| /*--------------------------------*- C++ -*----------------------------------*\ |
| ========= | |
| \\ / F ield | OpenFOAM: The Open Source CFD Toolbox |
| \\ / O peration | Website: https://openfoam.org |
| \\ / A nd | Version: dev |
| \\/ M anipulation | |
| \*---------------------------------------------------------------------------*/ |
| FoamFile |
| { |
| format ascii; |
| class dictionary; |
| object testCalcNewton; |
| } |
| // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // |
| |
| // Find the root of f(x) = x + B*x/sqrt(1 + sqr(x)) - A |
| // using Newton-Raphson iteration |
|
|
| A 1; |
| B 1; |
|
|
| x |
| |
| // Lookup the coefficients |
| const scalar A = $A; |
| const scalar B = $B; |
|
|
| // Initial guess for x |
| scalar x = 0; |
|
|
| scalar x0 = x; |
|
|
| do |
| { |
| // Store the previous iteration x for the convergence check |
| x0 = x; |
|
|
| // Temporary sub-function evaluations |
| const scalar f1 = 1 + sqr(x); |
| const scalar f2 = sqrt(f1); |
|
|
| // Evaluate the function |
| const scalar f = x + B*x/f2 - A; |
|
|
| // Evaluate the derivative |
| const scalar df = 1 + B/(f1*f2); |
|
|
| // Update x |
| x = x0 - f/df; |
|
|
| // Test for convergence |
| } while (mag(x - x0) > 1e-6); |
|
|
| os << x; |
| |
|
|
|
|
| // Write a x-y data for plotting with |
| // gnuplot -e 'plot "fx.xy" us 1:2 title "f(x)" with lines; pause mouse close' |
| x0 -2; // Start x |
| xn 2; // End x |
| n 101; // Number of x increments |
|
|
| y |
| { |
| code |
| |
| // Lookup the coefficients |
| const scalar A = $A; |
| const scalar B = $B; |
|
|
| const scalar x0 = $x0; |
| const scalar xn = $xn; |
| const int n = $n; |
|
|
| const scalar deltax = (xn - x0)/(n - 1); |
|
|
| Field<scalar> x(n); |
| Field<scalar> fx(n); |
|
|
| forAll(x, i) |
| { |
| x[i] = x0 + i*deltax; |
| fx[i] = x[i] + B*x[i]/sqrt(1 + sqr(x[i])) - A; |
| } |
|
|
| // Write the x-y data |
| setWriter::New("raw")->write |
| ( |
| ".", |
| "fx", |
| coordSet(true,"x", x), |
| "f(x)", |
| fx |
| ); |
| |
|
|
| codeInclude |
| |
| |
| |
|
|
| codeOptions |
| |
| -I$(LIB_SRC)/sampling/lnInclude |
| |
|
|
| codeLibs |
| |
| -lsampling |
| |
| }; |
|
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| |
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|
| // ************************************************************************* // |
|
|
