,old_stps,Hdiag] = lbfgsUpdate(g-g_old,t*d,corrections,debug,old_dirs,old_stps,Hdiag);\n\n if useMex\n s = lbfgsC(-g,old_dirs,old_stps,Hdiag);\n else\n s = lbfgs(-g,old_dirs,old_stps,Hdiag);\n end\n end\n else % User-supplied preconditioner\n s = precFunc(-g,x,varargin{:});\n end\n\n if i == 1\n d = s;\n else\n\n if cgUpdate == 0\n % Preconditioned Fletcher-Reeves\n beta = (g'*s)/(g_old'*s_old);\n elseif cgUpdate < 3\n % Preconditioned Polak-Ribiere\n beta = (g'*(s-s_old))/(g_old'*s_old);\n else\n % Preconditioned Gilbert-Nocedal\n beta_FR = (g'*s)/(g_old'*s_old);\n beta_PR = (g'*(s-s_old))/(g_old'*s_old);\n beta = max(-beta_FR,min(beta_PR,beta_FR));\n end\n d = s + beta*d;\n\n if g'*d > -tolX\n if debug\n fprintf('Restarting CG\\n');\n end\n beta = 0;\n d = s;\n end\n\n end\n g_old = g;\n s_old = s;\n case LBFGS % L-BFGS\n\n % Update the direction and step sizes\n\n if i == 1\n d = -g; % Initially use steepest descent direction\n old_dirs = zeros(length(g),0);\n old_stps = zeros(length(d),0);\n Hdiag = 1;\n else\n if Damped\n [old_dirs,old_stps,Hdiag] = dampedUpdate(g-g_old,t*d,corrections,debug,old_dirs,old_stps,Hdiag);\n else\n [old_dirs,old_stps,Hdiag] = lbfgsUpdate(g-g_old,t*d,corrections,debug,old_dirs,old_stps,Hdiag);\n end\n\n if useMex\n d = lbfgsC(-g,old_dirs,old_stps,Hdiag);\n else\n d = lbfgs(-g,old_dirs,old_stps,Hdiag);\n end\n end\n g_old = g;\n\n case QNEWTON % Use quasi-Newton Hessian approximation\n\n if i == 1\n d = -g;\n else\n % Compute difference vectors\n y = g-g_old;\n s = t*d;\n\n if i == 2\n % Make initial Hessian approximation\n if initialHessType == 0\n % Identity\n if qnUpdate <= 1\n R = eye(length(g));\n else\n H = eye(length(g));\n end\n else\n % Scaled Identity\n if debug\n fprintf('Scaling Initial Hessian Approximation\\n');\n end\n if qnUpdate <= 1\n % Use Cholesky of Hessian approximation\n R = sqrt((y'*y)/(y'*s))*eye(length(g));\n else\n % Use Inverse of Hessian approximation\n H = eye(length(g))*(y'*s)/(y'*y);\n end\n end\n end\n\n if qnUpdate == 0 % Use BFGS updates\n Bs = R'*(R*s);\n if Damped\n eta = .02;\n if y'*s < eta*s'*Bs\n if debug\n fprintf('Damped Update\\n');\n end\n theta = min(max(0,((1-eta)*s'*Bs)/(s'*Bs - y'*s)),1);\n y = theta*y + (1-theta)*Bs;\n end\n R = cholupdate(cholupdate(R,y/sqrt(y'*s)),Bs/sqrt(s'*Bs),'-');\n else\n if y'*s > 1e-10\n R = cholupdate(cholupdate(R,y/sqrt(y'*s)),Bs/sqrt(s'*Bs),'-');\n else\n if debug\n fprintf('Skipping Update\\n');\n end\n end\n end\n elseif qnUpdate == 1 % Perform SR1 Update if it maintains positive-definiteness\n\n Bs = R'*(R*s);\n ymBs = y-Bs;\n if abs(s'*ymBs) >= norm(s)*norm(ymBs)*1e-8 && (s-((R\\(R'\\y))))'*y > 1e-10\n R = cholupdate(R,-ymBs/sqrt(ymBs'*s),'-');\n else\n if debug\n fprintf('SR1 not positive-definite, doing BFGS Update\\n');\n end\n if Damped\n eta = .02;\n if y'*s < eta*s'*Bs\n if debug\n fprintf('Damped Update\\n');\n end\n theta = min(max(0,((1-eta)*s'*Bs)/(s'*Bs - y'*s)),1);\n y = theta*y + (1-theta)*Bs;\n end\n R = cholupdate(cholupdate(R,y/sqrt(y'*s)),Bs/sqrt(s'*Bs),'-');\n else\n if y'*s > 1e-10\n R = cholupdate(cholupdate(R,y/sqrt(y'*s)),Bs/sqrt(s'*Bs),'-');\n else\n if debug\n fprintf('Skipping Update\\n');\n end\n end\n end\n end\n elseif qnUpdate == 2 % Use Hoshino update\n v = sqrt(y'*H*y)*(s/(s'*y) - (H*y)/(y'*H*y));\n phi = 1/(1 + (y'*H*y)/(s'*y));\n H = H + (s*s')/(s'*y) - (H*y*y'*H)/(y'*H*y) + phi*v*v';\n\n elseif qnUpdate == 3 % Self-Scaling BFGS update\n ys = y'*s;\n Hy = H*y;\n yHy = y'*Hy;\n gamma = ys/yHy;\n v = sqrt(yHy)*(s/ys - Hy/yHy);\n H = gamma*(H - Hy*Hy'/yHy + v*v') + (s*s')/ys;\n elseif qnUpdate == 4 % Oren's Self-Scaling Variable Metric update\n\n % Oren's method\n if (s'*y)/(y'*H*y) > 1\n phi = 1; % BFGS\n omega = 0;\n elseif (s'*(H\\s))/(s'*y) < 1\n phi = 0; % DFP\n omega = 1;\n else\n phi = (s'*y)*(y'*H*y-s'*y)/((s'*(H\\s))*(y'*H*y)-(s'*y)^2);\n omega = phi;\n end\n\n gamma = (1-omega)*(s'*y)/(y'*H*y) + omega*(s'*(H\\s))/(s'*y);\n v = sqrt(y'*H*y)*(s/(s'*y) - (H*y)/(y'*H*y));\n H = gamma*(H - (H*y*y'*H)/(y'*H*y) + phi*v*v') + (s*s')/(s'*y);\n\n elseif qnUpdate == 5 % McCormick-Huang asymmetric update\n theta = 1;\n phi = 0;\n psi = 1;\n omega = 0;\n t1 = s*(theta*s + phi*H'*y)';\n t2 = (theta*s + phi*H'*y)'*y;\n t3 = H*y*(psi*s + omega*H'*y)';\n t4 = (psi*s + omega*H'*y)'*y;\n H = H + t1/t2 - t3/t4;\n end\n\n if qnUpdate <= 1\n d = -R\\(R'\\g);\n else\n d = -H*g;\n end\n\n end\n g_old = g;\n\n case NEWTON0 % Hessian-Free Newton\n\n cgMaxIter = min(p,maxFunEvals-funEvals);\n cgForce = min(0.5,sqrt(norm(g)))*norm(g);\n\n % Set-up preconditioner\n precondFunc = [];\n precondArgs = [];\n if cgSolve == 1\n if isempty(precFunc) % Apply L-BFGS preconditioner\n if i == 1\n old_dirs = zeros(length(g),0);\n old_stps = zeros(length(g),0);\n Hdiag = 1;\n else\n [old_dirs,old_stps,Hdiag] = lbfgsUpdate(g-g_old,t*d,corrections,debug,old_dirs,old_stps,Hdiag);\n if useMex\n precondFunc = @lbfgsC;\n else\n precondFunc = @lbfgs;\n end\n precondArgs = {old_dirs,old_stps,Hdiag};\n end\n g_old = g;\n else\n % Apply user-defined preconditioner\n precondFunc = precFunc;\n precondArgs = {x,varargin{:}};\n end\n end\n\n % Solve Newton system using cg and hessian-vector products\n if isempty(HvFunc)\n % No user-supplied Hessian-vector function,\n % use automatic differentiation\n HvFun = @autoHv;\n HvArgs = {x,g,useComplex,funObj,varargin{:}};\n else\n % Use user-supplid Hessian-vector function\n HvFun = HvFunc;\n HvArgs = {x,varargin{:}};\n end\n \n if useNegCurv\n [d,cgIter,cgRes,negCurv] = conjGrad([],-g,cgForce,cgMaxIter,debug,precondFunc,precondArgs,HvFun,HvArgs);\n else\n [d,cgIter,cgRes] = conjGrad([],-g,cgForce,cgMaxIter,debug,precondFunc,precondArgs,HvFun,HvArgs);\n end\n\n funEvals = funEvals+cgIter;\n if debug\n fprintf('newtonCG stopped on iteration %d w/ residual %.5e\\n',cgIter,cgRes);\n\n end\n\n if useNegCurv\n if ~isempty(negCurv)\n %if debug\n fprintf('Using negative curvature direction\\n');\n %end\n d = negCurv/norm(negCurv);\n d = d/sum(abs(g));\n end\n end\n\n case NEWTON % Newton search direction\n\n if cgSolve == 0\n if HessianModify == 0\n % Attempt to perform a Cholesky factorization of the Hessian\n [R,posDef] = chol(H);\n\n % If the Cholesky factorization was successful, then the Hessian is\n % positive definite, solve the system\n if posDef == 0\n d = -R\\(R'\\g);\n\n else\n % otherwise, adjust the Hessian to be positive definite based on the\n % minimum eigenvalue, and solve with QR\n % (expensive, we don't want to do this very much)\n if debug\n fprintf('Adjusting Hessian\\n');\n end\n H = H + eye(length(g)) * max(0,1e-12 - min(real(eig(H))));\n d = -H\\g;\n end\n elseif HessianModify == 1\n % Modified Incomplete Cholesky\n R = mcholinc(H,debug);\n d = -R\\(R'\\g);\n elseif HessianModify == 2\n % Modified Generalized Cholesky\n if useMex\n [L D perm] = mcholC(H);\n else\n [L D perm] = mchol(H);\n end\n d(perm) = -L' \\ ((D.^-1).*(L \\ g(perm)));\n\n elseif HessianModify == 3\n % Modified Spectral Decomposition\n [V,D] = eig((H+H')/2);\n D = diag(D);\n D = max(abs(D),max(max(abs(D)),1)*1e-12);\n d = -V*((V'*g)./D);\n elseif HessianModify == 4\n % Modified Symmetric Indefinite Factorization\n [L,D,perm] = ldl(H,'vector');\n [blockPos junk] = find(triu(D,1));\n for diagInd = setdiff(setdiff(1:p,blockPos),blockPos+1)\n if D(diagInd,diagInd) < 1e-12\n D(diagInd,diagInd) = 1e-12;\n end\n end\n for blockInd = blockPos'\n block = D(blockInd:blockInd+1,blockInd:blockInd+1);\n block_a = block(1);\n block_b = block(2);\n block_d = block(4);\n lambda = (block_a+block_d)/2 - sqrt(4*block_b^2 + (block_a - block_d)^2)/2;\n D(blockInd:blockInd+1,blockInd:blockInd+1) = block+eye(2)*(lambda+1e-12);\n end\n d(perm) = -L' \\ (D \\ (L \\ g(perm)));\n else\n % Take Newton step if Hessian is pd,\n % otherwise take a step with negative curvature\n [R,posDef] = chol(H);\n if posDef == 0\n d = -R\\(R'\\g);\n else\n if debug\n fprintf('Taking Direction of Negative Curvature\\n');\n end\n [V,D] = eig(H);\n u = V(:,1);\n d = -sign(u'*g)*u;\n end\n end\n\n else\n % Solve with Conjugate Gradient\n cgMaxIter = p;\n cgForce = min(0.5,sqrt(norm(g)))*norm(g);\n\n % Select Preconditioner\n if cgSolve == 1\n % No preconditioner\n precondFunc = [];\n precondArgs = [];\n elseif cgSolve == 2\n % Diagonal preconditioner\n precDiag = diag(H);\n precDiag(precDiag < 1e-12) = 1e-12 - min(precDiag);\n precondFunc = @precondDiag;\n precondArgs = {precDiag.^-1};\n elseif cgSolve == 3\n % L-BFGS preconditioner\n if i == 1\n old_dirs = zeros(length(g),0);\n old_stps = zeros(length(g),0);\n Hdiag = 1;\n else\n [old_dirs,old_stps,Hdiag] = lbfgsUpdate(g-g_old,t*d,corrections,debug,old_dirs,old_stps,Hdiag);\n end\n g_old = g;\n if useMex\n precondFunc = @lbfgsC;\n else\n precondFunc = @lbfgs;\n end\n precondArgs = {old_dirs,old_stps,Hdiag};\n elseif cgSolve > 0\n % Symmetric Successive Overelaxation Preconditioner\n omega = cgSolve;\n D = diag(H);\n D(D < 1e-12) = 1e-12 - min(D);\n precDiag = (omega/(2-omega))*D.^-1;\n precTriu = diag(D/omega) + triu(H,1);\n precondFunc = @precondTriuDiag;\n precondArgs = {precTriu,precDiag.^-1};\n else\n % Incomplete Cholesky Preconditioner\n opts.droptol = -cgSolve;\n opts.rdiag = 1;\n R = cholinc(sparse(H),opts);\n if min(diag(R)) < 1e-12\n R = cholinc(sparse(H + eye*(1e-12 - min(diag(R)))),opts);\n end\n precondFunc = @precondTriu;\n precondArgs = {R};\n end\n\n % Run cg with the appropriate preconditioner\n if isempty(HvFunc)\n % No user-supplied Hessian-vector function\n [d,cgIter,cgRes] = conjGrad(H,-g,cgForce,cgMaxIter,debug,precondFunc,precondArgs);\n else\n % Use user-supplied Hessian-vector function\n [d,cgIter,cgRes] = conjGrad(H,-g,cgForce,cgMaxIter,debug,precondFunc,precondArgs,HvFunc,{x,varargin{:}});\n end\n if debug\n fprintf('CG stopped after %d iterations w/ residual %.5e\\n',cgIter,cgRes);\n %funEvals = funEvals + cgIter;\n end\n end\n\n case TENSOR % Tensor Method\n\n if numDiff\n % Compute 3rd-order Tensor Numerically\n [junk1 junk2 junk3 T] = autoTensor(x,useComplex,funObj,varargin{:});\n else\n % Use user-supplied 3rd-derivative Tensor\n [junk1 junk2 junk3 T] = feval(funObj, x, varargin{:});\n end\n options_sub.Method = 'newton';\n options_sub.Display = 'none';\n options_sub.TolX = tolX;\n options_sub.TolFun = tolFun;\n d = minFunc(@taylorModel,zeros(p,1),options_sub,f,g,H,T);\n\n if any(abs(d) > 1e5) || all(abs(d) < 1e-5) || g'*d > -tolX\n if debug\n fprintf('Using 2nd-Order Step\\n');\n end\n [V,D] = eig((H+H')/2);\n D = diag(D);\n D = max(abs(D),max(max(abs(D)),1)*1e-12);\n d = -V*((V'*g)./D);\n else\n if debug\n fprintf('Using 3rd-Order Step\\n');\n end\n end\n end\n\n if ~isLegal(d)\n fprintf('Step direction is illegal!\\n');\n pause;\n return\n end\n\n % ****************** COMPUTE STEP LENGTH ************************\n\n % Directional Derivative\n gtd = g'*d;\n\n % Check that progress can be made along direction\n if gtd > -tolX\n exitflag=2;\n msg = 'Directional Derivative below TolX';\n break;\n end\n\n % Select Initial Guess\n if i == 1\n if method < NEWTON0\n t = min(1,1/sum(abs(g)));\n else\n t = 1;\n end\n else\n if LS_init == 0\n % Newton step\n t = 1;\n elseif LS_init == 1\n % Close to previous step length\n t = t*min(2,(gtd_old)/(gtd));\n elseif LS_init == 2\n % Quadratic Initialization based on {f,g} and previous f\n t = min(1,2*(f-f_old)/(gtd));\n elseif LS_init == 3\n % Double previous step length\n t = min(1,t*2);\n elseif LS_init == 4\n % Scaled step length if possible\n if isempty(HvFunc)\n % No user-supplied Hessian-vector function,\n % use automatic differentiation\n dHd = d'*autoHv(d,x,g,0,funObj,varargin{:});\n else\n % Use user-supplid Hessian-vector function\n dHd = d'*HvFunc(d,x,varargin{:});\n end\n\n funEvals = funEvals + 1;\n if dHd > 0\n t = -gtd/(dHd);\n else\n t = min(1,2*(f-f_old)/(gtd));\n end\n end\n\n if t <= 0\n t = 1;\n end\n end\n f_old = f;\n gtd_old = gtd;\n\n % Compute reference fr if using non-monotone objective\n if Fref == 1\n fr = f;\n else\n if i == 1\n old_fvals = repmat(-inf,[Fref 1]);\n end\n\n if i <= Fref\n old_fvals(i) = f;\n else\n old_fvals = [old_fvals(2:end);f];\n end\n fr = max(old_fvals);\n end\n\n computeHessian = 0;\n if method >= NEWTON\n if HessianIter == 1\n computeHessian = 1;\n elseif i > 1 && mod(i-1,HessianIter) == 0\n computeHessian = 1;\n end\n end\n\n % Line Search\n f_old = f;\n if LS < 3 % Use Armijo Bactracking\n % Perform Backtracking line search\n if computeHessian\n [t,x,f,g,LSfunEvals,H] = ArmijoBacktrack(x,t,d,f,fr,g,gtd,c1,LS,tolX,debug,doPlot,LS_saveHessianComp,funObj,varargin{:});\n else\n [t,x,f,g,LSfunEvals] = ArmijoBacktrack(x,t,d,f,fr,g,gtd,c1,LS,tolX,debug,doPlot,1,funObj,varargin{:});\n end\n funEvals = funEvals + LSfunEvals;\n\n elseif LS < 6\n % Find Point satisfying Wolfe\n\n if computeHessian\n [t,f,g,LSfunEvals,H] = WolfeLineSearch(x,t,d,f,g,gtd,c1,c2,LS,25,tolX,debug,doPlot,LS_saveHessianComp,funObj,varargin{:});\n else\n [t,f,g,LSfunEvals] = WolfeLineSearch(x,t,d,f,g,gtd,c1,c2,LS,25,tolX,debug,doPlot,1,funObj,varargin{:});\n end\n funEvals = funEvals + LSfunEvals;\n x = x + t*d;\n\n else\n % Use Matlab optim toolbox line search\n [t,f_new,fPrime_new,g_new,LSexitFlag,LSiter]=...\n lineSearch({'fungrad',[],funObj},x,p,1,p,d,f,gtd,t,c1,c2,-inf,maxFunEvals-funEvals,...\n tolX,[],[],[],varargin{:});\n funEvals = funEvals + LSiter;\n if isempty(t)\n exitflag = -2;\n msg = 'Matlab LineSearch failed';\n break;\n end\n\n if method >= NEWTON\n [f_new,g_new,H] = funObj(x + t*d,varargin{:});\n funEvals = funEvals + 1;\n end\n x = x + t*d;\n f = f_new;\n g = g_new;\n end\n\n % Output iteration information\n if verboseI\n fprintf('%10d %10d %15.5e %15.5e %15.5e\\n',i,funEvals*funEvalMultiplier,t,f,sum(abs(g)));\n end\n\n if logfile\n fid = fopen(logfile, 'a');\n if (fid > 0)\n fprintf(fid, '-- %10d %10d %15.5e %15.5e %15.5e\\n',i,funEvals*funEvalMultiplier,t,f,sum(abs(g)));\n fclose(fid);\n end\n end\n\n \n % Output Function\n if ~isempty(outputFcn)\n callOutput(outputFcn,x,'iter',i,funEvals,f,t,gtd,g,d,sum(abs(g)),varargin{:});\n end\n\n % Update Trace\n trace.fval(end+1,1) = f;\n trace.funcCount(end+1,1) = funEvals;\n\n % Check Optimality Condition\n if sum(abs(g)) <= tolFun\n exitflag=1;\n msg = 'Optimality Condition below TolFun';\n break;\n end\n\n % ******************* Check for lack of progress *******************\n\n if sum(abs(t*d)) <= tolX\n exitflag=2;\n msg = 'Step Size below TolX';\n break;\n end\n\n\n if abs(f-f_old) < tolX\n exitflag=2;\n msg = 'Function Value changing by less than TolX';\n break;\n end\n\n % ******** Check for going over iteration/evaluation limit *******************\n\n if funEvals*funEvalMultiplier > maxFunEvals\n exitflag = 0;\n msg = 'Exceeded Maximum Number of Function Evaluations';\n break;\n end\n\n if i == maxIter\n exitflag = 0;\n msg='Exceeded Maximum Number of Iterations';\n break;\n end\n\nend\n\nif verbose\n fprintf('%s\\n',msg);\nend\nif nargout > 3\n output = struct('iterations',i,'funcCount',funEvals*funEvalMultiplier,...\n 'algorithm',method,'firstorderopt',sum(abs(g)),'message',msg,'trace',trace);\nend\n\n% Output Function\nif ~isempty(outputFcn)\n callOutput(outputFcn,x,'done',i,funEvals,f,t,gtd,g,d,sum(abs(g)),varargin{:});\nend\n\nend\n", "meta": {"hexsha": "64f0b8043e5c9ab167d3b3ea21abb6e29cee2415", "size": 42488, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple/minFunc.mpl", "max_stars_repo_name": "ebertolazzi/NLtoolbox", "max_stars_repo_head_hexsha": "99e47bdc346f3ac7b4834f2a6b431327d00e5ab1", "max_stars_repo_licenses": ["BSD-2-Clause", "Unlicense"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-06-28T09:12:53.000Z", "max_stars_repo_stars_event_max_datetime": "2021-06-28T09:12:53.000Z", "max_issues_repo_path": "maple/minFunc.mpl", "max_issues_repo_name": "ebertolazzi/NLtoolbox", "max_issues_repo_head_hexsha": "99e47bdc346f3ac7b4834f2a6b431327d00e5ab1", "max_issues_repo_licenses": ["BSD-2-Clause", "Unlicense"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "maple/minFunc.mpl", "max_forks_repo_name": "ebertolazzi/NLtoolbox", "max_forks_repo_head_hexsha": "99e47bdc346f3ac7b4834f2a6b431327d00e5ab1", "max_forks_repo_licenses": ["BSD-2-Clause", "Unlicense"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 37.1074235808, "max_line_length": 134, "alphanum_fraction": 0.4954340049, "num_tokens": 10811, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8918110425624791, "lm_q2_score": 0.7905303285397349, "lm_q1q2_score": 0.7050036764722801}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: lda_exc *)\n\n$define lda_x_params\n$include \"lda_x.mpl\"\n$include \"attenuation.mpl\"\n\na_cnst := (4/(9*Pi))^(1/3)*p_a_hyb_omega_0_/2:\n\nlda_x_ax := -RS_FACTOR*X_FACTOR_C/2^(4/3):\nlda_x_erf_spin := (rs, z) ->\n lda_x_ax*opz_pow_n(z,4/3)/rs * attenuation_erf(a_cnst*rs/opz_pow_n(z,1/3)):\n\nf_lda_x_erf := (rs, z) -> lda_x_erf_spin(rs, z) + lda_x_erf_spin(rs, -z):\n\nf := (rs, z) -> f_lda_x_erf(rs, z):\n", "meta": {"hexsha": "31d99894382da94e15ea7639256d6019b16cca78", "size": 640, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_x_erf.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_x_erf.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_x_erf.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 26.6666666667, "max_line_length": 77, "alphanum_fraction": 0.6765625, "num_tokens": 241, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9263037363973295, "lm_q2_score": 0.7606506581031359, "lm_q1q2_score": 0.7045935466940224}} |
| {"text": "`permutation_matrix` := proc(s)\n local n,g,i;\n \n n := nops(s);\n g := Matrix(n,n);\n for i from 1 to n do\n g[s[i],i] := 1;\n od:\n return g;\nend:\n\n`elementary_matrix/D` := (n) -> proc(i,a)\n local g,k;\n g := Matrix(n,n);\n for k from 1 to n do g[k,k] := 1; od;\n g[i,i] := a;\n return g;\nend:\n\n`elementary_matrix/E` := (n) -> proc(i,j,a_)\n local g,k;\n g := Matrix(n,n);\n for k from 1 to n do g[k,k] := 1; od;\n g[i,j] := `if`(nargs > 2,a_,1);\n return g;\nend:\n\n`elementary_matrix/F` := (n) -> proc(i,j)\n local g,k;\n g := Matrix(n,n);\n for k from 1 to n do g[k,k] := 1; od;\n g[i,i] := 0; g[j,j] := 0;\n g[i,j] := 1; g[j,i] := 1;\n return g;\nend:\n\nmake_general_linear := proc(n,p)\n local G,i,j,k,m,g,L,f;\n \n m := n^2;\n \n G := table():\n G[\"p\"] := p;\n G[\"id\"] := IdentityMatrix(n);\n G[\"o\"] := (g,h) -> map(mods,g . h,G[\"p\"]);\n G[\"inv\"] := g -> map(mods,1/g,G[\"p\"]);\n G[\"order\"] := mul(p^n - p^i,i = 0..n-1);\n \n L := [[]];\n for i from 1 to m do\n L := [seq(seq([op(u),j],j=0..p-1),u in L)];\n od:\n\n f := proc(u)\n local i,j,k,g;\n g := Matrix(n,n);\n k := 1;\n for i from 1 to n do\n for j from 1 to n do\n g[i,j] := mods(u[k],p); k := k + 1;\n od:\n od:\n if mods(Determinant(g),p) <> 0 then\n return g;\n else\n return NULL;\n fi;\n end:\n \n G[\"elements\"] := map(f,L);\n\n return eval(G);\nend:\n\nbruhat_permutation := (n,p) -> proc(g)\n local h,i,j,k,a,q,qi;\n\n if [Dimension(g)] <> [n,n] then\n error(\"Not an n x n matrix\");\n fi;\n \n h := eval(g);\n q := [];\n for i from n to 1 by -1 do\n j := 1;\n while h[i,j] = 0 do j := j+1; od;\n q := [j,op(q)];\n a := mods(1/h[i,j],p);\n h := map(mods,`elementary_matrix/D`(n)(i,a) . h,p);\n for k from 1 to i-1 do\n h := map(mods,`elementary_matrix/E`(n)(k,i,-h[k,j]) . h,p);\n od; \n od;\n qi := table():\n for i from 1 to n do qi[q[i]] := i; od:\n \n return([seq(qi[i],i=1..n)]);\nend:\n\n# This returns a triple [b,w,c] where b is upper triangular,\n# w is a permutation matrix, c is upper unitriangular and g = bwc.\n\nbruhat_decomposition := (n,p) -> proc(g) \n local h,i,j,k,a,b,c,x,q,w;\n\n if [Dimension(g)] <> [n,n] then\n error(\"Not an n x n matrix\");\n fi;\n \n h := eval(g);\n q := [];\n b := Matrix(n,n);\n for k from 1 to n do b[k,k] := 1; od:\n\n for i from n to 1 by -1 do\n j := 1;\n while h[i,j] = 0 do j := j+1; od;\n q := [j,op(q)];\n x := mods(1/h[i,j],p);\n b := map(mods, b . `elementary_matrix/D`(n)(i,h[i,j]),p);\n h := map(mods, `elementary_matrix/D`(n)(i,x) . h,p);\n for k from 1 to i-1 do\n b := map(mods,b . `elementary_matrix/E`(n)(k,i,h[k,j]),p);\n h := map(mods,`elementary_matrix/E`(n)(k,i,-h[k,j]) . h,p);\n od; \n od;\n w := permutation_matrix(q);\n c := w . h;\n return([b,Transpose(w),c]);\nend:\n", "meta": {"hexsha": "7505128cbe08585e0c692ba5a44c821ae46ad249", "size": 2691, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/groups/general_linear.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/groups/general_linear.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/groups/general_linear.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 20.5419847328, "max_line_length": 66, "alphanum_fraction": 0.5001858045, "num_tokens": 1081, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8902942319436397, "lm_q2_score": 0.7905303211371898, "lm_q1q2_score": 0.7038045850849932}} |
| {"text": "HagerZhang := module()\n\n description \"HagerZhang\";\n\n # Module defined as a package (i.e.) collection of procedures\n option package, load = ModuleLoad, unload = ModuleUnLoad;\n\n export lines, linesearch, esatta, AB_list, doplot, doplot2;\n \n local ModuleLoad,\n ModuleUnLoad,\n _debug,\n FINAL, ITER, PARAMETERS, GRADIENT, SEARCHDIR,\n ALPHA, BETA, BRACKET, LINESEARCH, UPDATE, SECANT2,\n BISECT, BARRIERCOEF, DEFAULTDELTA, DEFAULTSIGMA,\n max_iter, A_list, B_list;\n\n uses LinearAlgebra;\n\n ModuleUnLoad := proc()\n printf(\"HagerZhang unload\\n\");\n NULL;\n end proc:\n\n ModuleLoad := proc()\n printf(\"HagerZhang load\\n\");\n _debug := true;\n # Display flags are represented as a bitfield\n FINAL := 1;\n ITER := 2;\n PARAMETERS := 8;\n GRADIENT := 16;\n SEARCHDIR := 32;\n ALPHA := 64;\n BETA := 128;\n BRACKET := 256;\n LINESEARCH := 512;\n UPDATE := 1024;\n SECANT2 := 2048;\n BISECT := 4096;\n BARRIERCOEF := 8192;\n\n DEFAULTDELTA := 0.1; # Values taken from HZ paper (Nocedal & Wright recommends 0.01?)\n DEFAULTSIGMA := 0.9; # Values taken from HZ paper (Nocedal & Wright recommends 0.1 for GradientDescent)\n\n max_iter := 40;\n NULL;\n end proc;\n \n # Explicitly call ModuleLoad here so the type is registered when this\n # code is cut&pasted in. ModuleLoad gets called when the module is\n # read from the repository, but the code used to define a module\n # (like the command below) is not called at library read time.\n ModuleLoad();\n\n AB_list := proc()\n A_list, B_list;\n end proc;\n\n min_quadratic := proc ( a, fa, Dfa, b, fb )\n local t, delta; # A+B*(x-a)+C*(x-a)^2\n # p = fa + Dfa*(x-a)+t*(x-a)^2\n # p' = Dfa+2*t*(x-a)\n ##t := ((fb-fa)/(b-a)-Dfa)/(b-a);\n ##delta := -Dfa/(2*t);\n t := (fb-fa)/(b-a)-Dfa;\n delta := max(tau1,min(1-tau1,-Dfa/(2*t)));\n a+(b-a)*delta;\n end proc;\n\n lines := proc( f0, df0, L )\n [ [0,f0], [L,f0+L*rho*df0] ], [ [0,f0], [L,f0+L*sigma*df0] ];\n end proc;\n\n #\n # Conjugate gradient line search implementation from:\n # W. W. Hager and H. Zhang (2006) Algorithm 851: CG_DESCENT, a\n # conjugate gradient method with guaranteed descent. ACM\n # Transactions on Mathematical Software 32: 113–137.\n #\n # Code comments such as \"HZ, stage X\" or \"HZ, eqs Y\" are with\n # reference to a particular point in this paper.\n #\n # There are some modifications and/or extensions from what's in the\n # paper (these may or may not be extensions of the cg_descent code\n # that can be downloaded from Hager's site; his code has undergone\n # numerous revisions since publication of the paper):\n # linesearch: the Wolfe conditions are checked only after alpha is\n # generated either by quadratic interpolation or secant\n # interpolation, not when alpha is generated by bisection or\n # expansion. This increases the likelihood that alpha will be a\n # good approximation of the minimum.\n #\n # linesearch: In step I2, we multiply by psi2 only if the convexity\n # test failed, not if the function-value test failed. This\n # prevents one from going uphill further when you already know\n # you're already higher than the point at alpha=0.\n #\n # both: checks for Inf/NaN function values\n #\n # both: support maximum value of alpha (equivalently, c). This\n # facilitates using these routines for constrained minimization\n # when you can calculate the distance along the path to the\n # disallowed region. (When you can't easily calculate that\n # distance, it can still be handled by returning Inf/NaN for\n # exterior points. It's just more efficient if you know the\n # maximum, because you don't have to test values that won't\n # work.) The maximum should be specified as the largest value for\n # which a finite value will be returned. See, e.g., limits_box\n # below. The default value for alphamax is Inf. See alphamaxfunc\n # for cgdescent and alphamax for HagerZhang.\n\n #const DEFAULTDELTA = 0.1 # Values taken from HZ paper (Nocedal & Wright recommends 0.01?)\n #const DEFAULTSIGMA = 0.9 # Values taken from HZ paper (Nocedal & Wright recommends 0.1 for GradientDescent)\n\n\n # NOTE:\n # [1] The type `T` in the `HagerZhang{T}` need not be the same `T` as in\n # `hagerzhang!{T}`; in the latter, `T` comes from the input vector `x`.\n # [2] the only method parameter that is not included in the\n # type is `iterfinitemax` since this value needs to be\n # inferred from the input vector `x` and not from the type information\n # on the parameters\n #\n # Conjugate gradient line search implementation from:\n # W. W. Hager and H. Zhang (2006) Algorithm 851: CG_DESCENT, a\n # conjugate gradient method with guaranteed descent. ACM\n # Transactions on Mathematical Software 32: 113–137.\n\n # TODO: Should we deprecate the interface that only uses the phi and phid\\phi arguments?\n linesearch := proc( phi, dphi, c, phi_0, dphi_0 )\n local delta, sigma, alphamax, rho, epsilon, gamma,\n linesearchmax, psi3, display, mayterminate;\n\n if not (isfinite(phi_0) and isfinite(dphi_0)) then\n error(\"Value and slope at step length = 0 must be finite.\");\n end;\n if dphi_0 >= eps * abs(phi_0) then\n error(\"Search direction is not a descent direction.\");\n elif dphi_0 >= 0 then\n return 0, phi_0\n end\n\n # Prevent values of x_new = x+αs that are likely to make\n # phi(x_new) infinite\n iterfinitemax::Int = ceil(Int, -log2(eps(T)))\n alphas = [0] # for bisection\n values = [phi_0]\n slopes = [dphi_0]\n if display and LINESEARCH > 0 then\n println(\"New linesearch\\n\");\n end\n\n phi_lim = phi_0 + epsilon * abs(phi_0);\n @assert c >= 0\n c <= eps(T) && return zeroT, phi_0\n @assert isfinite(c) && c <= alphamax\n phi_c, dphi_c = phidphi(c)\n iterfinite = 1\n while !(isfinite(phi_c) && isfinite(dphi_c)) && iterfinite < iterfinitemax\n mayterminate[] = false\n iterfinite += 1\n c *= psi3\n phi_c, dphi_c = phidphi(c)\n end\n if !(isfinite(phi_c) && isfinite(dphi_c))\n @warn(\"Failed to achieve finite new evaluation point, using alpha=0\")\n mayterminate[] = false # reset in case another initial guess is used next\n return zeroT, phi_0\n end\n push!(alphas, c)\n push!(values, phi_c)\n push!(slopes, dphi_c)\n\n # If c was generated by quadratic interpolation, check whether it\n # satisfies the Wolfe conditions\n if mayterminate[] &&\n satisfies_wolfe(c, phi_c, dphi_c, phi_0, dphi_0, phi_lim, delta, sigma)\n if display & LINESEARCH > 0\n println(\"Wolfe condition satisfied on point alpha = \", c)\n end\n mayterminate[] = false # reset in case another initial guess is used next\n return c, phi_c # phi_c\n end\n # Initial bracketing step (HZ, stages B0-B3)\n isbracketed = false\n ia = 1\n ib = 2\n @assert length(alphas) == 2\n iter = 1\n cold = -one(T)\n while !isbracketed && iter < linesearchmax\n if display & BRACKET > 0\n println(\"bracketing: ia = \", ia,\n \", ib = \", ib,\n \", c = \", c,\n \", phi_c = \", phi_c,\n \", dphi_c = \", dphi_c)\n end\n if dphi_c >= zeroT\n # We've reached the upward slope, so we have b; examine\n # previous values to find a\n ib = length(alphas)\n for i = (ib - 1):-1:1\n if values[i] <= phi_lim\n ia = i\n break\n end\n end\n isbracketed = true\n elseif values[end] > phi_lim\n # The value is higher, but the slope is downward, so we must\n # have crested over the peak. Use bisection.\n ib = length(alphas)\n ia = 1\n if c ≉ alphas[ib] || slopes[ib] >= zeroT\n error(\"c = \", c)\n end\n # ia, ib = bisect(phi, lsr, ia, ib, phi_lim) # TODO: Pass options\n ia, ib = bisect!(phidphi, alphas, values, slopes, ia, ib, phi_lim, display)\n isbracketed = true\n else\n # We'll still going downhill, expand the interval and try again.\n # Reaching this branch means that dphi_c < 0 and phi_c <= phi_0 + ϵ_k\n # So cold = c has a lower objective than phi_0 up to epsilon. \n # This makes it a viable step to return if bracketing fails.\n\n # Bracketing can fail if no cold < c <= alphamax can be found with finite phi_c and dphi_c. \n # Going back to the loop with c = cold will only result in infinite cycling.\n # So returning (cold, phi_cold) and exiting the line search is the best move.\n cold = c\n phi_cold = phi_c\n if nextfloat(cold) >= alphamax\n mayterminate[] = false # reset in case another initial guess is used next\n return cold, phi_cold\n end\n c *= rho\n if c > alphamax\n c = alphamax\n if display & BRACKET > 0\n println(\"bracket: exceeding alphamax, using c = alphamax = \", alphamax,\n \", cold = \", cold)\n end\n end\n phi_c, dphi_c = phidphi(c)\n iterfinite = 1\n while !(isfinite(phi_c) && isfinite(dphi_c)) && c > nextfloat(cold) && iterfinite < iterfinitemax\n alphamax = c # shrinks alphamax, assumes that steps >= c can never have finite phi_c and dphi_c\n iterfinite += 1\n if display & BRACKET > 0\n println(\"bracket: non-finite value, bisection\")\n end\n c = (cold + c) / 2\n phi_c, dphi_c = phidphi(c)\n end\n if !(isfinite(phi_c) && isfinite(dphi_c))\n if display & BRACKET > 0\n println(\"Warning: failed to expand interval to bracket with finite values. If this happens frequently, check your function and gradient.\")\n println(\"c = \", c,\n \", alphamax = \", alphamax,\n \", phi_c = \", phi_c,\n \", dphi_c = \", dphi_c)\n end\n return cold, phi_cold\n end\n push!(alphas, c)\n push!(values, phi_c)\n push!(slopes, dphi_c)\n end\n iter += 1\n end\n while iter < linesearchmax\n a = alphas[ia]\n b = alphas[ib]\n @assert b > a\n if display & LINESEARCH > 0\n println(\"linesearch: ia = \", ia,\n \", ib = \", ib,\n \", a = \", a,\n \", b = \", b,\n \", phi(a) = \", values[ia],\n \", phi(b) = \", values[ib])\n end\n if b - a <= eps(b)\n mayterminate[] = false # reset in case another initial guess is used next\n return a, values[ia] # lsr.value[ia]\n end\n iswolfe, iA, iB = secant2!(phidphi, alphas, values, slopes, ia, ib, phi_lim, delta, sigma, display)\n if iswolfe\n mayterminate[] = false # reset in case another initial guess is used next\n return alphas[iA], values[iA] # lsr.value[iA]\n end\n A = alphas[iA]\n B = alphas[iB]\n @assert B > A\n if B - A < gamma * (b - a)\n if display & LINESEARCH > 0\n println(\"Linesearch: secant succeeded\")\n end\n if nextfloat(values[ia]) >= values[ib] && nextfloat(values[iA]) >= values[iB]\n # It's so flat, secant didn't do anything useful, time to quit\n if display & LINESEARCH > 0\n println(\"Linesearch: secant suggests it's flat\")\n end\n mayterminate[] = false # reset in case another initial guess is used next\n return A, values[iA]\n end\n ia = iA\n ib = iB\n else\n # Secant is converging too slowly, use bisection\n if display & LINESEARCH > 0\n println(\"Linesearch: secant failed, using bisection\")\n end\n c = (A + B) / convert(T, 2)\n\n phi_c, dphi_c = phidphi(c)\n @assert isfinite(phi_c) && isfinite(dphi_c)\n push!(alphas, c)\n push!(values, phi_c)\n push!(slopes, dphi_c)\n\n ia, ib = update!(phidphi, alphas, values, slopes, iA, iB, length(alphas), phi_lim, display)\n end\n iter += 1\n end\n\n throw(LineSearchException(\"Linesearch failed to converge, reached maximum iterations $(linesearchmax).\",\n alphas[ia]))\n\n\nend\n\n# Check Wolfe & approximate Wolfe\nfunction satisfies_wolfe(c::T,\n phi_c::Real,\n dphi_c::Real,\n phi_0::Real,\n dphi_0::Real,\n phi_lim::Real,\n delta::Real,\n sigma::Real) where T<:Number\n wolfe1 = delta * dphi_0 >= (phi_c - phi_0) / c &&\n dphi_c >= sigma * dphi_0\n wolfe2 = (2 * delta - 1) * dphi_0 >= dphi_c >= sigma * dphi_0 &&\n phi_c <= phi_lim\n return wolfe1 || wolfe2\nend\n\n# HZ, stages S1-S4\nfunction secant(a::Real, b::Real, dphi_a::Real, dphi_b::Real)\n return (a * dphi_b - b * dphi_a) / (dphi_b - dphi_a)\nend\nfunction secant(alphas, values, slopes, ia::Integer, ib::Integer)\n return secant(alphas[ia], alphas[ib], slopes[ia], slopes[ib])\nend\n# phi\nfunction secant2!(phidphi,\n alphas,\n values,\n slopes,\n ia::Integer,\n ib::Integer,\n phi_lim::Real,\n delta::Real = DEFAULTDELTA,\n sigma::Real = DEFAULTSIGMA,\n display::Integer = 0)\n phi_0 = values[1]\n dphi_0 = slopes[1]\n a = alphas[ia]\n b = alphas[ib]\n dphi_a = slopes[ia]\n dphi_b = slopes[ib]\n T = eltype(slopes)\n zeroT = convert(T, 0)\n if !(dphi_a < zeroT && dphi_b >= zeroT)\n error(string(\"Search direction is not a direction of descent; \",\n \"this error may indicate that user-provided derivatives are inaccurate. \",\n @sprintf \"(dphi_a = %f; dphi_b = %f)\" dphi_a dphi_b))\n end\n c = secant(a, b, dphi_a, dphi_b)\n if display & SECANT2 > 0\n println(\"secant2: a = \", a, \", b = \", b, \", c = \", c)\n end\n @assert isfinite(c)\n # phi_c = phi(tmpc, c) # Replace\n phi_c, dphi_c = phidphi(c)\n @assert isfinite(phi_c) && isfinite(dphi_c)\n\n push!(alphas, c)\n push!(values, phi_c)\n push!(slopes, dphi_c)\n\n ic = length(alphas)\n if satisfies_wolfe(c, phi_c, dphi_c, phi_0, dphi_0, phi_lim, delta, sigma)\n if display & SECANT2 > 0\n println(\"secant2: first c satisfied Wolfe conditions\")\n end\n return true, ic, ic\n end\n\n iA, iB = update!(phidphi, alphas, values, slopes, ia, ib, ic, phi_lim, display)\n if display & SECANT2 > 0\n println(\"secant2: iA = \", iA, \", iB = \", iB, \", ic = \", ic)\n end\n a = alphas[iA]\n b = alphas[iB]\n doupdate = false\n if iB == ic\n # we updated b, make sure we also update a\n c = secant(alphas, values, slopes, ib, iB)\n elseif iA == ic\n # we updated a, do it for b too\n c = secant(alphas, values, slopes, ia, iA)\n end\n if (iA == ic || iB == ic) && a <= c <= b\n if display & SECANT2 > 0\n println(\"secant2: second c = \", c)\n end\n # phi_c = phi(tmpc, c) # TODO: Replace\n phi_c, dphi_c = phidphi(c)\n @assert isfinite(phi_c) && isfinite(dphi_c)\n\n push!(alphas, c)\n push!(values, phi_c)\n push!(slopes, dphi_c)\n\n ic = length(alphas)\n # Check arguments here\n if satisfies_wolfe(c, phi_c, dphi_c, phi_0, dphi_0, phi_lim, delta, sigma)\n if display & SECANT2 > 0\n println(\"secant2: second c satisfied Wolfe conditions\")\n end\n return true, ic, ic\n end\n iA, iB = update!(phidphi, alphas, values, slopes, iA, iB, ic, phi_lim, display)\n end\n if display & SECANT2 > 0\n println(\"secant2 output: a = \", alphas[iA], \", b = \", alphas[iB])\n end\n return false, iA, iB\nend\n\n# HZ, stages U0-U3\n# Given a third point, pick the best two that retain the bracket\n# around the minimum (as defined by HZ, eq. 29)\n# b will be the upper bound, and a the lower bound\nfunction update!(phidphi,\n alphas,\n values,\n slopes,\n ia::Integer,\n ib::Integer,\n ic::Integer,\n phi_lim::Real,\n display::Integer = 0)\n a = alphas[ia]\n b = alphas[ib]\n T = eltype(slopes)\n zeroT = convert(T, 0)\n # Debugging (HZ, eq. 4.4):\n @assert slopes[ia] < zeroT\n @assert values[ia] <= phi_lim\n @assert slopes[ib] >= zeroT\n @assert b > a\n c = alphas[ic]\n phi_c = values[ic]\n dphi_c = slopes[ic]\n if display & UPDATE > 0\n println(\"update: ia = \", ia,\n \", a = \", a,\n \", ib = \", ib,\n \", b = \", b,\n \", c = \", c,\n \", phi_c = \", phi_c,\n \", dphi_c = \", dphi_c)\n end\n if c < a || c > b\n return ia, ib #, 0, 0 # it's out of the bracketing interval\n end\n if dphi_c >= zeroT\n return ia, ic #, 0, 0 # replace b with a closer point\n end\n # We know dphi_c < 0. However, phi may not be monotonic between a\n # and c, so check that the value is also smaller than phi_0. (It's\n # more dangerous to replace a than b, since we're leaving the\n # secure environment of alpha=0; that's why we didn't check this\n # above.)\n if phi_c <= phi_lim\n return ic, ib#, 0, 0 # replace a\n end\n # phi_c is bigger than phi_0, which implies that the minimum\n # lies between a and c. Find it via bisection.\n return bisect!(phidphi, alphas, values, slopes, ia, ic, phi_lim, display)\nend\n\n# HZ, stage U3 (with theta=0.5)\nfunction bisect!(phidphi,\n alphas::AbstractArray{T},\n values,\n slopes,\n ia::Integer,\n ib::Integer,\n phi_lim::Real,\n display::Integer = 0) where T\n gphi = convert(T, NaN)\n a = alphas[ia]\n b = alphas[ib]\n # Debugging (HZ, conditions shown following U3)\n zeroT = convert(T, 0)\n @assert slopes[ia] < zeroT\n @assert values[ia] <= phi_lim\n @assert slopes[ib] < zeroT # otherwise we wouldn't be here\n @assert values[ib] > phi_lim\n @assert b > a\n while b - a > eps(b)\n if display & BISECT > 0\n println(\"bisect: a = \", a, \", b = \", b, \", b - a = \", b - a)\n end\n d = (a + b) / convert(T, 2)\n phi_d, gphi = phidphi(d)\n @assert isfinite(phi_d) && isfinite(gphi)\n\n push!(alphas, d)\n push!(values, phi_d)\n push!(slopes, gphi)\n\n id = length(alphas)\n if gphi >= zeroT\n return ia, id # replace b, return\n end\n if phi_d <= phi_lim\n a = d # replace a, but keep bisecting until dphi_b > 0\n ia = id\n else\n b = d\n ib = id\n end\n end\n return ia, ib\nend\n© 2021 GitHub, Inc.\nTerms\nPrivacy\nSecurity\nStatus\nDocs\nContact GitHub\nPricing\nAPI\nTraining\nBlog\nAbout\nLoading complete\n\n esatta := proc( fun )\n local res, alpha;\n #res := Optimization[Minimize](\n res := Optimization[NLPSolve](\n fun(alpha),\n {alpha >= 0, alpha <= 3},\n #initialpoint={alpha=1},\n iterationlimit=50\n ):\n subs(res[2],alpha);\n end proc:\n\n doplot := proc( f_in, df_in, alpha, amax)\n local f0, df0, x, AA, BB, CC, DD;\n f0 := evalf(f_in(0));\n df0 := evalf(df_in(0));\n\n AA := plot(f_in(x),x=0..amax);\n BB := plot([[0,f0],[amax,f0+amax*rho*df0]],color=\"LimeGreen\");\n CC := plot([[0,f0],[amax,f0+amax*sigma*df0]],color=\"blue\");\n DD := plot([[alpha,f_in(alpha)]],color=\"red\",style = point);\n display(AA,BB,CC,DD);\n end;\n\n doplot2 := proc( f_in, df_in, alpha, amax, A_list, B_list )\n local i, f0, df0, x, AA, BB, CC, DD, EE;\n f0 := evalf(f_in(0));\n df0 := evalf(df_in(0));\n\n AA := plot(f_in(x),x=0..amax);\n BB := plot([[0,f0],[amax,f0+amax*rho*df0]],color=\"LimeGreen\");\n CC := plot([[0,f0],[amax,f0+amax*sigma*df0]],color=\"blue\");\n DD := plot([[alpha,f_in(alpha)]],color=\"red\",style = point);\n EE := plot([seq([[A_list[i],-i/5],[B_list[i],-i/5]],i=1..nops(A_list))],color=\"black\");\n display(AA,BB,CC,DD,EE);\n end;\n\nend module:\n", "meta": {"hexsha": "39a33e2068ce0d0cfae16b5e9acafc3cf67b41e7", "size": 20852, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple/NL-HagerZhang.mpl", "max_stars_repo_name": "ebertolazzi/NLtoolbox", "max_stars_repo_head_hexsha": "99e47bdc346f3ac7b4834f2a6b431327d00e5ab1", "max_stars_repo_licenses": ["BSD-2-Clause", "Unlicense"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-06-28T09:12:53.000Z", "max_stars_repo_stars_event_max_datetime": "2021-06-28T09:12:53.000Z", "max_issues_repo_path": "maple/NL-HagerZhang.mpl", "max_issues_repo_name": "ebertolazzi/NLtoolbox", "max_issues_repo_head_hexsha": "99e47bdc346f3ac7b4834f2a6b431327d00e5ab1", "max_issues_repo_licenses": ["BSD-2-Clause", "Unlicense"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "maple/NL-HagerZhang.mpl", "max_forks_repo_name": "ebertolazzi/NLtoolbox", "max_forks_repo_head_hexsha": "99e47bdc346f3ac7b4834f2a6b431327d00e5ab1", "max_forks_repo_licenses": ["BSD-2-Clause", "Unlicense"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 35.1043771044, "max_line_length": 158, "alphanum_fraction": 0.5537598312, "num_tokens": 6026, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8558511469672594, "lm_q2_score": 0.822189134878876, "lm_q1q2_score": 0.7036715141101048}} |
| {"text": "\nTITLE \n Invest4Scen;\n\nINDEX\n invtype := (Stock, Bond) -> (S,B);\n\nSTOCHASTIC\n\nSTAGES\n period := 1..4;\n\nSCENARIOS\n sc := 1..8;\n\nTREE\n BINARY;\n\nPROBABILITIES\n prob[sc] := ALLEQUAL;\n\nRANDOM DATA\n Returns[invtype, period, sc] := \n [Stock, 1, 1, 1.25,\n Stock, 1, 2, 1.25,\n Stock, 1, 3, 1.25,\n Stock, 1, 4, 1.25,\n Stock, 1, 5, 1.06,\n Stock, 1, 6, 1.06,\n Stock, 1, 7, 1.06,\n Stock, 1, 8, 1.06,\n Stock, 2, 1, 1.25,\n Stock, 2, 2, 1.25,\n Stock, 2, 3, 1.06,\n Stock, 2, 4, 1.06,\n Stock, 2, 5, 1.25,\n Stock, 2, 6, 1.25,\n Stock, 2, 7, 1.06,\n Stock, 2, 8, 1.06,\n Stock, 3, 1, 1.25,\n Stock, 3, 2, 1.06,\n Stock, 3, 3, 1.25,\n Stock, 3, 4, 1.06,\n Stock, 3, 5, 1.25,\n Stock, 3, 6, 1.06,\n Stock, 3, 7, 1.25,\n Stock, 3, 8, 1.06,\n Bond, 1, 1, 1.14,\n Bond, 1, 2, 1.14,\n Bond, 1, 3, 1.14,\n Bond, 1, 4, 1.14,\n Bond, 1, 5, 1.12,\n Bond, 1, 6, 1.12,\n Bond, 1, 7, 1.12,\n Bond, 1, 8, 1.12,\n Bond, 2, 1, 1.14,\n Bond, 2, 2, 1.14,\n Bond, 2, 3, 1.12,\n Bond, 2, 4, 1.12,\n Bond, 2, 5, 1.14,\n Bond, 2, 6, 1.14,\n Bond, 2, 7, 1.12,\n Bond, 2, 8, 1.12,\n Bond, 3, 1, 1.14,\n Bond, 3, 2, 1.12,\n Bond, 3, 3, 1.14,\n Bond, 3, 4, 1.12,\n Bond, 3, 5, 1.14,\n Bond, 3, 6, 1.12,\n Bond, 3, 7, 1.14,\n Bond, 3, 8, 1.12];\n\nDATA\n InitialWealth = 55;\n Goal := 80;\n SurplusReward := 1;\n ShortPenalty := 4;\n\nVARIABLES\n Invest[period<LAST(period),invtype] -> x;\n\nLASTSTAGE VARIABLES\n Shortage -> Sh;\n Excess -> Ex;\n\nMODEL\n\n MAX obj = SurplusReward*Excess - ShortPenalty*Shortage;\n\nSUBJECT TO\n\n InitInvest[period=1] -> InitInv: \n InitialWealth\n = \n SUM(invtype: Invest);\n\n InvestBal[period=2..LAST(period)-1] -> InvBal: \n SUM(invtype: Invest[period-1] * Returns[period-1])\n = \n SUM(invtype: Invest);\n\n EndInvest[period=LAST(period)] -> EndInv: \n SUM(invtype: Invest[period-1]* Returns[period-1]) + Shortage - Excess \n = \n Goal;\n\nEND", "meta": {"hexsha": "244d129ad813e61f281b182cb16064e99f2b8fb2", "size": 2156, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Stochastic/Invest4Scen.mpl", "max_stars_repo_name": "BjarniMax/mpl-models", "max_stars_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Stochastic/Invest4Scen.mpl", "max_issues_repo_name": "BjarniMax/mpl-models", "max_issues_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Stochastic/Invest4Scen.mpl", "max_forks_repo_name": "BjarniMax/mpl-models", "max_forks_repo_head_hexsha": "be22a81b3b42cdf63c933b010c1a2a9764127c98", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 20.1495327103, "max_line_length": 78, "alphanum_fraction": 0.4707792208, "num_tokens": 975, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8918110569397307, "lm_q2_score": 0.7879311956428946, "lm_q1q2_score": 0.7026857523820755}} |
| {"text": "`is_element/E/subdiv` := (p::nonnegint,n::nonnegint,m::nonnegint) -> proc(theta)\n global reason;\n local tag,src,tgt,i,t;\n tag := \"is_element/E/subdiv\";\n\n if p = 0 then\n return evalb(n = m and theta = []);\n fi;\n\n if not(type(theta,list(list(nonnegint)))) then\n reason := [tag,\"theta is not a list of lists of natural numbers\",theta];\n return false;\n fi;\n\n if nops(theta) <> p then\n reason := [tag,\"theta is not a list of length p\",theta,p];\n return false;\n fi;\n\n tgt := NULL;\n for i from 1 to p do\n if theta[i] = [] then\n reason := [tag,\"theta[i] is empty\",theta,i];\n return false;\n fi;\n t := max(op(theta[i]));\n if {op(theta[i])} <> {seq(j,j=0..t)} then\n reason := [tag,\"theta[i] does not give an epimorphism\",theta,i,t];\n return false;\n fi;\n tgt := tgt,t;\n od:\n tgt := [tgt];\n\n src := map(nops,theta) -~ 1;\n\n if src[1] <> n then\n reason := [tag,\"chain does not start with [n]\",theta,src,n];\n return false;\n fi;\n\n if tgt[p] <> m then\n reason := [tag,\"chain does not end with [m]\",theta,tgt,m];\n return false;\n fi;\n \n if [op(src),m] <> [n,op(tgt)] then\n reason := [tag,\"sources and targets do not match\",theta,src,tgt,n,m];\n return false;\n fi;\n\n return true;\nend:\n\n`is_leq/E/subdiv` := NULL;\n\n`list_elements/E/subdiv/aux` := proc(n::nonnegint,m::nonnegint)\n option remember;\n local N,M,E;\n\n N := {seq(i,i=0..n)};\n M := {seq(i,i=0..m)};\n E := `list_elements/epi`(N,M);\n E := map(f -> [seq(f[i],i=0..n)],E);\n return E;\nend:\n\n`list_elements/E/subdiv` := proc(p::nonnegint,n::nonnegint,m::nonnegint)\n option remember;\n local L,k,E0,E1;\n\n if p = 0 then\n if n = m then\n return [[]];\n else\n return [];\n fi;\n else\n L := NULL;\n for k from m to n do\n E0 := `list_elements/E/subdiv`(p-1,n,k);\n E1 := `list_elements/E/subdiv/aux`(k,m);\n L := L,seq(seq([op(e0),e1],e1 in E1),e0 in E0);\n od:\n fi;\n return [L];\nend:\n\n`random_element/E/subdiv` := (p::nonnegint,n::nonnegint,m::nonnegint) -> proc()\n local k,q,f,g;\n \n if m > n then\n return FAIL;\n fi;\n\n if p = 0 then\n if m = n then\n return [];\n else\n return FAIL;\n fi;\n elif p = 1 then\n g := `random_element/epi`({seq(j,j=0..n)},{seq(j,j=0..m)})();\n return [[seq(g[j],j=0..n)]]; \n else\n k := rand(m..n)();\n q := rand(1..p-1)();\n f := `random_element/E/subdiv`(q,n,k)();\n g := `random_element/E/subdiv`(p-q,k,m)();\n return [op(f),op(g)];\n fi;\nend:\n\n`count_elements/E/subdiv` := proc(p::nonnegint,n::nonnegint,m::nonnegint)\n option remember;\n if p = 0 then\n return `if`(n = m,1,0);\n else\n return add(`count_elements/E/subdiv`(p-1,n,k) *\n Stirling2(k+1,m+1) * (m+1)!,k=m..n);\n fi;\nend:\n\n`degrees/E/subdiv` := (p,n,m) -> (theta) ->\n [op(map(nops,theta) -~ 1),m];\n\n######################################################################\n\n`is_element/EE/subdiv` := (p::nonnegint,n::nonnegint) -> proc(theta)\n global reason;\n local tag,src,tgt,i,m,t,b;\n tag := \"is_element/EE/subdiv\";\n\n if p = 0 then\n if theta = [] then\n return true;\n else\n reason := [tag,\"for p=0 the only element is []\",theta];\n return phi;\n fi;\n fi;\n\n if not(type(theta,list(list(nonnegint)))) then\n reason := [tag,\"theta is not a list of lists of natural numbers\",theta];\n return false;\n fi;\n\n if nops(theta) <> p then\n reason := [tag,\"theta is not a list of length p\",theta,p];\n return false;\n fi;\n\n if theta[p] = [] then\n reason := [tag,\"theta[p] = []\",theta,p];\n return false;\n fi;\n\n m := max(op(theta[p]));\n \n b := `is_element/E/subdiv`(p,n,m)(theta);\n if not(b) then\n reason := [tag,\"is_element/E/subdiv failed\",m,reason];\n return false;\n fi;\n\n return true;\nend:\n\n`is_leq/EE/subdiv` := NULL;\n\n`list_elements/EE/subdiv` := proc(p::nonnegint,n::nonnegint)\n option remember;\n [seq(op(`list_elements/E/subdiv`(p,n,m)),m=0..n)];\nend:\n\n`random_element/EE/subdiv` := (p::nonnegint,n::nonnegint) -> proc()\n local m;\n m := rand(0..n)();\n return `random_element/E/subdiv`(p,n,m)();\nend:\n\n`count_elements/EE/subdiv` := proc(p::nonnegint,n::nonnegint)\n add(`count_elements/E/subdiv`(p,n,m),m=0..n);\nend:\n\n`find_count_coeffs/EE/subdiv` := proc(n)\n local E,a,p,k;\n E := [seq(`count_elements/EE/subdiv`(p,n) - add((-1)^(n+k)*a[n,k]*((k+1)!)^p,k=0..n),p=1..n+5)];\n return solve(E);\nend:\n\n`degrees/EE/subdiv` := (p,n) -> (theta) ->\n [op(map(nops,theta) -~ 1),max(op(theta[p]))];\n\n######################################################################\n\n`is_element/threads/subdiv` := (p::nonnegint,n::nonnegint) -> (theta) -> proc(i)\n global reason;\n local tag,k,m;\n\n tag := \"is_element/threads/subdiv\";\n \n if not(type(i,list(nonnegint)) and nops(i) = p+1) then\n reason := [tag,\"i is not a list of p+1 natural numbers\",i,p];\n return false;\n fi;\n\n k := `degrees/EE/subdiv`(p,n)(theta);\n \n for m from 0 to p do\n if i[m+1] > k[m+1] then\n return false;\n fi;\n \n if m < p and theta[m+1][i[m+1]+1] > i[m+2] then\n return false;\n fi;\n od:\n\n return true;\nend:\n\n`is_leq/threads/subdiv` := NULL;\n\n`list_elements/threads/subdiv` := (p::nonnegint,n::nonnegint) -> proc(theta)\n local i,k,m,phi,L,M;\n\n if p = 0 then\n return [seq([i],i=0..n)];\n else\n m := max(op(theta[p]));\n phi := [op(1..p-1,theta)];\n L := `list_elements/threads/subdiv`(p-1,n)(phi);\n M := NULL;\n for i in L do\n k := theta[p][i[p]+1];\n M := M,seq([op(i),j],j=k..m);\n od:\n return [M];\n fi;\nend:\n\n`random_element/threads/subdiv` := (p::nonnegint,n::nonnegint) -> (theta) -> proc()\n local i,j,k,m0,m1;\n\n k := `degrees/EE/subdiv`(p,n)(theta);\n i := [rand(0..n)()];\n for j from 1 to p do\n m0 := theta[j][i[j]+1];\n m1 := k[j+1];\n i := [op(i),rand(m0..m1)()];\n od;\n \n return i;\nend:\n\n`count_elements/threads/subdiv` := NULL;\n\n`mu/threads/subdiv` := (p::nonnegint,n::nonnegint) -> (theta) -> proc(i)\n local k,u,m;\n \n k := `degrees/EE/subdiv`(p,n)(theta);\n\n u := k[p+1]+1;\n for m from 0 to p-1 do\n u := u * nops(select(j -> (j <= i[m+2]),theta[m+1]));\n od:\n\n return u;\nend:\n\n`xi/EE/subdiv` := (p::nonnegint,n::nonnegint) -> proc(theta)\n local x,II,i;\n \n if p = 0 then\n return [1$(n+1)]/~(n+1);\n fi;\n \n x := table([seq(i=0,i=0..n)]);\n II := `list_elements/threads/subdiv`(p,n)(theta);\n for i in II do\n x[i[1]] := x[i[1]] + 1/`mu/threads/subdiv`(p,n)(theta)(i);\n od:\n return [seq(x[i],i=0..n)];\nend:\n\n######################################################################\n# F(p,n) is the set of vertices in the (p+1)-fold barycentric\n# subdivision of the n-simplex\n\n`is_element/FF/subdiv` := (p::nonnegint,n::nonnegint) -> proc(alpha_theta)\n local alpha,theta,m;\n\n if not(type(alpha_theta,list) and nops(alpha_theta) = 2) then\n return false;\n fi;\n\n alpha,theta := op(alpha_theta);\n\n if not(type(alpha,list(nonnegint)) and nops(alpha) > 0) then\n return false;\n fi;\n\n m := nops(alpha) - 1;\n\n if not(`is_element/simplicial_mono_alt`(m,n)(alpha)) then\n return false;\n fi;\n\n if not(`is_element/EE/subdiv`(p,m)(theta)) then\n return false;\n fi;\n\n return true; \nend:\n\n`list_elements/FF/subdiv` := proc(p,n)\n local L,N,m,alpha,theta;\n \n L := NULL:\n N := [seq(i,i=0..n)];\n for alpha in combinat[powerset](N) do\n m := nops(alpha) - 1;\n if m >= 0 then\n L := L,seq([alpha,theta],theta in `list_elements/EE/subdiv`(p,m));\n fi;\n od:\n\n return [L];\nend:\n\n`random_element/FF/subdiv` := (p,n) -> proc()\n local d,m,alpha,theta;\n \n d := rand(1..n)();\n alpha := `random_subset_of`({seq(i,i=0..n)},d);\n alpha := sort([op(alpha)]);\n m := nops(alpha) - 1;\n theta := `random_element/EE/subdiv`(p,m)();\n return [alpha,theta];\nend:\n\n# This function is not quite right. It seems to find a correct morphism\n# when one exists, but it claims that morphisms exist when that is not the case.\n\n`find_morphism/FF/subdiv` := (p::nonnegint,n::nonnegint) -> proc(alpha_theta0,alpha_theta1)\n local alpha0,alpha1,theta0,theta1,m0,m1,k0,k1,f,h,i,j,u,v,xi,V,W,G,H;\n\n alpha0,theta0 := op(alpha_theta0);\n alpha1,theta1 := op(alpha_theta1);\n m0 := nops(alpha0) - 1;\n m1 := nops(alpha1) - 1;\n k0 := `degrees/EE/subdiv`(p,m0)(theta0);\n k1 := `degrees/EE/subdiv`(p,m1)(theta1);\n\n f := table([seq(i=FAIL,i=0..n)]);\n for i from 0 to m1 do f[alpha1[i+1]] := i; od;\n xi := [[seq(f[alpha0[i+1]],i=0..m0)]];\n if member(FAIL,xi[1]) then return FAIL; fi;\n for j from 0 to p-1 do\n V := {seq(w,w=0..k0[j+1])};\n W := {seq(w,w=0..k0[j+1+1])};\n G := [seq(select(v -> theta0[j+1][v+1] <= w,V),w in W)];\n H := map(A -> map(v -> theta1[j+1][xi[j+1][v+1]+1],A),G);\n h := map(max,H);\n if h <> sort([op({op(h)})]) then\n return false;\n fi;\n xi := [op(xi),h];\n od;\n\n return xi;\nend:\n\n`is_leq/FF/subdiv` := (p::nonnegint,n::nonnegint) -> proc(alpha_theta0,alpha_theta1)\n evalb(`find_morphism/FF/subdiv`(p,n)(alpha_theta0,alpha_theta1) <> FAIL);\nend:\n\n`xi/FF/subdiv` := (p::nonnegint,n::nonnegint) -> proc(alpha_theta)\n local alpha,theta,i,m,x,y,yt;\n \n alpha,theta := op(alpha_theta);\n m := nops(alpha) - 1;\n x := `xi/EE/subdiv`(p,m)(theta);\n yt := table([seq(i=0,i=0..n)]);\n for i from 0 to m do\n yt[alpha[i+1]] := x[i+1];\n od:\n y := [seq(yt[i],i=0..n)];\n return y;\nend:\n\n# Every vertex of the (p+1)-fold subdivision is the barycentre of\n# a d-simplex of the p-fold subdivision for some d. This function\n# returns d.\n\n`rank/FF/subdiv` := (p::nonnegint,n::nonnegint) -> proc(alpha_theta)\n local alpha,theta,m;\n \n alpha,theta := op(alpha_theta);\n m := nops(alpha) - 1;\n \n if p = 0 then\n return m;\n else\n return max(op(theta[p]));\n fi;\nend:\n\n######################################################################\n# Here zeta is a strictly increasing map [j] -> [k] and theta is an\n# unordered surjective map [m] -> [k]. The function returns a triple\n# [n,beta,phi] where beta : [n] -> [m] is strictly increasing and\n# phi : [n] -> [j] is surjective. In an appropriate context we will\n# have alpha^*([x,theta]) = [beta^*(x),phi].\n\n`rewrite/epi/subdiv` := proc(zeta,theta)\n local i,j,m,J,M,k1,N,n,xi,phi;\n \n j := nops(zeta) - 1;\n m := nops(theta) - 1;\n J := {seq(j0,j0=0..j)};\n M := {seq(m0,m0=0..m)};\n \n k1 := op(-1,zeta);\n N := select(m0 -> theta[m0+1] <= k1,M);\n n := nops(N) - 1;\n xi := sort([op(N)]);\n phi := NULL;\n \n for i from 0 to n do\n phi := phi,min(select(j0 -> zeta[j0+1] >= theta[xi[i+1]+1],J));\n od:\n phi := [phi];\n\n return [n,xi,phi];\nend:\n\n`rewrite/FF/subdiv` := (p,n) -> (zeta) -> proc(alpha_theta)\n local alpha,theta,k0,m,xi,phi,alpha1,theta1;\n alpha,theta := op(alpha_theta);\n \n if p = 0 then\n k0 := nops(zeta) - 1;\n return [[seq(alpha[zeta[i+1]+1],i=0..k0)],[]];\n else \n k0 := nops(zeta) - 1;\n m,xi,phi := op(`rewrite/epi/subdiv`(zeta,theta[p]));\n alpha1,theta1 := op(`rewrite/FF/subdiv`(p-1,n)(xi)([alpha,[op(1..-2,theta)]]));\n return [alpha1,[op(theta1),phi]];\n fi;\nend:\n\n`rewrite_aux/FF/subdiv` := (p,n) -> (zeta) -> proc(alpha_theta)\n local alpha,theta,k0,m,xi,phi,xi1,alpha1,theta1;\n alpha,theta := op(alpha_theta);\n \n if p = 0 then\n k0 := nops(zeta) - 1;\n return [[zeta],[seq(alpha[zeta[i+1]+1],i=0..k0)],[]];\n else \n k0 := nops(zeta) - 1;\n m,xi,phi := op(`rewrite/epi/subdiv`(zeta,theta[p]));\n xi1,alpha1,theta1 := op(`rewrite_aux/FF/subdiv`(p-1,n)(xi)([alpha,[op(1..-2,theta)]]));\n return [[op(xi1),zeta],alpha1,[op(theta1),phi]];\n fi;\nend:\n\n`vertices/FF/subdiv` := (p,n) -> proc(alpha_theta)\n local r;\n r := `rank/FF/subdiv`(p,n)(alpha_theta);\n return [seq(`rewrite/FF/subdiv`(p,n)([i])(alpha_theta),i=0..r)];\nend:\n\n", "meta": {"hexsha": "d6a93cce68b5a56e1827c0ed42069673cb1d1dcc", "size": 11149, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/subdiv.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/subdiv.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/subdiv.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 23.4715789474, "max_line_length": 97, "alphanum_fraction": 0.5799623285, "num_tokens": 3972, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8615382200964035, "lm_q2_score": 0.8152324826183822, "lm_q1q2_score": 0.7023539420398132}} |
| {"text": "with(Groebner):\nF:={2*x1 + 5*x2 + x3,2*x1 + x2 + x3,9*x1 + 6*x2 + x3,x1^2 + x2^2 + x3^2 - 1}:\nm_ord:=tdeg(x1,x2,x3):\nG:=Basis(F,m_ord):\nNormalSet(G,m_ord)[1]\n", "meta": {"hexsha": "ec4a5e4030d4057a57257867f9596c448490e4c9", "size": 158, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "matlab/tmp.mpl", "max_stars_repo_name": "marcusvaltonen/alggeompoly", "max_stars_repo_head_hexsha": "9cd9b7dcd278174a29d118e13ab4fdba31ab576f", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-08-18T22:05:47.000Z", "max_stars_repo_stars_event_max_datetime": "2021-08-18T22:05:47.000Z", "max_issues_repo_path": "matlab/tmp.mpl", "max_issues_repo_name": "marcusvaltonen/alggeompoly", "max_issues_repo_head_hexsha": "9cd9b7dcd278174a29d118e13ab4fdba31ab576f", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "matlab/tmp.mpl", "max_forks_repo_name": "marcusvaltonen/alggeompoly", "max_forks_repo_head_hexsha": "9cd9b7dcd278174a29d118e13ab4fdba31ab576f", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2020-09-15T17:36:06.000Z", "max_forks_repo_forks_event_max_datetime": "2020-09-15T17:36:06.000Z", "avg_line_length": 26.3333333333, "max_line_length": 77, "alphanum_fraction": 0.5632911392, "num_tokens": 89, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9511422199928904, "lm_q2_score": 0.7371581684030623, "lm_q1q2_score": 0.7011422567807816}} |
| {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* nop scaling *)\ns_scaling_0 := s -> s:\n\n(* original scaling of Heyd *)\nstrans := 8.3:\nsmax := 8.572844:\nsconst := 18.79622316:\ns_scaling_1 := s -> my_piecewise3(\n s < strans, s,\n smax - sconst/s^2\n):\n\n(* first version of the scaling by TM Henderson, apparently used by Gaussian *)\ns_scaling_2 := s -> my_piecewise3(\n s < 1, s,\n my_piecewise3(s > 15, smax, m_max(m_min(s, 15), 1) - log(1 + exp(m_max(m_min(s, 15), 1) - smax)))\n):\n\n(* second version of the scaling by TM Henderson *)\ns_scaling_3 := s -> s - (1 - exp(-s))*log(1 + exp(s - smax)):\n\n(* appendix of JCP 128, 194105 (2008) *)\ns_p := [0.615482, 1.136921, -0.449154, 0.0175739*8.572844]:\ns_q := [1.229195, -0.0269253, 0.313417, -0.0508314, 0.0175739]:\n\ns_scaling_4 := s->\n s*(1 + s^3*add(s_p[i]*s^i, i=1..4))/(1 + s^3*add(s_q[i]*s^i, i=1..5)):\n", "meta": {"hexsha": "9be49e0fe12d87412bb6a393737a6f1dbea3b999", "size": 1055, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/scaling.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/scaling.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/scaling.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 29.3055555556, "max_line_length": 99, "alphanum_fraction": 0.6236966825, "num_tokens": 410, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9111797124237605, "lm_q2_score": 0.7690802476562641, "lm_q1q2_score": 0.7007703188902292}} |
| {"text": "`is_element/nat_partitions` := (total::nonnegint,num_parts::nonnegint) -> proc(u)\n return type(u,list(nonnegint)) and nops(u) = num_parts and `+`(op(u)) = total;\nend:\n\n`is_leq/nat_partitions` := NULL;\n\n`list_elements/nat_partitions` := proc(total,num_parts)\n local L,M,i,j,m,u;\n\n if num_parts = 0 then \n if total = 0 then \n return [[]];\n else\n return [];\n fi;\n fi;\n\n if num_parts = 1 then return [[total]]; fi;\n\n L := [seq([i],i=0..total)];\n for j from 2 to num_parts-1 do\n M := NULL;\n for u in L do\n m := total - `+`(op(u));\n M := M,seq([op(u),j],j=0..m);\n od:\n L := [M];\n od:\n L := map(u -> [op(u),total - `+`(op(u))],L);\n\n return L;\nend:\n\n`count_elements/nat_partitions` := (total::nonnegint,num_parts::nonnegint) ->\n binomial(total+num_parts-1,total);\n\n`random_element/nat_partitions` := (total::nonnegint,num_parts::nonnegint) -> proc()\n local X,i;\n if total = 0 and num_parts = 0 then\n return [];\n fi;\n\n X := random_subset_of({seq(i,i=1..total+num_parts-1)},num_parts-1);\n X := [0,op(sort(X)),total+num_parts];\n return [seq(X[i+1]-X[i]-1,i=1..num_parts)];\nend:\n\n`is_element/pos_partitions` := (total::nonnegint,num_parts::nonnegint) -> proc(u)\n return type(u,list(posint)) and nops(u) = num_parts and `+`(op(u)) = total;\nend:\n\n`is_leq/pos_partitions` := NULL;\n\n`random_element/pos_partitions` := (total::nonnegint,num_parts::nonnegint) -> proc()\n local p;\n if num_parts > total then return FAIL; fi;\n p := `random_element/nat_partitions`(total - num_parts,num_parts)();\n return p +~ 1;\nend:\n\n`list_elements/pos_partitions` := proc(total,num_parts)\n map(u -> u +~ 1,`list_elements/nat_partitions`(total - num_parts,num_parts));\nend:\n\n`count_elements/pos_partitions` := (total::nonnegint,num_parts::nonnegint) ->\n binomial(total-1,num_parts-1);\n\n\n\n", "meta": {"hexsha": "b07b6c78ebca264f4f15d137775558fb039ec8c2", "size": 1768, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/nat_partitions.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/nat_partitions.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/nat_partitions.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 25.2571428571, "max_line_length": 84, "alphanum_fraction": 0.6549773756, "num_tokens": 565, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8539127641048444, "lm_q2_score": 0.8198933359135361, "lm_q1q2_score": 0.7001173847410693}} |
|
|
