149 lines
3.8 KiB
C
149 lines
3.8 KiB
C
#ifndef QPMS_TYPES_H
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#define QPMS_TYPES_H
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#include <complex.h>
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#include <stdbool.h>
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#include <stddef.h>
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#ifndef M_PI_2
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#define M_PI_2 (1.570796326794896619231321691639751442098584699687552910487)
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#endif
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#ifndef M_PI
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#define M_PI (3.14159265358979323846)
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#endif
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// integer index types
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typedef int qpms_lm_t;
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typedef int qpms_l_t; // can't be unsigned because of the behaviour under - operator
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typedef qpms_lm_t qpms_m_t;
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typedef size_t qpms_y_t;
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typedef enum {
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QPMS_SUCCESS = 0,
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QPMS_ERROR = 1
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} qpms_errno_t;
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// Normalisations
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//const int QPMS_NORMALISATION_T_CSBIT = 128;
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#define QPMS_NORMALISATION_T_CSBIT 128
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typedef enum {
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// As in TODO
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QPMS_NORMALISATION_XU = 3,
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QPMS_NORMALISATION_NONE = QPMS_NORMALISATION_XU,
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// As in http://www.eit.lth.se/fileadmin/eit/courses/eit080f/Literature/book.pdf, power-normalised
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QPMS_NORMALISATION_KRISTENSSON = 2,
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QPMS_NORMALISATION_POWER = QPMS_NORMALISATION_KRISTENSSON,
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// as in TODO
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QPMS_NORMALISATION_TAYLOR = 1,
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QPMS_NORMALISATION_SPHARM = QPMS_NORMALISATION_TAYLOR,
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// Variants with Condon-Shortley phase
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QPMS_NORMALISATION_XU_CS = QPMS_NORMALISATION_XU | QPMS_NORMALISATION_T_CSBIT,
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QPMS_NORMALISATION_NONE_CS = QPMS_NORMALISATION_XU_CS,
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QPMS_NORMALISATION_KRISTENSSON_CS = QPMS_NORMALISATION_KRISTENSSON | QPMS_NORMALISATION_T_CSBIT,
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QPMS_NORMALISATION_POWER_CS = QPMS_NORMALISATION_KRISTENSSON_CS,
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QPMS_NORMALISATION_TAYLOR_CS = QPMS_NORMALISATION_TAYLOR | QPMS_NORMALISATION_T_CSBIT,
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QPMS_NORMALISATION_SPHARM_CS = QPMS_NORMALISATION_TAYLOR_CS,
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QPMS_NORMALISATION_UNDEF = 0
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} qpms_normalisation_t;
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static inline int qpms_normalisation_t_csphase(qpms_normalisation_t norm) {
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return (norm & QPMS_NORMALISATION_T_CSBIT)? -1 : 1;
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}
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static inline int qpms_normalisation_t_normonly(qpms_normalisation_t norm) {
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return norm & (~QPMS_NORMALISATION_T_CSBIT);
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}
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// TODO move the inlines elsewhere
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#include <math.h>
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#include <assert.h>
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// relative to QPMS_NORMALISATION_KRISTENSSON_CS, i.e.
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// P_l^m[normtype] = P_l^m[Kristensson]
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static inline double qpms_normalisation_t_factor(qpms_normalisation_t norm, qpms_l_t l, qpms_m_t m) {
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int csphase = qpms_normalisation_t_csphase(norm);
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norm = qpms_normalisation_t_normonly(norm);
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double factor;
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switch (norm) {
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case QPMS_NORMALISATION_KRISTENSSON:
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factor = 1.;
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break;
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case QPMS_NORMALISATION_TAYLOR:
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factor = sqrt(l*(l+1));
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break;
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case QPMS_NORMALISATION_XU:
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factor = sqrt(l*(l+1) * 4 * M_PI / (2*l+1) * exp(lgamma(l+m+1)-lgamma(l-m+1)));
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break;
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default:
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assert(0);
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}
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factor *= (m%2)?(-csphase):1;
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return factor;
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}
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// TODO move elsewhere
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static inline double qpms_normalisation_t_factor_abssquare(qpms_normalisation_t norm, qpms_l_t l, qpms_m_t m) {
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norm = qpms_normalisation_t_normonly(norm);
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switch (norm) {
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case QPMS_NORMALISATION_KRISTENSSON:
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return 1.;
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break;
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case QPMS_NORMALISATION_TAYLOR:
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return l*(l+1);
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break;
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case QPMS_NORMALISATION_XU:
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return l*(l+1) * 4 * M_PI / (2*l+1) * exp(lgamma(l+m+1)-lgamma(l-m+1));
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break;
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default:
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assert(0);
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return NAN;
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}
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}
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typedef enum {
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QPMS_BESSEL_REGULAR = 1, // regular function j
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QPMS_BESSEL_SINGULAR = 2, // singular function y
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QPMS_HANKEL_PLUS = 3, // hankel function h1 = j + I*y
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QPMS_HANKEL_MINUS = 4, // hankel function h2 = j - I*y
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QPMS_BESSEL_UNDEF = 0
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} qpms_bessel_t;
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// coordinate system types
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typedef struct {
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double x, y, z;
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} cart3_t;
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typedef struct {
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complex double x, y, z;
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} ccart3_t;
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typedef struct {
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double x, y;
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} cart2_t;
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typedef struct {
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double r, theta, phi;
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} sph_t;
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typedef struct { // Do I really need this???
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complex double r;
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double theta, phi;
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} csph_t;
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// complex vector components in local spherical basis
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typedef struct {
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complex double rc, thetac, phic;
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} csphvec_t;
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typedef struct {
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double r, phi;
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} pol_t;
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#define lmcheck(l,m) assert((l) >= 1 && abs(m) <= (l))
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#endif // QPMS_TYPES
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