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-rw-r--r--libcrystfel/src/cell.c1164
1 files changed, 1164 insertions, 0 deletions
diff --git a/libcrystfel/src/cell.c b/libcrystfel/src/cell.c
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+++ b/libcrystfel/src/cell.c
@@ -0,0 +1,1164 @@
+/*
+ * cell.c
+ *
+ * Unit Cell Calculations
+ *
+ * (c) 2006-2010 Thomas White <taw@physics.org>
+ *
+ * Part of CrystFEL - crystallography with a FEL
+ *
+ */
+
+#ifdef HAVE_CONFIG_H
+#include <config.h>
+#endif
+
+#include <math.h>
+#include <stdlib.h>
+#include <stdio.h>
+#include <string.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_blas.h>
+#include <gsl/gsl_linalg.h>
+
+#include "cell.h"
+#include "utils.h"
+#include "image.h"
+
+
+/**
+ * SECTION:unitcell
+ * @short_description: Unit cell
+ * @title: UnitCell
+ * @section_id:
+ * @see_also:
+ * @include: "cell.h"
+ * @Image:
+ *
+ * This structure represents a unit cell.
+ */
+
+
+
+/* Weighting factor of lengths relative to angles */
+#define LWEIGHT (10.0e-9)
+
+typedef enum {
+ CELL_REP_CRYST,
+ CELL_REP_CART,
+ CELL_REP_RECIP
+} CellRepresentation;
+
+struct _unitcell {
+
+ CellRepresentation rep;
+
+ /* Crystallographic representation */
+ double a; /* m */
+ double b; /* m */
+ double c; /* m */
+ double alpha; /* Radians */
+ double beta; /* Radians */
+ double gamma; /* Radians */
+
+ /* Cartesian representation */
+ double ax; double bx; double cx;
+ double ay; double by; double cy;
+ double az; double bz; double cz;
+
+ /* Cartesian representation of reciprocal axes */
+ double axs; double bxs; double cxs;
+ double ays; double bys; double cys;
+ double azs; double bzs; double czs;
+
+ char *pointgroup;
+ char *spacegroup;
+};
+
+
+/************************** Setters and Constructors **************************/
+
+
+/**
+ * cell_new:
+ *
+ * Create a new %UnitCell.
+ *
+ * Returns: the new unit cell, or NULL on failure.
+ *
+ */
+UnitCell *cell_new()
+{
+ UnitCell *cell;
+
+ cell = malloc(sizeof(UnitCell));
+ if ( cell == NULL ) return NULL;
+
+ cell->a = 1.0;
+ cell->b = 1.0;
+ cell->c = 1.0;
+ cell->alpha = M_PI_2;
+ cell->beta = M_PI_2;
+ cell->gamma = M_PI_2;
+
+ cell->rep = CELL_REP_CRYST;
+
+ cell->pointgroup = strdup("1");
+ cell->spacegroup = strdup("P 1");
+
+ return cell;
+}
+
+
+/**
+ * cell_free:
+ * @cell: A %UnitCell to free.
+ *
+ * Frees a %UnitCell, and all internal resources concerning that cell.
+ *
+ */
+void cell_free(UnitCell *cell)
+{
+ if ( cell == NULL ) return;
+ free(cell->pointgroup);
+ free(cell->spacegroup);
+ free(cell);
+}
+
+
+void cell_set_parameters(UnitCell *cell, double a, double b, double c,
+ double alpha, double beta, double gamma)
+{
+ if ( cell == NULL ) return;
+
+ cell->a = a;
+ cell->b = b;
+ cell->c = c;
+ cell->alpha = alpha;
+ cell->beta = beta;
+ cell->gamma = gamma;
+
+ cell->rep = CELL_REP_CRYST;
+}
+
+
+void cell_set_cartesian(UnitCell *cell,
+ double ax, double ay, double az,
+ double bx, double by, double bz,
+ double cx, double cy, double cz)
+{
+ if ( cell == NULL ) return;
+
+ cell->ax = ax; cell->ay = ay; cell->az = az;
+ cell->bx = bx; cell->by = by; cell->bz = bz;
+ cell->cx = cx; cell->cy = cy; cell->cz = cz;
+
+ cell->rep = CELL_REP_CART;
+}
+
+
+void cell_set_cartesian_a(UnitCell *cell, double ax, double ay, double az)
+{
+ if ( cell == NULL ) return;
+ cell->ax = ax; cell->ay = ay; cell->az = az;
+ cell->rep = CELL_REP_CART;
+}
+
+
+void cell_set_cartesian_b(UnitCell *cell, double bx, double by, double bz)
+{
+ if ( cell == NULL ) return;
+ cell->bx = bx; cell->by = by; cell->bz = bz;
+ cell->rep = CELL_REP_CART;
+}
+
+
+void cell_set_cartesian_c(UnitCell *cell, double cx, double cy, double cz)
+{
+ if ( cell == NULL ) return;
+ cell->cx = cx; cell->cy = cy; cell->cz = cz;
+ cell->rep = CELL_REP_CART;
+}
+
+
+UnitCell *cell_new_from_parameters(double a, double b, double c,
+ double alpha, double beta, double gamma)
+{
+ UnitCell *cell;
+
+ cell = cell_new();
+ if ( cell == NULL ) return NULL;
+
+ cell_set_parameters(cell, a, b, c, alpha, beta, gamma);
+
+ return cell;
+}
+
+
+UnitCell *cell_new_from_reciprocal_axes(struct rvec as, struct rvec bs,
+ struct rvec cs)
+{
+ UnitCell *cell;
+
+ cell = cell_new();
+ if ( cell == NULL ) return NULL;
+
+ cell->axs = as.u; cell->ays = as.v; cell->azs = as.w;
+ cell->bxs = bs.u; cell->bys = bs.v; cell->bzs = bs.w;
+ cell->cxs = cs.u; cell->cys = cs.v; cell->czs = cs.w;
+
+ cell->rep = CELL_REP_RECIP;
+
+ return cell;
+}
+
+
+UnitCell *cell_new_from_direct_axes(struct rvec a, struct rvec b, struct rvec c)
+{
+ UnitCell *cell;
+
+ cell = cell_new();
+ if ( cell == NULL ) return NULL;
+
+ cell->ax = a.u; cell->ay = a.v; cell->az = a.w;
+ cell->bx = b.u; cell->by = b.v; cell->bz = b.w;
+ cell->cx = c.u; cell->cy = c.v; cell->cz = c.w;
+
+ cell->rep = CELL_REP_CART;
+
+ return cell;
+}
+
+
+UnitCell *cell_new_from_cell(UnitCell *orig)
+{
+ UnitCell *new;
+ double ax, ay, az, bx, by, bz, cx, cy, cz;
+
+ new = cell_new();
+
+ cell_get_cartesian(orig, &ax, &ay, &az, &bx, &by, &bz, &cx, &cy, &cz);
+ cell_set_cartesian(new, ax, ay, az, bx, by, bz, cx, cy, cz);
+ cell_set_pointgroup(new, orig->pointgroup);
+ cell_set_spacegroup(new, orig->spacegroup);
+
+ return new;
+}
+
+
+void cell_set_reciprocal(UnitCell *cell,
+ double asx, double asy, double asz,
+ double bsx, double bsy, double bsz,
+ double csx, double csy, double csz)
+{
+ if ( cell == NULL ) return;
+
+ cell->axs = asx; cell->ays = asy; cell->azs = asz;
+ cell->bxs = bsx; cell->bys = bsy; cell->bzs = bsz;
+ cell->cxs = csx; cell->cys = csy; cell->czs = csz;
+
+ cell->rep = CELL_REP_RECIP;
+}
+
+
+void cell_set_spacegroup(UnitCell *cell, const char *sym)
+{
+ free(cell->spacegroup);
+ cell->spacegroup = strdup(sym);
+}
+
+
+void cell_set_pointgroup(UnitCell *cell, const char *sym)
+{
+ free(cell->pointgroup);
+ cell->pointgroup = strdup(sym);
+}
+
+
+/************************* Getter helper functions ****************************/
+
+static int cell_crystallographic_to_cartesian(UnitCell *cell,
+ double *ax, double *ay, double *az,
+ double *bx, double *by, double *bz,
+ double *cx, double *cy, double *cz)
+{
+ double tmp, V, cosalphastar, cstar;
+
+ /* Firstly: Get a in terms of x, y and z
+ * +a (cryst) is defined to lie along +x (cart) */
+ *ax = cell->a;
+ *ay = 0.0;
+ *az = 0.0;
+
+ /* b in terms of x, y and z
+ * b (cryst) is defined to lie in the xy (cart) plane */
+ *bx = cell->b*cos(cell->gamma);
+ *by = cell->b*sin(cell->gamma);
+ *bz = 0.0;
+
+ tmp = cos(cell->alpha)*cos(cell->alpha)
+ + cos(cell->beta)*cos(cell->beta)
+ + cos(cell->gamma)*cos(cell->gamma)
+ - 2.0*cos(cell->alpha)*cos(cell->beta)*cos(cell->gamma);
+ V = cell->a * cell->b * cell->c * sqrt(1.0 - tmp);
+
+ cosalphastar = cos(cell->beta)*cos(cell->gamma) - cos(cell->alpha);
+ cosalphastar /= sin(cell->beta)*sin(cell->gamma);
+
+ cstar = (cell->a * cell->b * sin(cell->gamma))/V;
+
+ /* c in terms of x, y and z */
+ *cx = cell->c*cos(cell->beta);
+ *cy = -cell->c*sin(cell->beta)*cosalphastar;
+ *cz = 1.0/cstar;
+
+ return 0;
+}
+
+
+/* Why yes, I do enjoy long argument lists...! */
+static int cell_invert(double ax, double ay, double az,
+ double bx, double by, double bz,
+ double cx, double cy, double cz,
+ double *asx, double *asy, double *asz,
+ double *bsx, double *bsy, double *bsz,
+ double *csx, double *csy, double *csz)
+{
+ int s;
+ gsl_matrix *m;
+ gsl_matrix *inv;
+ gsl_permutation *perm;
+
+ m = gsl_matrix_alloc(3, 3);
+ if ( m == NULL ) {
+ ERROR("Couldn't allocate memory for matrix\n");
+ return 1;
+ }
+ gsl_matrix_set(m, 0, 0, ax);
+ gsl_matrix_set(m, 0, 1, bx);
+ gsl_matrix_set(m, 0, 2, cx);
+ gsl_matrix_set(m, 1, 0, ay);
+ gsl_matrix_set(m, 1, 1, by);
+ gsl_matrix_set(m, 1, 2, cy);
+ gsl_matrix_set(m, 2, 0, az);
+ gsl_matrix_set(m, 2, 1, bz);
+ gsl_matrix_set(m, 2, 2, cz);
+
+ /* Invert */
+ perm = gsl_permutation_alloc(m->size1);
+ if ( perm == NULL ) {
+ ERROR("Couldn't allocate permutation\n");
+ gsl_matrix_free(m);
+ return 1;
+ }
+ inv = gsl_matrix_alloc(m->size1, m->size2);
+ if ( inv == NULL ) {
+ ERROR("Couldn't allocate inverse\n");
+ gsl_matrix_free(m);
+ gsl_permutation_free(perm);
+ return 1;
+ }
+ if ( gsl_linalg_LU_decomp(m, perm, &s) ) {
+ ERROR("Couldn't decompose matrix\n");
+ gsl_matrix_free(m);
+ gsl_permutation_free(perm);
+ return 1;
+ }
+ if ( gsl_linalg_LU_invert(m, perm, inv) ) {
+ ERROR("Couldn't invert matrix\n");
+ gsl_matrix_free(m);
+ gsl_permutation_free(perm);
+ return 1;
+ }
+ gsl_permutation_free(perm);
+ gsl_matrix_free(m);
+
+ /* Transpose */
+ gsl_matrix_transpose(inv);
+
+ *asx = gsl_matrix_get(inv, 0, 0);
+ *bsx = gsl_matrix_get(inv, 0, 1);
+ *csx = gsl_matrix_get(inv, 0, 2);
+ *asy = gsl_matrix_get(inv, 1, 0);
+ *bsy = gsl_matrix_get(inv, 1, 1);
+ *csy = gsl_matrix_get(inv, 1, 2);
+ *asz = gsl_matrix_get(inv, 2, 0);
+ *bsz = gsl_matrix_get(inv, 2, 1);
+ *csz = gsl_matrix_get(inv, 2, 2);
+
+ gsl_matrix_free(inv);
+
+ return 0;
+}
+
+
+/********************************** Getters ***********************************/
+
+int cell_get_parameters(UnitCell *cell, double *a, double *b, double *c,
+ double *alpha, double *beta, double *gamma)
+{
+ double ax, ay, az, bx, by, bz, cx, cy, cz;
+
+ if ( cell == NULL ) return 1;
+
+ switch ( cell->rep ) {
+
+ case CELL_REP_CRYST:
+ /* Direct response */
+ *a = cell->a;
+ *b = cell->b;
+ *c = cell->c;
+ *alpha = cell->alpha;
+ *beta = cell->beta;
+ *gamma = cell->gamma;
+ return 0;
+
+ case CELL_REP_CART:
+ /* Convert cartesian -> crystallographic */
+ *a = modulus(cell->ax, cell->ay, cell->az);
+ *b = modulus(cell->bx, cell->by, cell->bz);
+ *c = modulus(cell->cx, cell->cy, cell->cz);
+
+ *alpha = angle_between(cell->bx, cell->by, cell->bz,
+ cell->cx, cell->cy, cell->cz);
+ *beta = angle_between(cell->ax, cell->ay, cell->az,
+ cell->cx, cell->cy, cell->cz);
+ *gamma = angle_between(cell->ax, cell->ay, cell->az,
+ cell->bx, cell->by, cell->bz);
+ return 0;
+
+ case CELL_REP_RECIP:
+ /* Convert reciprocal -> crystallographic.
+ * Start by converting reciprocal -> cartesian */
+ cell_invert(cell->axs, cell->ays, cell->azs,
+ cell->bxs, cell->bys, cell->bzs,
+ cell->cxs, cell->cys, cell->czs,
+ &ax, &ay, &az, &bx, &by, &bz, &cx, &cy, &cz);
+
+ /* Now convert cartesian -> crystallographic */
+ *a = modulus(ax, ay, az);
+ *b = modulus(bx, by, bz);
+ *c = modulus(cx, cy, cz);
+
+ *alpha = angle_between(bx, by, bz, cx, cy, cz);
+ *beta = angle_between(ax, ay, az, cx, cy, cz);
+ *gamma = angle_between(ax, ay, az, bx, by, bz);
+ return 0;
+ }
+
+ return 1;
+}
+
+
+int cell_get_cartesian(UnitCell *cell,
+ double *ax, double *ay, double *az,
+ double *bx, double *by, double *bz,
+ double *cx, double *cy, double *cz)
+{
+ if ( cell == NULL ) return 1;
+
+ switch ( cell->rep ) {
+
+ case CELL_REP_CRYST:
+ /* Convert crystallographic -> cartesian. */
+ return cell_crystallographic_to_cartesian(cell,
+ ax, ay, az,
+ bx, by, bz,
+ cx, cy, cz);
+
+ case CELL_REP_CART:
+ /* Direct response */
+ *ax = cell->ax; *ay = cell->ay; *az = cell->az;
+ *bx = cell->bx; *by = cell->by; *bz = cell->bz;
+ *cx = cell->cx; *cy = cell->cy; *cz = cell->cz;
+ return 0;
+
+ case CELL_REP_RECIP:
+ /* Convert reciprocal -> cartesian */
+ return cell_invert(cell->axs, cell->ays, cell->azs,
+ cell->bxs, cell->bys, cell->bzs,
+ cell->cxs, cell->cys, cell->czs,
+ ax, ay, az, bx, by, bz, cx, cy, cz);
+
+ }
+
+ return 1;
+}
+
+
+int cell_get_reciprocal(UnitCell *cell,
+ double *asx, double *asy, double *asz,
+ double *bsx, double *bsy, double *bsz,
+ double *csx, double *csy, double *csz)
+{
+ int r;
+ double ax, ay, az, bx, by, bz, cx, cy, cz;
+ if ( cell == NULL ) return 1;
+
+ switch ( cell->rep ) {
+
+ case CELL_REP_CRYST:
+ /* Convert crystallographic -> reciprocal */
+ r = cell_crystallographic_to_cartesian(cell,
+ &ax, &ay, &az,
+ &bx, &by, &bz,
+ &cx, &cy, &cz);
+ if ( r ) return r;
+ return cell_invert(ax, ay, az,bx, by, bz, cx, cy, cz,
+ asx, asy, asz, bsx, bsy, bsz, csx, csy, csz);
+
+ case CELL_REP_CART:
+ /* Convert cartesian -> reciprocal */
+ cell_invert(cell->ax, cell->ay, cell->az,
+ cell->bx, cell->by, cell->bz,
+ cell->cx, cell->cy, cell->cz,
+ asx, asy, asz, bsx, bsy, bsz, csx, csy, csz);
+ return 0;
+
+ case CELL_REP_RECIP:
+ /* Direct response */
+ *asx = cell->axs; *asy = cell->ays; *asz = cell->azs;
+ *bsx = cell->bxs; *bsy = cell->bys; *bsz = cell->bzs;
+ *csx = cell->cxs; *csy = cell->cys; *csz = cell->czs;
+ return 0;
+
+ }
+
+ return 1;
+}
+
+
+const char *cell_get_pointgroup(UnitCell *cell)
+{
+ return cell->pointgroup;
+}
+
+
+const char *cell_get_spacegroup(UnitCell *cell)
+{
+ return cell->spacegroup;
+}
+
+
+
+
+
+/********************************* Utilities **********************************/
+
+static const char *cell_rep(UnitCell *cell)
+{
+ switch ( cell->rep ) {
+ case CELL_REP_CRYST:
+ return "crystallographic, direct space";
+ case CELL_REP_CART:
+ return "cartesian, direct space";
+ case CELL_REP_RECIP:
+ return "cartesian, reciprocal space";
+ }
+
+ return "unknown";
+}
+
+
+/**
+ * cell_rotate:
+ * @in: A %UnitCell to rotate
+ * @quat: A %quaternion
+ *
+ * Rotate a %UnitCell using a %quaternion.
+ *
+ * Returns: a newly allocated rotated copy of @in.
+ *
+ */
+UnitCell *cell_rotate(UnitCell *in, struct quaternion quat)
+{
+ struct rvec a, b, c;
+ struct rvec an, bn, cn;
+ UnitCell *out = cell_new_from_cell(in);
+
+ cell_get_cartesian(in, &a.u, &a.v, &a.w,
+ &b.u, &b.v, &b.w,
+ &c.u, &c.v, &c.w);
+
+ an = quat_rot(a, quat);
+ bn = quat_rot(b, quat);
+ cn = quat_rot(c, quat);
+
+ cell_set_cartesian(out, an.u, an.v, an.w,
+ bn.u, bn.v, bn.w,
+ cn.u, cn.v, cn.w);
+
+ return out;
+}
+
+
+void cell_print(UnitCell *cell)
+{
+ double asx, asy, asz;
+ double bsx, bsy, bsz;
+ double csx, csy, csz;
+ double a, b, c, alpha, beta, gamma;
+ double ax, ay, az, bx, by, bz, cx, cy, cz;
+
+ cell_get_parameters(cell, &a, &b, &c, &alpha, &beta, &gamma);
+
+ STATUS(" a b c alpha beta gamma\n");
+ STATUS("%5.2f %5.2f %5.2f nm %6.2f %6.2f %6.2f deg\n",
+ a*1e9, b*1e9, c*1e9,
+ rad2deg(alpha), rad2deg(beta), rad2deg(gamma));
+
+ cell_get_cartesian(cell, &ax, &ay, &az, &bx, &by, &bz, &cx, &cy, &cz);
+
+ STATUS("a = %10.3e %10.3e %10.3e m\n", ax, ay, az);
+ STATUS("b = %10.3e %10.3e %10.3e m\n", bx, by, bz);
+ STATUS("c = %10.3e %10.3e %10.3e m\n", cx, cy, cz);
+
+ cell_get_reciprocal(cell, &asx, &asy, &asz,
+ &bsx, &bsy, &bsz,
+ &csx, &csy, &csz);
+
+ STATUS("astar = %10.3e %10.3e %10.3e m^-1 (modulus = %10.3e m^-1)\n",
+ asx, asy, asz, modulus(asx, asy, asz));
+ STATUS("bstar = %10.3e %10.3e %10.3e m^-1 (modulus = %10.3e m^-1)\n",
+ bsx, bsy, bsz, modulus(bsx, bsy, bsz));
+ STATUS("cstar = %10.3e %10.3e %10.3e m^-1 (modulus = %10.3e m^-1)\n",
+ csx, csy, csz, modulus(csx, csy, csz));
+
+ STATUS("Point group: %s\n", cell_get_pointgroup(cell));
+ STATUS("Cell representation is %s.\n", cell_rep(cell));
+}
+
+
+#define MAX_CAND (1024)
+
+static int right_handed(struct rvec a, struct rvec b, struct rvec c)
+{
+ struct rvec aCb;
+ double aCb_dot_c;
+
+ /* "a" cross "b" */
+ aCb.u = a.v*b.w - a.w*b.v;
+ aCb.v = - (a.u*b.w - a.w*b.u);
+ aCb.w = a.u*b.v - a.v*b.u;
+
+ /* "a cross b" dot "c" */
+ aCb_dot_c = aCb.u*c.u + aCb.v*c.v + aCb.w*c.w;
+
+ if ( aCb_dot_c > 0.0 ) return 1;
+ return 0;
+}
+
+
+struct cvec {
+ struct rvec vec;
+ float na;
+ float nb;
+ float nc;
+ float fom;
+};
+
+
+static int same_vector(struct cvec a, struct cvec b)
+{
+ if ( a.na != b.na ) return 0;
+ if ( a.nb != b.nb ) return 0;
+ if ( a.nc != b.nc ) return 0;
+ return 1;
+}
+
+
+/* Attempt to make 'cell' fit into 'template' somehow */
+UnitCell *match_cell(UnitCell *cell, UnitCell *template, int verbose,
+ int reduce)
+{
+ signed int n1l, n2l, n3l;
+ double asx, asy, asz;
+ double bsx, bsy, bsz;
+ double csx, csy, csz;
+ int i, j;
+ double lengths[3];
+ double angles[3];
+ struct cvec *cand[3];
+ UnitCell *new_cell = NULL;
+ float best_fom = +999999999.9; /* Large number.. */
+ int ncand[3] = {0,0,0};
+ signed int ilow, ihigh;
+ float ltl = 5.0; /* percent */
+ float angtol = deg2rad(1.5);
+
+ if ( cell_get_reciprocal(template, &asx, &asy, &asz,
+ &bsx, &bsy, &bsz,
+ &csx, &csy, &csz) ) {
+ ERROR("Couldn't get reciprocal cell for template.\n");
+ return NULL;
+ }
+
+ lengths[0] = modulus(asx, asy, asz);
+ lengths[1] = modulus(bsx, bsy, bsz);
+ lengths[2] = modulus(csx, csy, csz);
+
+ angles[0] = angle_between(bsx, bsy, bsz, csx, csy, csz);
+ angles[1] = angle_between(asx, asy, asz, csx, csy, csz);
+ angles[2] = angle_between(asx, asy, asz, bsx, bsy, bsz);
+
+ cand[0] = malloc(MAX_CAND*sizeof(struct cvec));
+ cand[1] = malloc(MAX_CAND*sizeof(struct cvec));
+ cand[2] = malloc(MAX_CAND*sizeof(struct cvec));
+
+ if ( cell_get_reciprocal(cell, &asx, &asy, &asz,
+ &bsx, &bsy, &bsz,
+ &csx, &csy, &csz) ) {
+ ERROR("Couldn't get reciprocal cell.\n");
+ return NULL;
+ }
+
+ if ( reduce ) {
+ ilow = -2; ihigh = 4;
+ } else {
+ ilow = 0; ihigh = 1;
+ }
+
+ /* Negative values mean 1/n, positive means n, zero means zero */
+ for ( n1l=ilow; n1l<=ihigh; n1l++ ) {
+ for ( n2l=ilow; n2l<=ihigh; n2l++ ) {
+ for ( n3l=ilow; n3l<=ihigh; n3l++ ) {
+
+ float n1, n2, n3;
+ signed int b1, b2, b3;
+
+ n1 = (n1l>=0) ? (n1l) : (1.0/n1l);
+ n2 = (n2l>=0) ? (n2l) : (1.0/n2l);
+ n3 = (n3l>=0) ? (n3l) : (1.0/n3l);
+
+ if ( !reduce ) {
+ if ( n1l + n2l + n3l > 1 ) continue;
+ }
+
+ /* 'bit' values can be +1 or -1 */
+ for ( b1=-1; b1<=1; b1+=2 ) {
+ for ( b2=-1; b2<=1; b2+=2 ) {
+ for ( b3=-1; b3<=1; b3+=2 ) {
+
+ double tx, ty, tz;
+ double tlen;
+ int i;
+
+ n1 *= b1; n2 *= b2; n3 *= b3;
+
+ tx = n1*asx + n2*bsx + n3*csx;
+ ty = n1*asy + n2*bsy + n3*csy;
+ tz = n1*asz + n2*bsz + n3*csz;
+ tlen = modulus(tx, ty, tz);
+
+ /* Test modulus for agreement with moduli of template */
+ for ( i=0; i<3; i++ ) {
+
+ if ( !within_tolerance(lengths[i], tlen, ltl) )
+ continue;
+
+ cand[i][ncand[i]].vec.u = tx;
+ cand[i][ncand[i]].vec.v = ty;
+ cand[i][ncand[i]].vec.w = tz;
+ cand[i][ncand[i]].na = n1;
+ cand[i][ncand[i]].nb = n2;
+ cand[i][ncand[i]].nc = n3;
+ cand[i][ncand[i]].fom = fabs(lengths[i] - tlen);
+ if ( ncand[i] == MAX_CAND ) {
+ ERROR("Too many candidates\n");
+ } else {
+ ncand[i]++;
+ }
+ }
+
+ }
+ }
+ }
+
+ }
+ }
+ }
+
+ if ( verbose ) {
+ STATUS("Candidates: %i %i %i\n", ncand[0], ncand[1], ncand[2]);
+ }
+
+ for ( i=0; i<ncand[0]; i++ ) {
+ for ( j=0; j<ncand[1]; j++ ) {
+
+ double ang;
+ int k;
+ float fom1;
+
+ if ( same_vector(cand[0][i], cand[1][j]) ) continue;
+
+ /* Measure the angle between the ith candidate for axis 0
+ * and the jth candidate for axis 1 */
+ ang = angle_between(cand[0][i].vec.u, cand[0][i].vec.v,
+ cand[0][i].vec.w, cand[1][j].vec.u,
+ cand[1][j].vec.v, cand[1][j].vec.w);
+
+ /* Angle between axes 0 and 1 should be angle 2 */
+ if ( fabs(ang - angles[2]) > angtol ) continue;
+
+ fom1 = fabs(ang - angles[2]);
+
+ for ( k=0; k<ncand[2]; k++ ) {
+
+ float fom2, fom3;
+
+ if ( same_vector(cand[1][j], cand[2][k]) ) continue;
+
+ /* Measure the angle between the current candidate for
+ * axis 0 and the kth candidate for axis 2 */
+ ang = angle_between(cand[0][i].vec.u, cand[0][i].vec.v,
+ cand[0][i].vec.w, cand[2][k].vec.u,
+ cand[2][k].vec.v, cand[2][k].vec.w);
+
+ /* ... it should be angle 1 ... */
+ if ( fabs(ang - angles[1]) > angtol ) continue;
+
+ fom2 = fom1 + fabs(ang - angles[1]);
+
+ /* Finally, the angle between the current candidate for
+ * axis 1 and the kth candidate for axis 2 */
+ ang = angle_between(cand[1][j].vec.u, cand[1][j].vec.v,
+ cand[1][j].vec.w, cand[2][k].vec.u,
+ cand[2][k].vec.v, cand[2][k].vec.w);
+
+ /* ... it should be angle 0 ... */
+ if ( fabs(ang - angles[0]) > angtol ) continue;
+
+ /* Unit cell must be right-handed */
+ if ( !right_handed(cand[0][i].vec, cand[1][j].vec,
+ cand[2][k].vec) ) continue;
+
+ fom3 = fom2 + fabs(ang - angles[0]);
+ fom3 += LWEIGHT * (cand[0][i].fom + cand[1][j].fom
+ + cand[2][k].fom);
+
+ if ( fom3 < best_fom ) {
+ if ( new_cell != NULL ) free(new_cell);
+ new_cell = cell_new_from_reciprocal_axes(
+ cand[0][i].vec, cand[1][j].vec,
+ cand[2][k].vec);
+ best_fom = fom3;
+ }
+
+ }
+
+ }
+ }
+
+ free(cand[0]);
+ free(cand[1]);
+ free(cand[2]);
+
+ return new_cell;
+}
+
+
+
+UnitCell *match_cell_ab(UnitCell *cell, UnitCell *template)
+{
+ double ax, ay, az;
+ double bx, by, bz;
+ double cx, cy, cz;
+ int i;
+ double lengths[3];
+ int used[3];
+ struct rvec real_a, real_b, real_c;
+ struct rvec params[3];
+ double alen, blen, clen;
+ float ltl = 5.0; /* percent */
+ int have_real_a;
+ int have_real_b;
+ int have_real_c;
+
+ /* Get the lengths to match */
+ if ( cell_get_cartesian(template, &ax, &ay, &az,
+ &bx, &by, &bz,
+ &cx, &cy, &cz) )
+ {
+ ERROR("Couldn't get cell for template.\n");
+ return NULL;
+ }
+ alen = modulus(ax, ay, az);
+ blen = modulus(bx, by, bz);
+ clen = modulus(cx, cy, cz);
+
+ /* Get the lengths from the cell and turn them into anonymous vectors */
+ if ( cell_get_cartesian(cell, &ax, &ay, &az,
+ &bx, &by, &bz,
+ &cx, &cy, &cz) )
+ {
+ ERROR("Couldn't get cell.\n");
+ return NULL;
+ }
+ lengths[0] = modulus(ax, ay, az);
+ lengths[1] = modulus(bx, by, bz);
+ lengths[2] = modulus(cx, cy, cz);
+ used[0] = 0; used[1] = 0; used[2] = 0;
+ params[0].u = ax; params[0].v = ay; params[0].w = az;
+ params[1].u = bx; params[1].v = by; params[1].w = bz;
+ params[2].u = cx; params[2].v = cy; params[2].w = cz;
+
+ real_a.u = 0.0; real_a.v = 0.0; real_a.w = 0.0;
+ real_b.u = 0.0; real_b.v = 0.0; real_b.w = 0.0;
+ real_c.u = 0.0; real_c.v = 0.0; real_c.w = 0.0;
+
+ /* Check each vector against a and b */
+ have_real_a = 0;
+ have_real_b = 0;
+ for ( i=0; i<3; i++ ) {
+ if ( within_tolerance(lengths[i], alen, ltl)
+ && !used[i] && !have_real_a )
+ {
+ used[i] = 1;
+ memcpy(&real_a, &params[i], sizeof(struct rvec));
+ have_real_a = 1;
+ }
+ if ( within_tolerance(lengths[i], blen, ltl)
+ && !used[i] && !have_real_b )
+ {
+ used[i] = 1;
+ memcpy(&real_b, &params[i], sizeof(struct rvec));
+ have_real_b = 1;
+ }
+ }
+
+ /* Have we matched both a and b? */
+ if ( !(have_real_a && have_real_b) ) return NULL;
+
+ /* "c" is "the other one" */
+ have_real_c = 0;
+ for ( i=0; i<3; i++ ) {
+ if ( !used[i] ) {
+ memcpy(&real_c, &params[i], sizeof(struct rvec));
+ have_real_c = 1;
+ }
+ }
+
+ if ( !have_real_c ) {
+ ERROR("Huh? Couldn't find the third vector.\n");
+ ERROR("Matches: %i %i %i\n", used[0], used[1], used[2]);
+ return NULL;
+ }
+
+ /* Flip c if not right-handed */
+ if ( !right_handed(real_a, real_b, real_c) ) {
+ real_c.u = -real_c.u;
+ real_c.v = -real_c.v;
+ real_c.w = -real_c.w;
+ }
+
+ return cell_new_from_direct_axes(real_a, real_b, real_c);
+}
+
+
+/* Return sin(theta)/lambda = 1/2d. Multiply by two if you want 1/d */
+double resolution(UnitCell *cell, signed int h, signed int k, signed int l)
+{
+ double a, b, c, alpha, beta, gamma;
+
+ cell_get_parameters(cell, &a, &b, &c, &alpha, &beta, &gamma);
+
+ const double Vsq = a*a*b*b*c*c*(1 - cos(alpha)*cos(alpha)
+ - cos(beta)*cos(beta)
+ - cos(gamma)*cos(gamma)
+ + 2*cos(alpha)*cos(beta)*cos(gamma) );
+
+ const double S11 = b*b*c*c*sin(alpha)*sin(alpha);
+ const double S22 = a*a*c*c*sin(beta)*sin(beta);
+ const double S33 = a*a*b*b*sin(gamma)*sin(gamma);
+ const double S12 = a*b*c*c*(cos(alpha)*cos(beta) - cos(gamma));
+ const double S23 = a*a*b*c*(cos(beta)*cos(gamma) - cos(alpha));
+ const double S13 = a*b*b*c*(cos(gamma)*cos(alpha) - cos(beta));
+
+ const double brackets = S11*h*h + S22*k*k + S33*l*l
+ + 2*S12*h*k + 2*S23*k*l + 2*S13*h*l;
+ const double oneoverdsq = brackets / Vsq;
+ const double oneoverd = sqrt(oneoverdsq);
+
+ return oneoverd / 2;
+}
+
+
+static void cell_set_pointgroup_from_pdb(UnitCell *cell, const char *sym)
+{
+ char *new = NULL;
+
+ if ( strcmp(sym, "P 1") == 0 ) new = "1";
+ if ( strcmp(sym, "P 63") == 0 ) new = "6";
+ if ( strcmp(sym, "P 21 21 21") == 0 ) new = "222";
+ if ( strcmp(sym, "P 2 2 2") == 0 ) new = "222";
+ if ( strcmp(sym, "P 43 21 2") == 0 ) new = "422";
+
+ if ( new != NULL ) {
+ cell_set_pointgroup(cell, new);
+ } else {
+ ERROR("Can't determine point group for '%s'\n", sym);
+ }
+}
+
+
+UnitCell *load_cell_from_pdb(const char *filename)
+{
+ FILE *fh;
+ char *rval;
+ UnitCell *cell = NULL;
+
+ fh = fopen(filename, "r");
+ if ( fh == NULL ) {
+ ERROR("Couldn't open '%s'\n", filename);
+ return NULL;
+ }
+
+ do {
+
+ char line[1024];
+
+ rval = fgets(line, 1023, fh);
+
+ if ( strncmp(line, "CRYST1", 6) == 0 ) {
+
+ float a, b, c, al, be, ga;
+ char as[10], bs[10], cs[10];
+ char als[8], bes[8], gas[8];
+ char *sym;
+ int r;
+
+ memcpy(as, line+6, 9); as[9] = '\0';
+ memcpy(bs, line+15, 9); bs[9] = '\0';
+ memcpy(cs, line+24, 9); cs[9] = '\0';
+ memcpy(als, line+33, 7); als[7] = '\0';
+ memcpy(bes, line+40, 7); bes[7] = '\0';
+ memcpy(gas, line+47, 7); gas[7] = '\0';
+
+ r = sscanf(as, "%f", &a);
+ r += sscanf(bs, "%f", &b);
+ r += sscanf(cs, "%f", &c);
+ r += sscanf(als, "%f", &al);
+ r += sscanf(bes, "%f", &be);
+ r += sscanf(gas, "%f", &ga);
+
+ if ( r != 6 ) {
+ STATUS("Couldn't understand CRYST1 line.\n");
+ continue;
+ }
+
+ cell = cell_new_from_parameters(a*1e-10,
+ b*1e-10, c*1e-10,
+ deg2rad(al),
+ deg2rad(be),
+ deg2rad(ga));
+
+ if ( strlen(line) > 65 ) {
+ sym = strndup(line+55, 10);
+ notrail(sym);
+ cell_set_pointgroup_from_pdb(cell, sym);
+ cell_set_spacegroup(cell, sym);
+ free(sym);
+ } else {
+ cell_set_pointgroup_from_pdb(cell, "P 1");
+ cell_set_spacegroup(cell, "P 1");
+ ERROR("CRYST1 line without space group.\n");
+ }
+
+ break; /* Done */
+ }
+
+ } while ( rval != NULL );
+
+ fclose(fh);
+
+ return cell;
+}
+
+
+#ifdef GSL_FUDGE
+/* Force the linker to bring in CBLAS to make GSL happy */
+void cell_fudge_gslcblas()
+{
+ STATUS("%p\n", cblas_sgemm);
+}
+#endif
+
+
+UnitCell *rotate_cell(UnitCell *in, double omega, double phi, double rot)
+{
+ UnitCell *out;
+ double asx, asy, asz;
+ double bsx, bsy, bsz;
+ double csx, csy, csz;
+ double xnew, ynew, znew;
+
+ cell_get_reciprocal(in, &asx, &asy, &asz, &bsx, &bsy,
+ &bsz, &csx, &csy, &csz);
+
+ /* Rotate by "omega" about +z (parallel to c* and c unless triclinic) */
+ xnew = asx*cos(omega) + asy*sin(omega);
+ ynew = -asx*sin(omega) + asy*cos(omega);
+ znew = asz;
+ asx = xnew; asy = ynew; asz = znew;
+ xnew = bsx*cos(omega) + bsy*sin(omega);
+ ynew = -bsx*sin(omega) + bsy*cos(omega);
+ znew = bsz;
+ bsx = xnew; bsy = ynew; bsz = znew;
+ xnew = csx*cos(omega) + csy*sin(omega);
+ ynew = -csx*sin(omega) + csy*cos(omega);
+ znew = csz;
+ csx = xnew; csy = ynew; csz = znew;
+
+ /* Rotate by "phi" about +x (not parallel to anything specific) */
+ xnew = asx;
+ ynew = asy*cos(phi) + asz*sin(phi);
+ znew = -asy*sin(phi) + asz*cos(phi);
+ asx = xnew; asy = ynew; asz = znew;
+ xnew = bsx;
+ ynew = bsy*cos(phi) + bsz*sin(phi);
+ znew = -bsy*sin(phi) + bsz*cos(phi);
+ bsx = xnew; bsy = ynew; bsz = znew;
+ xnew = csx;
+ ynew = csy*cos(phi) + csz*sin(phi);
+ znew = -csy*sin(phi) + csz*cos(phi);
+ csx = xnew; csy = ynew; csz = znew;
+
+ /* Rotate by "rot" about the new +z (in-plane rotation) */
+ xnew = asx*cos(rot) + asy*sin(rot);
+ ynew = -asx*sin(rot) + asy*cos(rot);
+ znew = asz;
+ asx = xnew; asy = ynew; asz = znew;
+ xnew = bsx*cos(rot) + bsy*sin(rot);
+ ynew = -bsx*sin(rot) + bsy*cos(rot);
+ znew = bsz;
+ bsx = xnew; bsy = ynew; bsz = znew;
+ xnew = csx*cos(rot) + csy*sin(rot);
+ ynew = -csx*sin(rot) + csy*cos(rot);
+ znew = csz;
+ csx = xnew; csy = ynew; csz = znew;
+
+ out = cell_new_from_cell(in);
+ cell_set_reciprocal(out, asx, asy, asz, bsx, bsy, bsz, csx, csy, csz);
+
+ return out;
+}
+
+
+int cell_is_sensible(UnitCell *cell)
+{
+ double a, b, c, al, be, ga;
+
+ cell_get_parameters(cell, &a, &b, &c, &al, &be, &ga);
+ if ( al + be + ga >= 2.0*M_PI ) return 0;
+ if ( al + be - ga >= 2.0*M_PI ) return 0;
+ if ( al - be + ga >= 2.0*M_PI ) return 0;
+ if ( - al + be + ga >= 2.0*M_PI ) return 0;
+ if ( al + be + ga <= 0.0 ) return 0;
+ if ( al + be - ga <= 0.0 ) return 0;
+ if ( al - be + ga <= 0.0 ) return 0;
+ if ( - al + be + ga <= 0.0 ) return 0;
+ if ( isnan(al) ) return 0;
+ if ( isnan(be) ) return 0;
+ if ( isnan(ga) ) return 0;
+ return 1;
+}
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