/* * cell.c * * Unit Cell Calculations * * (c) 2006-2010 Thomas White * * Part of CrystFEL - crystallography with a FEL * */ #ifdef HAVE_CONFIG_H #include #endif #include #include #include #include #include #include #include "cell.h" #include "utils.h" #include "image.h" /* 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; }; /************************** Setters and Constructors **************************/ 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"); return 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_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_cell(UnitCell *orig) { UnitCell *new; new = malloc(sizeof(UnitCell)); *new = *orig; 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; } /************************* 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; } /********************************* Utilities **********************************/ void cell_print(UnitCell *cell) { double asx, asy, asz; double bsx, bsy, bsz; double csx, csy, csz; double angles[3]; 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)); 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); } #define MAX_CAND (1024) static int within_tolerance(double a, double b, double percent) { double tol = a * (percent/100.0); if ( fabs(b-a) < tol ) 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) { 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}; float ltl = 5.0; /* percent */ float angtol = deg2rad(1.5); if ( verbose ) { STATUS("Matching with this model cell: " "----------------------------\n"); cell_print(template); STATUS("-------------------------------" "----------------------------\n"); } 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; } /* Negative values mean 1/n, positive means n, zero means zero */ for ( n1l=-2; n1l<=4; n1l++ ) { for ( n2l=-2; n2l<=4; n2l++ ) { for ( n3l=-2; n3l<=4; 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); /* '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 angtol ) continue; fom1 = fabs(ang - angles[2]); for ( k=0; k 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; 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_axes(cand[0][i].vec, cand[1][j].vec, cand[2][k].vec); best_fom = fom3; } } } } if ( new_cell != NULL ) { STATUS("Success! --------------- \n"); cell_print(new_cell); } free(cand[0]); free(cand[1]); free(cand[2]); return new_cell; } /* 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 63") == 0 ) new = "6"; if ( new != NULL ) { free(cell->pointgroup); cell->pointgroup = strdup(new); } else { ERROR("Can't determine point group for space group %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; int r; char *sym; r = sscanf(line+7, "%f %f %f %f %f %f\n", &a, &b, &c, &al, &be, &ga); if ( r != 6 ) { ERROR("Couldn't understand CRYST1 line\n"); return NULL; } cell = cell_new_from_parameters(a*1e-10, b*1e-10, c*1e-10, deg2rad(al), deg2rad(be), deg2rad(ga)); sym = strndup(line+55, 11); notrail(sym); cell_set_pointgroup_from_pdb(cell, sym); free(sym); } } while ( rval != NULL ); fclose(fh); return cell; }