Merge branch 'beyn_rework'
Former-commit-id: 3366b1421056a2ac097b79f62bfbccd82d87de1b
This commit is contained in:
Marek Nečada
commit
d79a35110c
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@ -12,7 +12,7 @@ add_library (qpms SHARED translations.c tmatrices.c vecprint.c vswf.c wigner.c e
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ewaldsf.c pointgroups.c latticegens.c
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lattices2d.c gaunt.c error.c legendre.c symmetries.c vecprint.c
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bessel.c own_zgemm.c parsing.c scatsystem.c materials.c drudeparam_data.c
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lll.c
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lll.c beyn.c
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)
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use_c99()
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@ -0,0 +1,667 @@
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#define STATIC_ASSERT(COND,MSG) typedef char static_assertion_##MSG[(COND)?1:-1]
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#define cg2s(x) gsl_complex_tostd(x)
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#define cs2g(x) gsl_complex_fromstd(x)
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#include <complex.h>
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#include <lapacke.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <math.h>
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#include <time.h>
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#include "qpms_error.h"
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// Maybe GSL works?
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#include <gsl/gsl_matrix.h>
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#include <gsl/gsl_complex_math.h>
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#include <gsl/gsl_linalg.h>
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#include <gsl/gsl_blas.h>
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#include <gsl/gsl_eigen.h>
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#include "beyn.h"
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#define SQ(x) ((x)*(x))
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STATIC_ASSERT((sizeof(lapack_complex_double) == sizeof(gsl_complex)), lapack_and_gsl_complex_must_be_consistent);
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typedef struct BeynSolver
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{
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int M; // dimension of matrices
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int L; // number of columns of VHat matrix
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gsl_vector_complex *eigenvalues, *eigenvalue_errors;
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gsl_matrix_complex *eigenvectors;
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gsl_matrix_complex *A0, *A1, *A0_coarse, *A1_coarse, *MInvVHat;
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gsl_matrix_complex *VHat;
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gsl_vector *Sigma, *residuals;
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} BeynSolver;
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// constructor, destructor
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BeynSolver *BeynSolver_create(int M, int L);
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void BeynSolver_free(BeynSolver *solver);
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// reset the random matrix VHat used in Beyn's algorithm
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void BeynSolver_srandom(BeynSolver *solver, unsigned int RandSeed);
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// Uniformly random number from interval [a, b].
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static double randU(double a, double b) { return a + (b-a) * random() * (1. / RAND_MAX); }
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// Random number from normal distribution (via Box-Muller transform, which is enough for our purposes).
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static double randN(double Sigma, double Mu) {
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double u1 = randU(0, 1);
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double u2 = randU(0, 1);
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return Mu + Sigma*sqrt(-2*log(u1))*cos(2.*M_PI*u2);
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}
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static complex double zrandN(double sigma, double mu){
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return randN(sigma, mu) + I*randN(sigma, mu);
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}
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static inline double dsq(double a) { return a * a; }
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static _Bool beyn_contour_ellipse_inside_test(struct beyn_contour_t *c, complex double z) {
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double rRe = c->z_dz[c->n][0];
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double rIm = c->z_dz[c->n][1];
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complex double zn = z - c->centre;
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return dsq(creal(zn)/rRe) + dsq(cimag(zn)/rIm) < 1;
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}
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beyn_contour_t *beyn_contour_ellipse(complex double centre, double rRe, double rIm, size_t n)
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{
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beyn_contour_t *c;
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QPMS_CRASHING_MALLOC(c, sizeof(beyn_contour_t) + (n+1)*sizeof(c->z_dz[0]));
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c->centre = centre;
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c->n = n;
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for(size_t i = 0; i < n; ++i) {
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double t = i*2*M_PI/n;
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double st = sin(t), ct = cos(t);
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c->z_dz[i][0] = centre + ct*rRe + I*st*rIm;
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c->z_dz[i][1] = (-rRe*st + I*rIm*ct) * (2*M_PI / n);
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}
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// We hide the half-axes metadata after the discretisation points.
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c->z_dz[n][0] = rRe;
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c->z_dz[n][1] = rIm;
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c->inside_test = beyn_contour_ellipse_inside_test;
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return c;
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}
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// Sets correct sign to zero for a given branch cut orientation
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static inline complex double
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align_zero(complex double z, beyn_contour_halfellipse_orientation or)
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{
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// Maybe redundant, TODO check the standard.
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const double positive_zero = copysign(0., +1.);
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const double negative_zero = copysign(0., -1.);
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switch(or) { // ensure correct zero signs; CHECKME!!!
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case BEYN_CONTOUR_HALFELLIPSE_RE_PLUS:
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if(creal(z) == 0 && signbit(creal(z)))
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z = positive_zero + I * cimag(z);
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break;
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case BEYN_CONTOUR_HALFELLIPSE_RE_MINUS:
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if(creal(z) == 0 && !signbit(creal(z)))
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z = negative_zero + I * cimag(z);
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break;
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case BEYN_CONTOUR_HALFELLIPSE_IM_PLUS:
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if(cimag(z) == 0 && signbit(cimag(z)))
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z = creal(z) + I * positive_zero;
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break;
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case BEYN_CONTOUR_HALFELLIPSE_IM_MINUS:
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if(cimag(z) == 0 && !signbit(cimag(z)))
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z = creal(z) + I * negative_zero;
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break;
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default: QPMS_WTF;
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}
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return z;
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}
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beyn_contour_t *beyn_contour_halfellipse(complex double centre, double rRe,
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double rIm, size_t n, beyn_contour_halfellipse_orientation or)
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{
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beyn_contour_t *c;
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QPMS_CRASHING_MALLOC(c, sizeof(beyn_contour_t) + (n+1)*sizeof(c->z_dz[0])
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+ sizeof(beyn_contour_halfellipse_orientation));
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c->centre = centre;
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c->n = n;
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const size_t nline = n/2;
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const size_t narc = n - nline;
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complex double faktor;
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double l = rRe, h = rIm;
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switch(or) {
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case BEYN_CONTOUR_HALFELLIPSE_RE_PLUS:
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faktor = -I;
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l = rIm; h = rRe;
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break;
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case BEYN_CONTOUR_HALFELLIPSE_RE_MINUS:
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faktor = I;
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l = rIm; h = rRe;
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break;
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case BEYN_CONTOUR_HALFELLIPSE_IM_PLUS:
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faktor = 1;
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break;
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case BEYN_CONTOUR_HALFELLIPSE_IM_MINUS:
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faktor = -1;
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break;
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default: QPMS_WTF;
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}
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for(size_t i = 0; i < narc; ++i) {
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double t = (i+0.5)*M_PI/narc;
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double st = sin(t), ct = cos(t);
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c->z_dz[i][0] = centre + faktor*(ct*l + I*st*h);
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c->z_dz[i][1] = faktor * (-l*st + I*h*ct) * (M_PI / narc);
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}
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for(size_t i = 0; i < nline; ++i) {
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double t = 0.5 * (1 - (double) nline) + i;
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c->z_dz[narc + i][0] = align_zero(centre + faktor * t * 2 * l / nline, or);
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c->z_dz[narc + i][1] = faktor * 2 * l / nline;
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}
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// We hide the half-axes metadata after the discretisation points.
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c->z_dz[n][0] = rRe;
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c->z_dz[n][1] = rIm;
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// ugly...
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*((beyn_contour_halfellipse_orientation *) &c->z_dz[n+1][0]) = or;
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c->inside_test = NULL; // TODO beyn_contour_halfellipse_inside_test;
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return c;
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}
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beyn_contour_t *beyn_contour_kidney(complex double centre, double rRe,
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double rIm, const double rounding, const size_t n, beyn_contour_halfellipse_orientation or)
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{
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beyn_contour_t *c;
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QPMS_ENSURE(rounding >= 0 && rounding < .5, "rounding must lie in the interval [0, 0.5)");
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QPMS_CRASHING_MALLOC(c, sizeof(beyn_contour_t) + (n+1)*sizeof(c->z_dz[0])
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+ sizeof(beyn_contour_halfellipse_orientation));
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c->centre = centre;
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c->n = n;
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complex double faktor;
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double l = rRe, h = rIm;
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switch(or) {
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case BEYN_CONTOUR_HALFELLIPSE_RE_PLUS:
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faktor = -I;
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l = rIm; h = rRe;
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break;
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case BEYN_CONTOUR_HALFELLIPSE_RE_MINUS:
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faktor = I;
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l = rIm; h = rRe;
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break;
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case BEYN_CONTOUR_HALFELLIPSE_IM_PLUS:
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faktor = 1;
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break;
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case BEYN_CONTOUR_HALFELLIPSE_IM_MINUS:
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faktor = -1;
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break;
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default: QPMS_WTF;
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}
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// Small circle centre coordinates.
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const double y = rounding * h; // distance from the cut / straight line
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const double x = sqrt(SQ(h - y) - SQ(y));
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const double alpha = asin(y/(h-y));
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const double ar = l/h; // aspect ratio
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// Parameter range (equal to the contour length if ar == 1)
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const double tmax = 2 * (x + (M_PI_2 + alpha) * y + (M_PI_2 - alpha) * h);
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const double dt = tmax / n;
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size_t i = 0;
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double t;
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// Straight line, first part
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double t_lo = 0, t_hi = x;
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for(; t = i * dt, t <= t_hi; ++i) {
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c->z_dz[i][0] = align_zero(centre + (t - t_lo) * ar * faktor, or);
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c->z_dz[i][1] = dt * ar * faktor;
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}
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// First small arc
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t_lo = t_hi; t_hi = t_lo + (M_PI_2 + alpha) * y;
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for(; t = i * dt, t < t_hi; ++i) {
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double phi = (t - t_lo) / y - M_PI_2;
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c->z_dz[i][0] = centre + (ar * (x + y * cos(phi)) + y * (1 + sin(phi)) * I) * faktor;
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c->z_dz[i][1] = dt * (- ar * sin(phi) + cos(phi) * I) * faktor;
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}
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// Big arc
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t_lo = t_hi; t_hi = t_lo + (M_PI - 2 * alpha) * h;
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for(; t = i * dt, t < t_hi; ++i) {
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double phi = (t - t_lo) / h + alpha;
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c->z_dz[i][0] = centre + (ar * (h * cos(phi)) + h * sin(phi) * I) * faktor;
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c->z_dz[i][1] = dt * (- ar * sin(phi) + cos(phi) * I) * faktor;
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}
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// Second small arc
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t_lo = t_hi; t_hi = t_lo + (M_PI_2 + alpha) * y;
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for(; t = i * dt, t < t_hi; ++i) {
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double phi = (t - t_lo) / y + M_PI - alpha;
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c->z_dz[i][0] = centre + (ar * (- x + y * cos(phi)) + y * (1 + sin(phi)) * I) * faktor;
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c->z_dz[i][1] = dt * (- ar * sin(phi) + cos(phi) * I) * faktor;
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}
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// Straight line, second part
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t_lo = t_hi; t_hi = tmax;
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for(; t = i * dt, i < n; ++i) {
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c->z_dz[i][0] = align_zero(centre + (t - t_lo - x) * ar * faktor, or);
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c->z_dz[i][1] = dt * ar * faktor;
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}
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#if 0 // TODO later
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// We hide the half-axes metadata after the discretisation points.
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c->z_dz[n][0] = rRe;
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c->z_dz[n][1] = rIm;
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// ugly...
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*((beyn_contour_halfellipse_orientation *) &c->z_dz[n+1][0]) = or;
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#endif
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c->inside_test = NULL; // TODO beyn_contour_halfellipse_inside_test;
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return c;
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}
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void beyn_result_gsl_free(beyn_result_gsl_t *r) {
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if(r) {
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gsl_vector_complex_free(r->eigval);
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gsl_vector_complex_free(r->eigval_err);
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gsl_vector_free(r->residuals);
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gsl_matrix_complex_free(r->eigvec);
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gsl_vector_free(r->ranktest_SV);
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free(r);
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}
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}
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BeynSolver *BeynSolver_create(int M, int L)
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{
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BeynSolver *solver= (BeynSolver *)malloc(sizeof(*solver));
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solver->M = M;
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solver->L = L;
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QPMS_ENSURE(L <= M, "We expect L <= M, but we got L = %d, M = %d ", L, M);
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// storage for eigenvalues and eigenvectors
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solver->eigenvalues = gsl_vector_complex_calloc(L);
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solver->eigenvalue_errors = gsl_vector_complex_calloc(L);
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solver->residuals = gsl_vector_calloc(L);
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solver->eigenvectors = gsl_matrix_complex_calloc(M, L);
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// storage for singular values, random VHat matrix, etc. used in algorithm
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solver->A0 = gsl_matrix_complex_calloc(M,L);
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solver->A1 = gsl_matrix_complex_calloc(M,L);
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solver->A0_coarse = gsl_matrix_complex_calloc(M,L);
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solver->A1_coarse = gsl_matrix_complex_calloc(M,L);
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solver->MInvVHat = gsl_matrix_complex_calloc(M,L);
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solver->VHat = gsl_matrix_complex_calloc(M,L);
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solver->Sigma = gsl_vector_calloc(L);
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// Beyn Step 1: Generate random matrix VHat
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BeynSolver_srandom(solver,(unsigned)time(NULL));
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return solver;
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}
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void BeynSolver_free(BeynSolver *solver)
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{
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gsl_vector_complex_free(solver->eigenvalues);
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gsl_vector_complex_free(solver->eigenvalue_errors);
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gsl_matrix_complex_free(solver->eigenvectors);
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gsl_matrix_complex_free(solver->A0);
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gsl_matrix_complex_free(solver->A1);
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gsl_matrix_complex_free(solver->A0_coarse);
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gsl_matrix_complex_free(solver->A1_coarse);
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gsl_matrix_complex_free(solver->MInvVHat);
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gsl_vector_free(solver->Sigma);
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gsl_vector_free(solver->residuals);
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gsl_matrix_complex_free(solver->VHat);
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free(solver);
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}
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void BeynSolver_free_partial(BeynSolver *solver)
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{
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gsl_matrix_complex_free(solver->A0);
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gsl_matrix_complex_free(solver->A1);
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gsl_matrix_complex_free(solver->A0_coarse);
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gsl_matrix_complex_free(solver->A1_coarse);
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gsl_matrix_complex_free(solver->MInvVHat);
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gsl_matrix_complex_free(solver->VHat);
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free(solver);
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}
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void BeynSolver_srandom(BeynSolver *solver, unsigned int RandSeed)
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{
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if (RandSeed==0)
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RandSeed=time(0);
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srandom(RandSeed);
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gsl_matrix_complex *VHat=solver->VHat;
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for(int nr=0; nr<VHat->size1; nr++)
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for(int nc=0; nc<VHat->size2; nc++)
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gsl_matrix_complex_set(VHat,nr,nc,cs2g(zrandN(1, 0)));
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}
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/*
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* linear-algebra manipulations on the A0 and A1 matrices
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* (obtained via numerical quadrature) to extract eigenvalues
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* and eigenvectors
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*/
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static int beyn_process_matrices(BeynSolver *solver, beyn_function_M_gsl_t M_function,
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void *Params,
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gsl_matrix_complex *A0, gsl_matrix_complex *A1, double complex z0,
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gsl_vector_complex *eigenvalues, gsl_matrix_complex *eigenvectors, const double rank_tol, const double res_tol)
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{
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const size_t m = solver->M;
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const size_t l = solver->L;
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gsl_vector *Sigma = solver->Sigma;
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int verbose = 1; // TODO
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// Beyn Step 3: Compute SVD: A0 = V0_full * Sigma * W0T_full
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if(verbose) printf(" Beyn: computing SVD...\n");
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gsl_matrix_complex* V0_full = gsl_matrix_complex_alloc(m,l);
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gsl_matrix_complex_memcpy(V0_full,A0);
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gsl_matrix_complex* W0T_full = gsl_matrix_complex_alloc(l,l);
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QPMS_ENSURE(Sigma->stride == 1, "Sigma vector stride must be 1 for LAPACKE_zgesdd, got %zd.", Sigma->stride);
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QPMS_ENSURE(V0_full->size1 >= V0_full->size2, "m = %zd, l = %zd, what the hell?");
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QPMS_ENSURE_SUCCESS(LAPACKE_zgesdd(LAPACK_ROW_MAJOR, // A = U*Σ*conjg(V')
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'O' /*jobz, 'O' overwrites a with U and saves conjg(V') in vt if m >= n, i.e. if M >= L, which holds*/,
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V0_full->size1 /* m, number of rows */,
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V0_full->size2 /* n, number of columns */,
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(lapack_complex_double *)(V0_full->data) /*a*/,
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V0_full->tda /*lda*/,
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Sigma->data /*s*/,
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NULL /*u; not used*/,
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m /*ldu; should not be really used but lapacke requires it for some obscure reason*/,
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(lapack_complex_double *)W0T_full->data /*vt*/,
|
||||
W0T_full->tda /*ldvt*/
|
||||
));
|
||||
|
||||
|
||||
// Beyn Step 4: Rank test for Sigma
|
||||
// compute effective rank K (number of eigenvalue candidates)
|
||||
int K=0;
|
||||
for (int k=0; k<Sigma->size /* this is l, actually */; k++) {
|
||||
if (verbose) printf("Beyn: SV(%d)=%e\n",k,gsl_vector_get(Sigma, k));
|
||||
if (gsl_vector_get(Sigma, k) > rank_tol)
|
||||
K++;
|
||||
}
|
||||
if (verbose)printf(" Beyn: %d/%zd relevant singular values\n",K,l);
|
||||
if (K==0) {
|
||||
QPMS_WARN("no singular values found in Beyn eigensolver\n");
|
||||
return 0;
|
||||
}
|
||||
|
||||
// Beyn step 5: B = V0' * A1 * W0 * Sigma^-1
|
||||
// set V0, W0T = matrices of first K right, left singular vectors
|
||||
gsl_matrix_complex *V0 = gsl_matrix_complex_alloc(m,K);
|
||||
gsl_matrix_complex *W0T= gsl_matrix_complex_alloc(K,l);
|
||||
|
||||
for (int k = 0; k < K; ++k) {
|
||||
gsl_vector_complex_view tmp;
|
||||
tmp = gsl_matrix_complex_column(V0_full, k);
|
||||
gsl_matrix_complex_set_col(V0, k, &(tmp.vector));
|
||||
tmp = gsl_matrix_complex_row(W0T_full, k);
|
||||
gsl_matrix_complex_set_row(W0T, k, &(tmp.vector));
|
||||
}
|
||||
|
||||
gsl_matrix_complex_free(V0_full);
|
||||
gsl_matrix_complex_free(W0T_full);
|
||||
|
||||
gsl_matrix_complex *TM2 = gsl_matrix_complex_calloc(K,l);
|
||||
gsl_matrix_complex *B = gsl_matrix_complex_calloc(K,K);
|
||||
|
||||
if(verbose) printf(" Multiplying V0*A1->TM...\n");
|
||||
|
||||
const gsl_complex one = gsl_complex_rect(1,0);
|
||||
const gsl_complex zero = gsl_complex_rect(0,0);
|
||||
gsl_blas_zgemm(CblasConjTrans, CblasNoTrans, one,
|
||||
V0, A1, zero, TM2);
|
||||
|
||||
if(verbose) printf(" Multiplying TM*W0T->B...\n");
|
||||
|
||||
gsl_blas_zgemm(CblasNoTrans, CblasConjTrans, one,
|
||||
TM2, W0T, zero, B);
|
||||
|
||||
gsl_matrix_complex_free(W0T);
|
||||
gsl_matrix_complex_free(TM2);
|
||||
|
||||
if(verbose) printf(" Scaling B <- B*Sigma^{-1}\n");
|
||||
gsl_vector_complex *tmp = gsl_vector_complex_calloc(K);
|
||||
for(int i = 0; i < K; i++) {
|
||||
gsl_matrix_complex_get_col(tmp, B, i);
|
||||
gsl_vector_complex_scale(tmp, gsl_complex_rect(1.0/gsl_vector_get(Sigma,i), 0));
|
||||
gsl_matrix_complex_set_col(B,i,tmp);
|
||||
}
|
||||
gsl_vector_complex_free(tmp);
|
||||
|
||||
//for(int m=0; m<K; m++) // B <- B * Sigma^{-1}
|
||||
|
||||
// Beyn step 6.
|
||||
// Eigenvalue decomposition B -> S*Lambda*S'
|
||||
/* According to Beyn's paper (Algorithm 1), one should check conditioning
|
||||
* of the eigenvalues; if they are ill-conditioned, one should perform
|
||||
* a procedure involving Schur decomposition and reordering.
|
||||
*
|
||||
* Beyn refers to MATLAB routines eig, condeig, schur, ordschur.
|
||||
* I am not sure about the equivalents in LAPACK, TODO check zgeevx, zgeesx.
|
||||
*/
|
||||
if(verbose) printf(" Eigensolving (%i,%i)\n",K,K);
|
||||
|
||||
gsl_vector_complex *Lambda = gsl_vector_complex_alloc(K); // eigenvalues
|
||||
gsl_matrix_complex *S = gsl_matrix_complex_alloc(K,K); // eigenvectors
|
||||
|
||||
QPMS_ENSURE(Sigma->stride == 1, "Sigma vector stride must be 1 for LAPACKE_zgesdd, got %zd.", Sigma->stride);
|
||||
QPMS_ENSURE(Lambda->stride == 1, "Lambda vector stride must be 1 for LAPACKE_zgesdd, got %zd.", Sigma->stride);
|
||||
QPMS_ENSURE_SUCCESS(LAPACKE_zgeev(
|
||||
LAPACK_ROW_MAJOR,
|
||||
'N' /* jobvl; don't compute left eigenvectors */,
|
||||
'V' /* jobvr; do compute right eigenvectors */,
|
||||
K /* n */,
|
||||
(lapack_complex_double *)(B->data) /* a */,
|
||||
B->tda /* lda */,
|
||||
(lapack_complex_double *) Lambda->data /* w */,
|
||||
NULL /* vl */,
|
||||
m /* ldvl, not used by for some reason needed */,
|
||||
(lapack_complex_double *)(S->data)/* vr */,
|
||||
S->tda/* ldvr */
|
||||
));
|
||||
|
||||
gsl_matrix_complex_free(B);
|
||||
|
||||
// V0S <- V0*S
|
||||
printf("Multiplying V0*S...\n");
|
||||
gsl_matrix_complex *V0S = gsl_matrix_complex_alloc(m, K);
|
||||
QPMS_ENSURE_SUCCESS(gsl_blas_zgemm(CblasNoTrans, CblasNoTrans,
|
||||
one, V0, S, zero, V0S));
|
||||
|
||||
gsl_matrix_complex_free(V0);
|
||||
|
||||
// FIXME!!! make clear relation between KRetained and K in the results!
|
||||
// (If they differ, there are possibly some spurious eigenvalues.)
|
||||
int KRetained = 0;
|
||||
gsl_matrix_complex *Mmat = gsl_matrix_complex_alloc(m, m);
|
||||
gsl_vector_complex *MVk = gsl_vector_complex_alloc(m);
|
||||
for (int k = 0; k < K; ++k) {
|
||||
const gsl_complex zgsl = gsl_complex_add(gsl_complex_rect(creal(z0), cimag(z0)), gsl_vector_complex_get(Lambda, k));
|
||||
const complex double z = GSL_REAL(zgsl) + I*GSL_IMAG(zgsl);
|
||||
gsl_vector_complex_const_view Vk = gsl_matrix_complex_const_column(V0S, k);
|
||||
|
||||
double residual = 0;
|
||||
if(res_tol > 0) {
|
||||
QPMS_ENSURE_SUCCESS(M_function(Mmat, z, Params));
|
||||
QPMS_ENSURE_SUCCESS(gsl_blas_zgemv(CblasNoTrans, one, Mmat, &(Vk.vector), zero, MVk));
|
||||
residual = gsl_blas_dznrm2(MVk);
|
||||
if (verbose) printf("Beyn: Residual(%i)=%e\n",k,residual);
|
||||
}
|
||||
if (res_tol > 0 && residual > res_tol) continue;
|
||||
|
||||
gsl_vector_complex_set(eigenvalues, KRetained, zgsl);
|
||||
if(eigenvectors) {
|
||||
gsl_matrix_complex_set_col(eigenvectors, KRetained, &(Vk.vector));
|
||||
gsl_vector_set(solver->residuals, KRetained, residual);
|
||||
}
|
||||
++KRetained;
|
||||
}
|
||||
|
||||
gsl_matrix_complex_free(V0S);
|
||||
gsl_matrix_complex_free(Mmat);
|
||||
gsl_vector_complex_free(MVk);
|
||||
gsl_matrix_complex_free(S);
|
||||
gsl_vector_complex_free(Lambda);
|
||||
|
||||
return KRetained;
|
||||
}
|
||||
|
||||
|
||||
beyn_result_gsl_t *beyn_solve_gsl(const size_t m, const size_t l,
|
||||
beyn_function_M_gsl_t M_function, beyn_function_M_inv_Vhat_gsl_t M_inv_Vhat_function,
|
||||
void *params, const beyn_contour_t *contour,
|
||||
double rank_tol, double res_tol)
|
||||
{
|
||||
BeynSolver *solver = BeynSolver_create(m, l);
|
||||
|
||||
gsl_matrix_complex *A0 = solver->A0;
|
||||
gsl_matrix_complex *A1 = solver->A1;
|
||||
gsl_matrix_complex *A0_coarse = solver->A0_coarse;
|
||||
gsl_matrix_complex *A1_coarse = solver->A1_coarse;
|
||||
gsl_matrix_complex *MInvVHat = solver->MInvVHat;
|
||||
gsl_matrix_complex *VHat = solver->VHat;
|
||||
|
||||
/***************************************************************/
|
||||
/* evaluate contour integrals by numerical quadrature to get */
|
||||
/* A0 and A1 matrices */
|
||||
/***************************************************************/
|
||||
|
||||
gsl_matrix_complex_set_zero(A0);
|
||||
gsl_matrix_complex_set_zero(A1);
|
||||
gsl_matrix_complex_set_zero(A0_coarse);
|
||||
gsl_matrix_complex_set_zero(A1_coarse);
|
||||
const size_t N = contour->n;
|
||||
if(N & 1) QPMS_WARN("Contour discretisation point number is odd (%zd),"
|
||||
" the error estimates might be a bit off.", N);
|
||||
|
||||
|
||||
// Beyn Step 2: Computa A0, A1
|
||||
const complex double z0 = contour->centre;
|
||||
for(int n=0; n<N; n++) {
|
||||
const complex double z = contour->z_dz[n][0];
|
||||
const complex double dz = contour->z_dz[n][1];
|
||||
|
||||
gsl_matrix_complex_memcpy(MInvVHat, VHat);
|
||||
|
||||
if(M_inv_Vhat_function) {
|
||||
QPMS_ENSURE_SUCCESS(M_inv_Vhat_function(MInvVHat, VHat, z, params));
|
||||
} else {
|
||||
lapack_int *pivot;
|
||||
gsl_matrix_complex *Mmat = gsl_matrix_complex_alloc(m,m);
|
||||
QPMS_ENSURE_SUCCESS(M_function(Mmat, z, params));
|
||||
QPMS_CRASHING_MALLOC(pivot, sizeof(lapack_int) * m);
|
||||
QPMS_ENSURE_SUCCESS(LAPACKE_zgetrf(LAPACK_ROW_MAJOR,
|
||||
m /*m*/, m /*n*/,(lapack_complex_double *) Mmat->data /*a*/, Mmat->tda /*lda*/, pivot /*ipiv*/));
|
||||
QPMS_ENSURE(MInvVHat->tda == l, "wut?");
|
||||
QPMS_ENSURE_SUCCESS(LAPACKE_zgetrs(LAPACK_ROW_MAJOR, 'N' /*trans*/,
|
||||
m /*n*/, l/*nrhs*/, (lapack_complex_double *)(Mmat->data) /*a*/, Mmat->tda /*lda*/, pivot/*ipiv*/,
|
||||
(lapack_complex_double *)(MInvVHat->data) /*b*/, MInvVHat->tda/*ldb*/));
|
||||
|
||||
free(pivot);
|
||||
gsl_matrix_complex_free(Mmat);
|
||||
}
|
||||
|
||||
gsl_matrix_complex_scale(MInvVHat, cs2g(dz));
|
||||
gsl_matrix_complex_add(A0, MInvVHat);
|
||||
if((n%2)==0) {
|
||||
gsl_matrix_complex_add(A0_coarse, MInvVHat);
|
||||
gsl_matrix_complex_add(A0_coarse, MInvVHat);
|
||||
}
|
||||
|
||||
gsl_matrix_complex_scale(MInvVHat, cs2g(z - z0)); // A_1 scaling as in Beyn's Remark 3.2(b) for numerical stability.
|
||||
gsl_matrix_complex_add(A1, MInvVHat);
|
||||
if((n%2)==0) {
|
||||
gsl_matrix_complex_add(A1_coarse, MInvVHat);
|
||||
gsl_matrix_complex_add(A1_coarse, MInvVHat);
|
||||
}
|
||||
}
|
||||
|
||||
gsl_vector_complex *eigenvalues = solver->eigenvalues;
|
||||
gsl_vector_complex *eigenvalue_errors = solver->eigenvalue_errors;
|
||||
gsl_matrix_complex *eigenvectors = solver->eigenvectors;
|
||||
|
||||
// Beyn Steps 3–6
|
||||
int K = beyn_process_matrices(solver, M_function, params, A0, A1, z0, eigenvalues, eigenvectors, rank_tol, res_tol);
|
||||
// Repeat Steps 3–6 with rougher contour approximation to get an error estimate.
|
||||
int K_coarse = beyn_process_matrices(solver, M_function, params, A0_coarse, A1_coarse, z0, eigenvalue_errors, eigenvectors, rank_tol, res_tol);
|
||||
|
||||
gsl_blas_zaxpy(gsl_complex_rect(-1,0), eigenvalues, eigenvalue_errors);
|
||||
// Reid did also fabs on the complex and real parts ^^^.
|
||||
|
||||
beyn_result_gsl_t *result;
|
||||
QPMS_CRASHING_MALLOC(result, sizeof(beyn_result_gsl_t));
|
||||
result->eigval = solver->eigenvalues;
|
||||
result->eigval_err = solver->eigenvalue_errors;
|
||||
result->residuals = solver->residuals;
|
||||
result->eigvec = solver->eigenvectors;
|
||||
result->ranktest_SV = solver->Sigma;
|
||||
result->neig = K;
|
||||
|
||||
BeynSolver_free_partial(solver);
|
||||
|
||||
return result;
|
||||
}
|
||||
|
||||
// Wrapper of pure C array M-matrix function to GSL.
|
||||
|
||||
struct beyn_function_M_carr2gsl_param {
|
||||
beyn_function_M_t M_function;
|
||||
beyn_function_M_inv_Vhat_t M_inv_Vhat_function;
|
||||
void *param;
|
||||
};
|
||||
|
||||
static int beyn_function_M_carr2gsl(gsl_matrix_complex *target_M, complex double z, void *params)
|
||||
{
|
||||
struct beyn_function_M_carr2gsl_param *p = params;
|
||||
// These could rather be asserts.
|
||||
QPMS_ENSURE(target_M->size2 == target_M->tda, "Target GSL matrix is not a C-contiguous array. This is a bug, please report!");
|
||||
QPMS_ENSURE(target_M->size1 == target_M->size2, "Target is not a square matrix. This is a bug, please report!");
|
||||
return p->M_function((complex double *) target_M->data, target_M->size1, z, p->param);
|
||||
}
|
||||
|
||||
static int beyn_function_M_inv_Vhat_carr2gsl(gsl_matrix_complex *target,
|
||||
const gsl_matrix_complex *Vhat, complex double z, void *params)
|
||||
{
|
||||
QPMS_UNTESTED;
|
||||
struct beyn_function_M_carr2gsl_param *p = params;
|
||||
// These could rather be asserts.
|
||||
QPMS_ENSURE(target->size2 == target->tda, "Target GSL matrix is not a C-contiguous array. This is a bug, please report!");
|
||||
QPMS_ENSURE(Vhat->size2 == Vhat->tda, "Source GSL matrix is not a C-contiguous array. This is a bug, please report!");
|
||||
// TODO here I could also check whether Vhat and target have compatible sizes.
|
||||
return p->M_inv_Vhat_function((complex double *) target->data, target->size1, target->size2,
|
||||
(complex double *) Vhat->data, z, p->param);
|
||||
}
|
||||
|
||||
beyn_result_t *beyn_solve(size_t m, size_t l, beyn_function_M_t M, beyn_function_M_inv_Vhat_t M_inv_Vhat,
|
||||
void *params, const beyn_contour_t *contour, double rank_tol, double res_tol) {
|
||||
struct beyn_function_M_carr2gsl_param p = {M, M_inv_Vhat, params};
|
||||
return beyn_result_from_beyn_result_gsl(
|
||||
beyn_solve_gsl(m, l, beyn_function_M_carr2gsl,
|
||||
(p.M_inv_Vhat_function) ? beyn_function_M_inv_Vhat_carr2gsl : NULL,
|
||||
(void *) &p, contour, rank_tol, res_tol)
|
||||
);
|
||||
}
|
||||
|
||||
beyn_result_t *beyn_result_from_beyn_result_gsl(beyn_result_gsl_t *g) {
|
||||
struct beyn_result_t *result;
|
||||
QPMS_CRASHING_MALLOC(result, sizeof(beyn_result_t));
|
||||
result->gsl = g;
|
||||
result->neig = result->gsl->neig;
|
||||
result->vlen = result->gsl->eigvec->size2;
|
||||
result->eigval = (complex double *) result->gsl->eigval->data;
|
||||
result->eigval_err = (complex double *) result->gsl->eigval_err->data;
|
||||
result->residuals = result->gsl->residuals->data;
|
||||
result->eigvec = (complex double *) result->gsl->eigvec->data;
|
||||
result->ranktest_SV = result->gsl->ranktest_SV->data;
|
||||
return result;
|
||||
}
|
||||
|
||||
void beyn_result_free(beyn_result_t *result) {
|
||||
if(result)
|
||||
beyn_result_gsl_free(result->gsl);
|
||||
free(result);
|
||||
}
|
||||
|
||||
|
|
@ -0,0 +1,129 @@
|
|||
/** \file beyn.h
|
||||
* \brief Beyn's algorithm for nonlinear eigenvalue problems.
|
||||
*/
|
||||
#ifndef BEYN_H
|
||||
#define BEYN_H
|
||||
|
||||
#include <complex.h>
|
||||
#include <gsl/gsl_matrix.h>
|
||||
#include <gsl/gsl_complex_math.h>
|
||||
|
||||
/// User-supplied function that provides the operator M(z) whose "roots" are to be found.
|
||||
/** GSL matrix version */
|
||||
typedef int (*beyn_function_M_gsl_t)(gsl_matrix_complex *target_M, complex double z, void *params);
|
||||
|
||||
/// (optional) User-supplied function that, given \f$ \hat V \f$, calculates \f$ M(z)^{-1} \hat V \f$.
|
||||
/** GSL matrix version */
|
||||
typedef int (*beyn_function_M_inv_Vhat_gsl_t)(gsl_matrix_complex *target_M_inv_Vhat,
|
||||
const gsl_matrix_complex *Vhat, complex double z, void *params);
|
||||
|
||||
/// User-supplied function that provides the operator M(z) whose "roots" are to be found.
|
||||
/** Pure C array version */
|
||||
typedef int (*beyn_function_M_t)(complex double *target_M, size_t m, complex double z, void *params);
|
||||
|
||||
/// (optional) User-supplied function that, given \f$ \hat V \f$, calculates \f$ M(z)^{-1} \hat V \f$.
|
||||
/** Pure C array version */
|
||||
typedef int (*beyn_function_M_inv_Vhat_t)(complex double *target_M_inv_Vhat, size_t m, size_t l,
|
||||
const complex double *Vhat, complex double z, void *params);
|
||||
|
||||
/// Complex plane integration contour structure.
|
||||
typedef struct beyn_contour_t {
|
||||
size_t n; ///< Number of discretisation points.
|
||||
/// "Centre" of the contour.
|
||||
/**
|
||||
* This point is used in the rescaling of the \f$ A_1 \f$ matrix as in
|
||||
* Beyn's Remark 3.2 (b) in order to improve the numerical stability.
|
||||
* It does not have to be a centre in some strictly defined sense,
|
||||
* but it should be "somewhere around" where the contour is.
|
||||
*/
|
||||
complex double centre;
|
||||
/// Function testing that a point \a z lies inside the contour (optional).
|
||||
_Bool (*inside_test)(struct beyn_contour_t *, complex double z);
|
||||
complex double z_dz[][2]; ///< Pairs of contour points and derivatives in that points.
|
||||
} beyn_contour_t;
|
||||
|
||||
/// Complex plane elliptic integration contour with axes parallel to the real, imaginary axes.
|
||||
/** Free using free(). */
|
||||
beyn_contour_t *beyn_contour_ellipse(complex double centre, double halfax_re, double halfax_im, size_t npoints);
|
||||
|
||||
|
||||
typedef enum {
|
||||
BEYN_CONTOUR_HALFELLIPSE_RE_PLUS = 3,
|
||||
BEYN_CONTOUR_HALFELLIPSE_RE_MINUS = 1,
|
||||
BEYN_CONTOUR_HALFELLIPSE_IM_PLUS = 0,
|
||||
BEYN_CONTOUR_HALFELLIPSE_IM_MINUS = 2,
|
||||
} beyn_contour_halfellipse_orientation;
|
||||
|
||||
|
||||
/// Complex plane "half-elliptic" integration contour with axes parallel to the real, imaginary axes.
|
||||
/** Free using free(). */
|
||||
beyn_contour_t *beyn_contour_halfellipse(complex double centre, double halfax_re, double halfax_im, size_t npoints,
|
||||
beyn_contour_halfellipse_orientation or);
|
||||
|
||||
/// Similar to halfellipse but with rounded corners.
|
||||
beyn_contour_t *beyn_contour_kidney(complex double centre, double halfax_re, double halfax_im,
|
||||
double rounding, ///< Must be in interval [0, 0.5)
|
||||
size_t n, beyn_contour_halfellipse_orientation or);
|
||||
|
||||
|
||||
/// Beyn algorithm result structure (GSL matrix/vector version).
|
||||
typedef struct beyn_result_gsl_t {
|
||||
size_t neig; ///< Number of eigenvalues found (a bit redundant?).
|
||||
gsl_vector_complex *eigval;
|
||||
gsl_vector_complex *eigval_err;
|
||||
gsl_vector *residuals;
|
||||
gsl_matrix_complex *eigvec;
|
||||
gsl_vector *ranktest_SV;
|
||||
} beyn_result_gsl_t;
|
||||
|
||||
void beyn_result_gsl_free(beyn_result_gsl_t *result);
|
||||
|
||||
/// Beyn algorithm result structure (pure C array version).
|
||||
typedef struct beyn_result_t {
|
||||
size_t neig; ///< Number of eigenvalues found.
|
||||
size_t vlen; ///< Vector space dimension (also the leading dimension of eigvec).
|
||||
complex double *eigval;
|
||||
complex double *eigval_err;
|
||||
double *residuals;
|
||||
complex double *eigvec;
|
||||
double *ranktest_SV;
|
||||
|
||||
/// Private, we wrap it around beyn_result_gsl_t for now.
|
||||
beyn_result_gsl_t *gsl;
|
||||
|
||||
} beyn_result_t;
|
||||
|
||||
/// Converts beyn_result_gsl_t from beyn_result_t.
|
||||
/** After calling this, use beyn_result_free() on the returned pointer;
|
||||
* do NOT run beyn_result_gsl_free() anymore.
|
||||
*/
|
||||
beyn_result_t *beyn_result_from_beyn_result_gsl(beyn_result_gsl_t *g);
|
||||
|
||||
void beyn_result_free(beyn_result_t *result);
|
||||
|
||||
beyn_result_gsl_t *beyn_solve_gsl(
|
||||
size_t m, ///< Dimension of the matrix \a M.
|
||||
size_t l, ///< Number of columns of the random matrix \f$ \hat V \f$ (larger than the expected number of solutions).
|
||||
beyn_function_M_gsl_t M, ///< Function providing the matrix \f$ M(z) \f$.
|
||||
beyn_function_M_inv_Vhat_gsl_t M_inv_Vhat, ///< Fuction providing the matrix \f$ M^{-1}(z) \hat V \f$ (optional).
|
||||
void *params, ///< Parameter pointer passed to M() and M_inv_Vhat().
|
||||
const beyn_contour_t *contour, ///< Integration contour.
|
||||
double rank_tol, ///< (default: `1e-4`) TODO DOC.
|
||||
double res_tol ///< (default: `0.0`) TODO DOC.
|
||||
);
|
||||
|
||||
beyn_result_t *beyn_solve(
|
||||
size_t m, ///< Dimension of the matrix \a M.
|
||||
size_t l, ///< Number of columns of the random matrix \f$ \hat V \f$ (larger than the expected number of solutions).
|
||||
beyn_function_M_t M, ///< Function providing the matrix \f$ M(z) \f$.
|
||||
beyn_function_M_inv_Vhat_t M_inv_Vhat, ///< Fuction providing the matrix \f$ M^{-1}(z) \hat V \f$ (optional).
|
||||
void *params, ///< Parameter pointer passed to M() and M_inv_Vhat().
|
||||
const beyn_contour_t *contour, ///< Integration contour.
|
||||
double rank_tol, ///< (default: `1e-4`) TODO DOC.
|
||||
double res_tol ///< (default: `0.0`) TODO DOC.
|
||||
);
|
||||
|
||||
static inline complex double gsl_complex_tostd(gsl_complex z) { return GSL_REAL(z) + I*GSL_IMAG(z); }
|
||||
static inline gsl_complex gsl_complex_fromstd(complex double z) { return gsl_complex_rect(creal(z), cimag(z)); }
|
||||
|
||||
#endif // BEYN_H
|
||||
|
|
@ -589,3 +589,62 @@ cdef extern from "ewald.h":
|
|||
bint pgen_generates_shifted_points, cart3_t k, cart3_t particle_shift)
|
||||
|
||||
|
||||
cdef extern from "gsl/gsl_complex.h":
|
||||
ctypedef struct gsl_complex:
|
||||
double dat[2]
|
||||
|
||||
cdef extern from "gsl/gsl_matrix.h":
|
||||
ctypedef struct gsl_matrix_complex:
|
||||
pass
|
||||
ctypedef struct gsl_vector:
|
||||
pass
|
||||
ctypedef struct gsl_vector_complex:
|
||||
pass
|
||||
|
||||
cdef extern from "beyn.h":
|
||||
ctypedef struct beyn_contour_t:
|
||||
bint (*inside_test)(beyn_contour_t *, cdouble z)
|
||||
pass
|
||||
ctypedef struct beyn_result_gsl_t:
|
||||
pass
|
||||
ctypedef struct beyn_result_t:
|
||||
size_t neig
|
||||
size_t vlen
|
||||
cdouble *eigval
|
||||
cdouble *eigval_err
|
||||
double *residuals
|
||||
cdouble *eigvec
|
||||
double *ranktest_SV
|
||||
beyn_result_gsl_t *gsl
|
||||
ctypedef enum beyn_contour_halfellipse_orientation:
|
||||
BEYN_CONTOUR_HALFELLIPSE_RE_PLUS
|
||||
BEYN_CONTOUR_HALFELLIPSE_IM_PLUS
|
||||
BEYN_CONTOUR_HALFELLIPSE_RE_MINUS
|
||||
BEYN_CONTOUR_HALFELLIPSE_IM_MINUS
|
||||
|
||||
ctypedef int (*beyn_function_M_gsl_t)(gsl_matrix_complex *target_M, cdouble z, void *params)
|
||||
ctypedef int (*beyn_function_M_inv_Vhat_gsl_t)(gsl_matrix_complex *target, const gsl_matrix_complex *Vhat, cdouble z, void *params)
|
||||
ctypedef int (*beyn_function_M_t)(cdouble *target_M, size_t m, cdouble z, void *params)
|
||||
ctypedef int (*beyn_function_M_inv_Vhat_t)(cdouble *target, size_t m, size_t l, const cdouble *Vhat, cdouble z, void *params)
|
||||
|
||||
void beyn_result_gsl_free(beyn_result_gsl_t *result)
|
||||
void beyn_result_free(beyn_result_t *result)
|
||||
|
||||
beyn_result_gsl_t *beyn_solve_gsl(size_t m, size_t l, beyn_function_M_gsl_t M,
|
||||
beyn_function_M_inv_Vhat_gsl_t M_inv_Vhat, void *params, const beyn_contour_t *contour,
|
||||
double rank_tol, double res_tol)
|
||||
|
||||
beyn_result_t *beyn_solve(size_t m, size_t l, beyn_function_M_t M,
|
||||
beyn_function_M_inv_Vhat_t M_inv_Vhat, void *params, const beyn_contour_t *contour,
|
||||
double rank_tol, double res_tol)
|
||||
|
||||
beyn_contour_t *beyn_contour_ellipse(cdouble centre, double halfax_re, double halfax_im, size_t npoints)
|
||||
beyn_contour_t *beyn_contour_halfellipse(cdouble centre, double halfax_re, double halfax_im, size_t npoints,
|
||||
beyn_contour_halfellipse_orientation ori)
|
||||
beyn_contour_t *beyn_contour_kidney(cdouble centre, double halfax_re, double halfax_im, size_t npoints,
|
||||
double rounding, beyn_contour_halfellipse_orientation ori)
|
||||
|
||||
|
||||
cdouble gsl_comlpex_tostd(gsl_complex z)
|
||||
gsl_complex gsl_complex_fromstd(cdouble z)
|
||||
|
||||
|
|
|
|||
|
|
@ -15,7 +15,68 @@ add_executable( test_scalar_ewald32 test_scalar_ewald32.c )
|
|||
target_link_libraries( test_scalar_ewald32 qpms gsl lapacke amos m )
|
||||
target_include_directories( test_scalar_ewald32 PRIVATE .. )
|
||||
|
||||
add_custom_target( mytests DEPENDS test_single_translations_vs_calc test_vswf_translations test_vswf_translations_array )
|
||||
add_executable( kidneycontour kidneycontour.c )
|
||||
target_link_libraries( kidneycontour qpms gsl lapacke amos m )
|
||||
target_include_directories( kidneycontour PRIVATE .. )
|
||||
|
||||
add_executable( tbeyn tbeyn.c )
|
||||
target_link_libraries( tbeyn qpms gsl lapacke amos m )
|
||||
target_include_directories( tbeyn PRIVATE .. )
|
||||
|
||||
add_executable( tbeyn2 tbeyn2.c )
|
||||
target_link_libraries( tbeyn2 qpms gsl lapacke amos m )
|
||||
target_include_directories( tbeyn2 PRIVATE .. )
|
||||
|
||||
add_executable( tbeyn3a tbeyn3.c )
|
||||
target_link_libraries( tbeyn3a qpms gsl lapacke amos m )
|
||||
target_include_directories( tbeyn3a PRIVATE .. )
|
||||
target_compile_definitions( tbeyn3a PRIVATE VARIANTA )
|
||||
|
||||
add_executable( tbeyn3a_implus tbeyn3.c )
|
||||
target_link_libraries( tbeyn3a_implus qpms gsl lapacke amos m )
|
||||
target_include_directories( tbeyn3a_implus PRIVATE .. )
|
||||
target_compile_definitions( tbeyn3a_implus PRIVATE VARIANTA IMPLUS )
|
||||
|
||||
add_executable( tbeyn3a_kidney tbeyn3.c )
|
||||
target_link_libraries( tbeyn3a_kidney qpms gsl lapacke amos m )
|
||||
target_include_directories( tbeyn3a_kidney PRIVATE .. )
|
||||
target_compile_definitions( tbeyn3a_kidney PRIVATE VARIANTA IMPLUS_KIDNEY )
|
||||
|
||||
add_executable( tbeyn3b tbeyn3.c )
|
||||
target_link_libraries( tbeyn3b qpms gsl lapacke amos m )
|
||||
target_include_directories( tbeyn3b PRIVATE .. )
|
||||
target_compile_definitions( tbeyn3b PRIVATE VARIANTB RXSMALL )
|
||||
|
||||
add_executable( tbeyn3bfail tbeyn3.c )
|
||||
target_link_libraries( tbeyn3bfail qpms gsl lapacke amos m )
|
||||
target_include_directories( tbeyn3bfail PRIVATE .. )
|
||||
target_compile_definitions( tbeyn3bfail PRIVATE VARIANTB )
|
||||
|
||||
add_executable( tbeyn3c tbeyn3.c )
|
||||
target_link_libraries( tbeyn3c qpms gsl lapacke amos m )
|
||||
target_include_directories( tbeyn3c PRIVATE .. )
|
||||
target_compile_definitions( tbeyn3c PRIVATE VARIANTC RXSMALL )
|
||||
|
||||
add_executable( tbeyn3d tbeyn3.c )
|
||||
target_link_libraries( tbeyn3d qpms gsl lapacke amos m )
|
||||
target_include_directories( tbeyn3d PRIVATE .. )
|
||||
target_compile_definitions( tbeyn3d PRIVATE VARIANTD RXSMALL )
|
||||
|
||||
add_executable( tbeyn3e tbeyn3.c )
|
||||
target_link_libraries( tbeyn3e qpms gsl lapacke amos m )
|
||||
target_include_directories( tbeyn3e PRIVATE .. )
|
||||
target_compile_definitions( tbeyn3e PRIVATE VARIANTE RXSMALL )
|
||||
|
||||
add_executable( tbeyn3f tbeyn3.c )
|
||||
target_link_libraries( tbeyn3f qpms gsl lapacke amos m )
|
||||
target_include_directories( tbeyn3f PRIVATE .. )
|
||||
target_compile_definitions( tbeyn3f PRIVATE VARIANTF )
|
||||
|
||||
add_executable( tbeyn_gsl tbeyn_gsl.c )
|
||||
target_link_libraries( tbeyn_gsl qpms gsl lapacke amos m )
|
||||
target_include_directories( tbeyn_gsl PRIVATE .. )
|
||||
|
||||
add_custom_target( mytests DEPENDS test_single_translations_vs_calc test_vswf_translations test_vswf_translations_array tbeyn )
|
||||
|
||||
add_test( NAME single_vs_array_translation_coeffs COMMAND test_single_translations_vs_calc )
|
||||
|
||||
|
|
|
|||
|
|
@ -0,0 +1,19 @@
|
|||
#include <qpms/beyn.h>
|
||||
#include <stdio.h>
|
||||
|
||||
#define CPAIR(x) creal(x), cimag(x)
|
||||
|
||||
int main(int argc, char **argv)
|
||||
{
|
||||
double rRe = 2e3, rIm = 1.5e3, rounding = 0.2;
|
||||
complex double centre = 1e3 * I;
|
||||
size_t n = 100;
|
||||
|
||||
beyn_contour_t *c = beyn_contour_kidney(centre, rRe, rIm, rounding, n, BEYN_CONTOUR_HALFELLIPSE_IM_PLUS);
|
||||
|
||||
for(size_t i = 0; i < n; ++i)
|
||||
printf("%g\t%g\t%g\t%g\n", CPAIR(c->z_dz[i][0]), CPAIR(c->z_dz[i][1]));
|
||||
|
||||
free(c);
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -0,0 +1,40 @@
|
|||
#include <qpms/beyn.h>
|
||||
#include <stdio.h>
|
||||
#include <string.h>
|
||||
|
||||
// Matrix as in Beyn, section 4.11
|
||||
int M_function(complex double *target, const size_t m, const complex double z, void *no_params) {
|
||||
complex double d = 2*m - 4*z / (6*m);
|
||||
complex double od = -((double)m) - z / (6*m);
|
||||
|
||||
memset(target, 0, m*m*sizeof(complex double));
|
||||
for (int i = 0; i < m; ++i) {
|
||||
target[i*m + i] = d;
|
||||
if(i > 0) target[i*m + i-1] = od;
|
||||
if(i < m - 1) target[i*m + i+1] = od;
|
||||
}
|
||||
target[m*(m-1) + m-1] = d/2 + z/(z-1);
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
int main() {
|
||||
complex double z0 = 150+2*I;
|
||||
double Rx = 148, Ry = 148;
|
||||
int L = 10, N = 50, dim = 400;
|
||||
beyn_contour_t *contour = beyn_contour_ellipse(z0, Rx, Ry, N);
|
||||
|
||||
beyn_result_t *result =
|
||||
beyn_solve(dim, L, M_function, NULL /*M_inv_Vhat_function*/, NULL /*params*/,
|
||||
contour, 1e-4, 1e-4);
|
||||
printf("Found %zd eigenvalues:\n", result->neig);
|
||||
for (size_t i = 0; i < result->neig; ++i) {
|
||||
complex double eig = result->eigval[i];
|
||||
printf("%zd: %g%+gj\n", i, creal(eig), cimag(eig));
|
||||
}
|
||||
free(contour);
|
||||
beyn_result_free(result);
|
||||
return 0;
|
||||
}
|
||||
|
||||
|
||||
|
|
@ -0,0 +1,62 @@
|
|||
#include <qpms/beyn.h>
|
||||
#include <stdio.h>
|
||||
#include <string.h>
|
||||
#include <stdlib.h>
|
||||
#include <math.h>
|
||||
|
||||
static double randU(double a, double b) {return a + (b-a) * random() * (1. / RAND_MAX); }
|
||||
// Normal distribution via Box-Muller transform
|
||||
static double randN(double sigma, double mu) {
|
||||
double u1 = randU(0,1);
|
||||
double u2 = randU(0,1);
|
||||
return mu + sigma*sqrt(-2*log(u1))*cos(2.*M_PI*u2);
|
||||
}
|
||||
|
||||
struct param49 {
|
||||
double *T0;
|
||||
double *T1;
|
||||
double *T2;
|
||||
};
|
||||
|
||||
// Matrix as in Beyn, example 4.9
|
||||
int M_function(complex double *target, const size_t m, const complex double z, void *params) {
|
||||
struct param49 *p = params;
|
||||
|
||||
for(size_t i = 0; i < m*m; ++i)
|
||||
target[i] = p->T0[i] + z*p->T1[i] + z*z*p->T2[i];
|
||||
return 0;
|
||||
}
|
||||
|
||||
int main(int argc, char **argv) {
|
||||
complex double z0 = 0;
|
||||
double Rx = .3, Ry = .3;
|
||||
int L = 30, N = 150, dim = 60;
|
||||
if (argc > 1) N = atoi(argv[1]);
|
||||
beyn_contour_t *contour = beyn_contour_ellipse(z0, Rx, Ry, N);
|
||||
struct param49 p;
|
||||
p.T0 = malloc(dim*dim*sizeof(double));
|
||||
p.T1 = malloc(dim*dim*sizeof(double));
|
||||
p.T2 = malloc(dim*dim*sizeof(double));
|
||||
for(size_t i = 0; i < dim*dim; ++i) {
|
||||
p.T0[i] = randN(1,0);
|
||||
p.T1[i] = randN(1,0);
|
||||
p.T2[i] = randN(1,0);
|
||||
}
|
||||
|
||||
beyn_result_t *result =
|
||||
beyn_solve(dim, L, M_function, NULL /*M_inv_Vhat_function*/, &p /*params*/,
|
||||
contour, 1e-4, 1e-4);
|
||||
printf("Found %zd eigenvalues:\n", result->neig);
|
||||
for (size_t i = 0; i < result->neig; ++i) {
|
||||
complex double eig = result->eigval[i];
|
||||
printf("%zd: %g%+gj\n", i, creal(eig), cimag(eig));
|
||||
}
|
||||
free(contour);
|
||||
beyn_result_free(result);
|
||||
free(p.T0);
|
||||
free(p.T1);
|
||||
free(p.T2);
|
||||
return 0;
|
||||
}
|
||||
|
||||
|
||||
|
|
@ -0,0 +1,98 @@
|
|||
#define _GNU_SOURCE
|
||||
#include <qpms/beyn.h>
|
||||
#include <stdio.h>
|
||||
#include <string.h>
|
||||
#include <stdlib.h>
|
||||
#include <math.h>
|
||||
#include <fenv.h>
|
||||
|
||||
static double randU(double a, double b) {return a + (b-a) * random() * (1. / RAND_MAX); }
|
||||
// Normal distribution via Box-Muller transform
|
||||
static double randN(double sigma, double mu) {
|
||||
double u1 = randU(0,1);
|
||||
double u2 = randU(0,1);
|
||||
return mu + sigma*sqrt(-2*log(u1))*cos(2.*M_PI*u2);
|
||||
}
|
||||
|
||||
struct param {
|
||||
double *T0;
|
||||
double *T1;
|
||||
double *T2;
|
||||
};
|
||||
|
||||
int M_function(complex double *target, const size_t m, const complex double z, void *params) {
|
||||
struct param *p = params;
|
||||
|
||||
for(size_t i = 0; i < m*m; ++i)
|
||||
target[i] = p->T0[i] + z*p->T1[i] + cexp(
|
||||
#ifdef VARIANTB // Also note that this case requires pretty large contour point number (>~ 3000)
|
||||
(1+3*I)
|
||||
#else // VARIANTA or VARIANTC
|
||||
(1+1*I)
|
||||
#endif
|
||||
*z*p->T2[i]) +
|
||||
#ifdef VARIANTC // Essential singularity at zero
|
||||
cexp(3/z);
|
||||
#elif defined VARIANTD // Essential singularity outside the contour
|
||||
cexp(3/(z-1))
|
||||
#elif defined VARIANTE // High-order pole at zero
|
||||
3/cpow(z,10);
|
||||
#elif defined VARIANTF // High-order pole at zero, higher order than dim
|
||||
.0003/cpow(z,12);
|
||||
#else // double pole at zero
|
||||
3/z/z
|
||||
#endif
|
||||
;
|
||||
return 0;
|
||||
}
|
||||
|
||||
int main(int argc, char **argv) {
|
||||
feenableexcept(FE_INVALID | FE_OVERFLOW);
|
||||
complex double z0 = 0+3e-1*I;
|
||||
#ifdef RXSMALL
|
||||
double Rx = .1;
|
||||
#else
|
||||
double Rx = .3; // Variant B will fail in this case due to large number of eigenvalues (>30)
|
||||
#endif
|
||||
double Ry = .25;
|
||||
#ifdef VARIANTF
|
||||
int L = 10, N = 150, dim = 10;
|
||||
#else
|
||||
int L = 30, N = 150, dim = 60;
|
||||
#endif
|
||||
if (argc > 1) N = atoi(argv[1]);
|
||||
if (argc > 2) L = atoi(argv[2]);
|
||||
#ifdef IMPLUS
|
||||
beyn_contour_t *contour = beyn_contour_halfellipse(z0, Rx, Ry, N, BEYN_CONTOUR_HALFELLIPSE_IM_PLUS);
|
||||
#elif defined IMPLUS_KIDNEY
|
||||
beyn_contour_t *contour = beyn_contour_kidney(z0, Rx, Ry, 0.3, N, BEYN_CONTOUR_HALFELLIPSE_IM_PLUS);
|
||||
#else
|
||||
beyn_contour_t *contour = beyn_contour_ellipse(z0, Rx, Ry, N);
|
||||
#endif
|
||||
struct param p;
|
||||
p.T0 = malloc(dim*dim*sizeof(double));
|
||||
p.T1 = malloc(dim*dim*sizeof(double));
|
||||
p.T2 = malloc(dim*dim*sizeof(double));
|
||||
for(size_t i = 0; i < dim*dim; ++i) {
|
||||
p.T0[i] = randN(1,0);
|
||||
p.T1[i] = randN(1,0);
|
||||
p.T2[i] = randN(1,0);
|
||||
}
|
||||
|
||||
beyn_result_t *result =
|
||||
beyn_solve(dim, L, M_function, NULL /*M_inv_Vhat_function*/, &p /*params*/,
|
||||
contour, 1e-4, 1e-4);
|
||||
printf("Found %zd eigenvalues:\n", result->neig);
|
||||
for (size_t i = 0; i < result->neig; ++i) {
|
||||
complex double eig = result->eigval[i];
|
||||
printf("%zd: %g%+gj\n", i, creal(eig), cimag(eig));
|
||||
}
|
||||
free(contour);
|
||||
beyn_result_free(result);
|
||||
free(p.T0);
|
||||
free(p.T1);
|
||||
free(p.T2);
|
||||
return 0;
|
||||
}
|
||||
|
||||
|
||||
|
|
@ -0,0 +1,42 @@
|
|||
#include <qpms/beyn.h>
|
||||
#include <stdio.h>
|
||||
|
||||
|
||||
// Matrix as in Beyn, section 4.11
|
||||
int M_function(gsl_matrix_complex *target, complex double z, void *no_params) {
|
||||
int m = target->size1;
|
||||
|
||||
gsl_complex d = gsl_complex_fromstd( 2*m - 4*z / (6*m) );
|
||||
gsl_complex od = gsl_complex_fromstd( -(double)m - z / (6*m) );
|
||||
|
||||
gsl_matrix_complex_set_zero(target);
|
||||
for (int i = 0; i < m; ++i) {
|
||||
gsl_matrix_complex_set(target, i, i, d);
|
||||
if(i > 0) gsl_matrix_complex_set(target, i, i-1, od);
|
||||
if(i < m - 1) gsl_matrix_complex_set(target, i, i+1, od);
|
||||
}
|
||||
gsl_matrix_complex_set(target, m-1, m-1, gsl_complex_fromstd(gsl_complex_tostd(d)/2 + z/(z-1)));
|
||||
|
||||
return 0;
|
||||
}
|
||||
|
||||
int main() {
|
||||
complex double z0 = 150+2*I;
|
||||
double Rx = 148, Ry = 148;
|
||||
int L = 10, N = 50, dim = 400;
|
||||
beyn_contour_t *contour = beyn_contour_ellipse(z0, Rx, Ry, N);
|
||||
|
||||
beyn_result_gsl_t *result =
|
||||
beyn_solve_gsl(dim, L, M_function, NULL /*M_inv_Vhat_function*/, NULL /*params*/,
|
||||
contour, 1e-4, 1e-4);
|
||||
printf("Found %zd eigenvalues:\n", result->neig);
|
||||
for (size_t i = 0; i < result->neig; ++i) {
|
||||
gsl_complex eig = gsl_vector_complex_get(result->eigval, i);
|
||||
printf("%zd: %g%+gj\n", i, GSL_REAL(eig), GSL_IMAG(eig));
|
||||
}
|
||||
free(contour);
|
||||
beyn_result_gsl_free(result);
|
||||
return 0;
|
||||
}
|
||||
|
||||
|
||||
Loading…
Reference in New Issue