WIP Alternative integration contour (untested)
Former-commit-id: c82da58ac33364797d7175a69feed475184937d9
This commit is contained in:
Marek Nečada
parent
2e7b925be2
commit
d6084f3264
142
qpms/beyn.c
142
qpms/beyn.c
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@ -19,6 +19,7 @@
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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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@ -85,6 +86,36 @@ beyn_contour_t *beyn_contour_ellipse(complex double centre, double rRe, double r
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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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@ -96,8 +127,6 @@ beyn_contour_t *beyn_contour_halfellipse(complex double centre, double rRe,
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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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const double positive_zero = copysign(0., +1.);
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const double negative_zero = copysign(0., -1.);
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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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@ -125,27 +154,7 @@ beyn_contour_t *beyn_contour_halfellipse(complex double centre, double rRe,
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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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complex double z = centre + faktor * t * 2 * l / nline;
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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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c->z_dz[narc + i][0] = z;
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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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@ -157,6 +166,93 @@ beyn_contour_t *beyn_contour_halfellipse(complex double centre, double rRe,
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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, dt < 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 * y * (- 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, dt < t_hi; ++i) {
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double phi = (t - t_lo) / h + M_PI_2 + alpha;
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c->z_dz[i][0] = centre + (ar * (h * cos(phi)) + h * (1 + sin(phi)) * I) * faktor;
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c->z_dz[i][1] = dt * h * (- 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, dt < 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 * y * (- 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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