final
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@ -50,6 +50,15 @@
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*
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* gcc -o main -lm Projekt2_Knuettel_Daniel.c lib/lrmp.c lib/vorrueckwaertsub.c
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*
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*
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* Preprocessor flags:
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*
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* - DEBUG turns on some more output.
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* - NOCRAPMODE enables a reusable interface which is not conformous to the
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* specification given but allowes to used the algorithms with arbitrary
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* functions. Also this adds the functions `write_error_(newton|bisek)`.
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* - ALLOW_NEGATGIVE_ERRORS allows negative errors which might be interesting.
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*
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*/
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@ -88,7 +97,8 @@ int bisec_one(double * x_minus
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* \param eps Used precision.
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* \param Nmax Stop searching after Nmax iterations.
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* \param flag Will be set to 0xf000, if the goal has been reached,
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* to 0xf001, if Nmax has been reached.
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* to 0xf001, if Nmax has been reached
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* , to 0xf004 if f(a)*f(b) >= 0.
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* Any other value indicates an unknown error.
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* \param file The function will not use this parameter, it is there just
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* for backwards compability.
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@ -104,6 +114,7 @@ double bisek(double (*f)(double)
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, int * flag
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, FILE * file);
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#ifdef NOCRAPMODE
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/*
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* \brief Calculate f(x) < eps using bisek and write the results to file.
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*
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@ -113,12 +124,15 @@ double bisek(double (*f)(double)
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* \param eps Used precision.
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* \param Nmax Stop searching after Nmax iterations.
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* \param flag Will be set to 0xf000, if the goal has been reached,
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* to 0xf001, if Nmax has been reached.
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* to 0xf001, if Nmax has been reached
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* , to 0xf004 if f(a)*f(b) >= 0.
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* Any other value indicates an unknown error.
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* \param file Write ``Nmax,error\n`` to this file.
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* \param x0 The real result for bisek.
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*
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* \return The result of the bisection
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* */
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int write_error_bisek(double (*f)(double)
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double write_error_bisek(double (*f)(double)
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, double a
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, double b
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, double eps
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@ -126,6 +140,7 @@ int write_error_bisek(double (*f)(double)
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, int * flag
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, FILE * file
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, double x0);
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#endif
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@ -155,6 +170,7 @@ double newton(double x0
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, FILE * file);
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#ifdef NOCRAPMODE
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/*
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* \brief Calculate f(x) < eps or a minimum of f. And write the results to file
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*
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@ -181,6 +197,7 @@ double write_error_newton(double x0
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, int * flag
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, FILE * file
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, double x1);
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#endif
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/*
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* \brief Calculate one step of the newton iteration.
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@ -282,6 +299,7 @@ double dg2(double x);
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void g(double * x, double * y, int N);
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void dg(double * x, double ** y, int N);
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int main(void)
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{
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@ -289,41 +307,57 @@ int main(void)
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int flag;
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double result;
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// // Calculate the bisection of g1.
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// for(i = 1, j = 0; i < 100 ;i += 1, j++)
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// {
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// write_error_bisek(g1, -2.5, -100, 1e-7, i, &flag, stdout, -6);
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// }
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// printf("XXX\n");
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// fprintf(stderr, "wrote %d lines for g1 to /dev/stdout\n", j);
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//
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// // Calculate the bisection of g2.
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// // Note that the output of this will be basically crap, because
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// // g2 does not meet the requirements for a bisection.
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// for(i = 1, j = 0; i < 100 ;i += 1, j++)
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// {
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// write_error_bisek(g2, -2.5, -100, 1e-7, i, &flag, stdout, -6);
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// }
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// printf("XXX\n");
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// fprintf(stderr, "wrote %d lines for g2 to /dev/stdout\n", j);
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//
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// // Calculate the newton iteration of g1.
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// for(i = 1, j = 0; i < 100 ;i += 1, j++)
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// {
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// write_error_newton(-100, g1, dg1, 1e-7, i, &flag, stdout, -6);
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// }
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// printf("XXX\n");
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// fprintf(stderr, "wrote %d lines for g1 to /dev/stdout\n", j);
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//
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// // Calculate the newton iteration of g2.
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// // Note that the output of this will be basically crap, because
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// // g2 does not meet the requirements for the newton iteration.
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// for(i = 1, j = 0; i < 100 ;i += 1, j++)
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// {
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// write_error_newton(-100, g2, dg1, 1e-7, i, &flag, stdout, -6);
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// }
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// printf("XXX\n");
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// fprintf(stderr, "wrote %d lines for g2 to /dev/stdout\n", j);
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// Calculate the bisection of g1.
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for(i = 1, j = 0; i < 100 ;i += 1, j++)
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{
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#ifdef NOCRAPMODE
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write_error_bisek(g1, -2.5, -100, 1e-7, i, &flag, stdout, -6);
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#else
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bisek(g1, -2.5, -100, 1e-7, i, &flag, stdout);
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#endif
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}
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printf("XXX\n");
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fprintf(stderr, "wrote %d lines for g1 to /dev/stdout\n", j);
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// Calculate the bisection of g2.
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// Note that the output of this will be basically crap, because
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// g2 does not meet the requirements for a bisection.
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for(i = 1, j = 0; i < 100 ;i += 1, j++)
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{
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#ifdef NOCRAPMODE
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write_error_bisek(g2, -2.5, -100, 1e-7, i, &flag, stdout, -6);
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#else
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bisek(g2, -2.5, -100, 1e-7, i, &flag, stdout);
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#endif
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}
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printf("XXX\n");
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fprintf(stderr, "wrote %d lines for g2 to /dev/stdout\n", j);
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// Calculate the newton iteration of g1.
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for(i = 1, j = 0; i < 100 ;i += 1, j++)
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{
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#ifdef NOCRAPMODE
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write_error_newton(-100, g1, dg1, 1e-7, i, &flag, stdout, -6);
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#else
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newton(-100, g1, dg1, 1e-7, i, &flag, stdout);
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#endif
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}
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printf("XXX\n");
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fprintf(stderr, "wrote %d lines for g1 to /dev/stdout\n", j);
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// Calculate the newton iteration of g2.
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// Note that the output of this will be basically crap, because
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// g2 does not meet the requirements for the newton iteration.
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for(i = 1, j = 0; i < 100 ;i += 1, j++)
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{
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#ifdef NOCRAPMODE
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write_error_newton(-100, g2, dg2, 1e-7, i, &flag, stdout, -6);
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#else
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newton(-100, g2, dg2, 1e-7, i, &flag, stdout);
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#endif
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}
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printf("XXX\n");
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fprintf(stderr, "wrote %d lines for g2 to /dev/stdout\n", j);
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// Calculate the multi dimensional newton iteration
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@ -433,7 +467,13 @@ int bisec_one(double * x_minus
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return 0;
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}
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double bisek(double (*f)(double)
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double
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#ifdef NOCRAPMODE
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bisek
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#else
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__inline_bisek
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#endif
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(double (*f)(double)
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, double a
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, double b
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, double eps
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@ -441,6 +481,11 @@ double bisek(double (*f)(double)
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, int * flag
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, FILE * file)
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{
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if(f(a)*f(b) >= 0)
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{
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*flag = 0xf004;
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return 0;
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}
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double x_minus = a
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, x_plus = b;
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if(a > b)
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@ -466,23 +511,45 @@ double bisek(double (*f)(double)
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return x_minus;
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}
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int write_error_bisek(double (*f)(double)
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double
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#ifdef NOCRAPMODE
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write_error_bisek
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#else
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bisek
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#endif
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(double (*f)(double)
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, double a
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, double b
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, double eps
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, int Nmax
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, int * flag
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, FILE * file
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, double x0)
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#ifdef NOCRAPMODE
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, double x0
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#endif
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)
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{
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#ifndef NOCRAPMODE
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double x0 = -6;
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#endif
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double result
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, error;
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result = bisek(f, a, b, eps, Nmax, flag, file);
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if(*flag & 0xff)
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result =
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#ifdef NOCRAPMODE
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bisek
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#else
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__inline_bisek
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#endif
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(f, a, b, eps, Nmax, flag, file);
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if(*flag & 0x0f == 0x01)
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{
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fprintf(stderr, "WARNING: bisek(..., eps = %.10e, Nmax = %d, ...) hit Nmax.\n", eps, Nmax);
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}
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if(*flag & 0x0f == 0x04)
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{
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fprintf(stderr, "WARNING: bisek(..., eps = %.10e, Nmax = %d, ...) conditions failed.\n", eps, Nmax);
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}
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if(!(*flag & 0xff00))
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{
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fprintf(stderr, "WARNING: bisek flag is invalid.\n");
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@ -494,12 +561,15 @@ int write_error_bisek(double (*f)(double)
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// FIXME:
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// Shold we allow negative errors? It is mathematically incorrect but
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// more interesting.
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// if(error < 0)
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// {
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// error *= -1;
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// }
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#ifndef ALLOW_NEGATGIVE_ERRORS
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if(error < 0)
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{
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error *= -1;
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}
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#endif
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return fprintf(file, "%d,%.10e\n", Nmax, error);
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fprintf(file, "%d,%.10e\n", Nmax, error);
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return result;
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}
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@ -511,7 +581,9 @@ int newton_one(double * x
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double y, yd;
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y = f(*x);
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yd = df(*x);
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#ifdef DEBUG
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fprintf(stderr, "f(%.4e) -> %.4e; df(%.4e) -> %.4e\n", *x, y, *x, yd);
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#endif
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if(abs(y) < eps)
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{
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return 0xe000;
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@ -522,12 +594,20 @@ int newton_one(double * x
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}
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*x -= y / yd;
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#ifdef DEBUG
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fprintf(stderr, "set new x: %.4e\n", *x);
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#endif
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return 0;
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}
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double newton(double x0
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double
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#ifdef NOCRAPMODE
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newton
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#else
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__inline_newton
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#endif
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(double x0
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, double (*f)(double)
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, double (*df)(double)
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, double eps
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@ -556,18 +636,36 @@ double newton(double x0
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}
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double write_error_newton(double x0
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double
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#ifdef NOCRAPMODE
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write_error_newton
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#else
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newton
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#endif
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(double x0
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, double (*f)(double)
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, double (*df)(double)
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, double eps
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, int Nmax
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, int * flag
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, FILE * file
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, double x1)
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#ifdef NOCRAPMODE
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, double x1
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#endif
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)
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{
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#ifndef NOCRAPMODE
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double x1 = -6;
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#endif
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double result, error;
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result = newton(x0, f, df, eps, Nmax, flag, file);
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result =
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#ifdef NOCRAPMODE
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newton
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#else
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__inline_newton
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#endif
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(x0, f, df, eps, Nmax, flag, file);
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if(*flag & 0xff)
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{
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@ -584,12 +682,15 @@ double write_error_newton(double x0
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// FIXME:
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// Shold we allow negative errors? It is mathematically incorrect but
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// more interesting.
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// if(error < 0)
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// {
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// error *= -1;
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// }
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#ifndef ALLOW_NEGATGIVE_ERRORS
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if(error < 0)
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{
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error *= -1;
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}
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#endif
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return fprintf(file, "%d,%.10e\n", Nmax, error);
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fprintf(file, "%d,%.10e\n", Nmax, error);
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return result;
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}
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int newton_mult(int N
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