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/*
* Example code for libmps
*
* This code computes the zeros of the secular equation
*
* S(x) = 1 / (x - 2) + 3 / (x - 4) + 5 / (x - 6) - 1
*
* using its representation as floating point, high precision
* floating point, and rational coefficients.
*
* Can be compiled with:
* gcc -o secular -lm -lgmp -lmps secular.c
*
* Author: Leonardo Robol <leonardo.robol@unipi.it>
*/
#include <mps/mps.h>
#include <stdlib.h>
#include <stdio.h>
#include <gmp.h>
#include <string.h>
int
main (int argc, char **argv)
{
mps_context * ctx = NULL;
int i;
long wp = 128;
cplx_t *af = NULL, *bf = NULL;
mpc_t *am = NULL, *bm = NULL;
mpq_t *aqr = NULL, *bqr = NULL;
mpq_t qzero;
cplx_t *roots = NULL;
mpc_t *mroots = NULL;
mps_secular_equation * p = NULL;
/* First version: floating point coefficients. */
printf("== Computing the roots using floating point coefficients \n");
af = cplx_valloc(3);
bf = cplx_valloc(3);
for (i = 0; i < 3; i++) {
cplx_set_d(af[i], 2.0 * i + 1, 0.0);
cplx_set_d(bf[i], 2.0 * i + 2.0, 0.0);
}
ctx = mps_context_new();
p = mps_secular_equation_new (ctx, af, bf, 3);
mps_context_set_input_poly (ctx, MPS_POLYNOMIAL (p));
mps_mpsolve(ctx);
mps_context_get_roots_d (ctx, &roots, NULL);
for (i = 0; i < 3; i++) {
printf("Root %d: %f + %f I\n", i, cplx_Re(roots[i]), cplx_Im(roots[i]));
}
free (roots);
mps_polynomial_free (ctx, MPS_POLYNOMIAL (p));
mps_context_free(ctx);
free(af);
free(bf);
/* Version 2: higher precision coefficients and approximations */
printf("\n\n== Computing the roots using multiprecision floating-point coefficients (asking 40 digits)\n");
am = mpc_valloc(3);
bm = mpc_valloc(3);
for (i = 0; i < 3; i++) {
mpc_init2(am[i], wp);
mpc_set_ui(am[i], 2U * i + 1U, 0U);
mpc_init2(bm[i], wp);
mpc_set_ui(bm[i], 2U * i + 2U, 0U);
}
ctx = mps_context_new();
p = mps_secular_equation_new_raw (ctx, 3);
for (i = 0; i < 3; i++) {
mps_secular_equation_set_coefficient_f (ctx, p, i, am[i], bm[i]);
}
mps_context_set_input_poly (ctx, MPS_POLYNOMIAL (p));
mps_context_set_output_goal (ctx, MPS_OUTPUT_GOAL_APPROXIMATE);
mps_context_set_output_prec (ctx, 40);
mps_mpsolve(ctx);
mps_context_get_roots_m (ctx, &mroots, NULL);
for (i = 0; i < 3; i++) {
printf("Root %d: ", i);
mpc_out_str(stdout, 10, wp, mroots[i]);
printf("\n");
mpc_clear(mroots[i]);
mpc_clear(am[i]);
mpc_clear(bm[i]);
}
free (mroots); mroots = NULL;
mps_polynomial_free (ctx, MPS_POLYNOMIAL (p));
mps_context_free(ctx);
free(am);
free(bm);
/* Version 3: higher precision coefficients and approximations */
printf("\n\n== Computing the roots using rational coefficients (asking 240 digits)\n");
aqr = mpq_valloc(3);
bqr = mpq_valloc(3);
mpq_init(qzero);
mpq_set_ui (qzero, 0U, 1U);
for (i = 0; i < 3; i++) {
mpq_init(aqr[i]);
mpq_set_ui(aqr[i], 2U * i + 1U, 1U);
mpq_init(bqr[i]);
mpq_set_ui(bqr[i], 2U * i + 2U, 1U);
}
ctx = mps_context_new();
p = mps_secular_equation_new_raw (ctx, 3);
for (i = 0; i < 3; i++) {
mps_secular_equation_set_coefficient_q (ctx, p, i, aqr[i], qzero, bqr[i], qzero);
}
mpq_clear(qzero);
mps_context_set_input_poly (ctx, MPS_POLYNOMIAL (p));
mps_context_set_output_goal (ctx, MPS_OUTPUT_GOAL_APPROXIMATE);
mps_context_set_output_prec (ctx, 240);
mps_mpsolve(ctx);
mps_context_get_roots_m (ctx, &mroots, NULL);
for (i = 0; i < 3; i++) {
printf("Root %d: ", i);
mpc_out_str(stdout, 10, wp, mroots[i]);
printf("\n");
mpc_clear(mroots[i]);
mpq_clear(aqr[i]);
mpq_clear(bqr[i]);
}
free (mroots);
mps_polynomial_free (ctx, MPS_POLYNOMIAL (p));
mps_context_free(ctx);
free(aqr);
free(bqr);
return EXIT_SUCCESS;
}
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