Merge branch 'tom/symmetry'

1 files changed, 1205 insertions, 0 deletions

diff --git a/libcrystfel/src/cell-utils.c b/libcrystfel/src/cell-utils.c
new file mode 100644
index 00000000..3aaae90e
--- /dev/null
+++ b/libcrystfel/src/cell-utils.c
@@ -0,0 +1,1205 @@
+/*
+ * cell-utils.c
+ *
+ * Unit Cell utility functions
+ *
+ * Copyright © 2012 Deutsches Elektronen-Synchrotron DESY,
+ *                  a research centre of the Helmholtz Association.
+ * Copyright © 2012 Lorenzo Galli
+ *
+ * Authors:
+ *   2009-2012 Thomas White <taw@physics.org>
+ *   2012      Lorenzo Galli
+ *
+ * This file is part of CrystFEL.
+ *
+ * CrystFEL is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * CrystFEL is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with CrystFEL.  If not, see <http://www.gnu.org/licenses/>.
+ *
+ */
+
+#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 <assert.h>
+
+#include "cell.h"
+#include "cell-utils.h"
+#include "utils.h"
+#include "image.h"
+
+
+/**
+ * SECTION:cell-utils
+ * @short_description: Unit cell utilities
+ * @title: Unit cell utilities
+ * @section_id:
+ * @see_also:
+ * @include: "cell-utils.h"
+ * @Image:
+ *
+ * There are some utility functions associated with the core %UnitCell.
+ **/
+
+
+/* Weighting factor of lengths relative to angles */
+#define LWEIGHT (10.0e-9)
+
+
+/**
+ * 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;
+}
+
+
+const char *str_lattice(LatticeType l)
+{
+	switch ( l )
+	{
+		case L_TRICLINIC :    return "triclinic";
+		case L_MONOCLINIC :   return "monoclinic";
+		case L_ORTHORHOMBIC : return "orthorhombic";
+		case L_TETRAGONAL :   return "tetragonal";
+		case L_RHOMBOHEDRAL : return "rhombohedral";
+		case L_HEXAGONAL :    return "hexagonal";
+		case L_CUBIC :        return "cubic";
+	}
+
+	return "unknown lattice";
+}
+
+
+int right_handed(UnitCell *cell)
+{
+	double asx, asy, asz;
+	double bsx, bsy, bsz;
+	double csx, csy, csz;
+	struct rvec aCb;
+	double aCb_dot_c;
+	int rh_reciprocal;
+	int rh_direct;
+
+	if ( cell_get_reciprocal(cell, &asx, &asy, &asz,
+	                               &bsx, &bsy, &bsz,
+	                               &csx, &csy, &csz) ) {
+		ERROR("Couldn't get reciprocal cell.\n");
+		return 0;
+	}
+
+	/* "a" cross "b" */
+	aCb.u = asy*bsz - asz*bsy;
+	aCb.v = - (asx*bsz - asz*bsx);
+	aCb.w = asx*bsy - asy*bsx;
+
+	/* "a cross b" dot "c" */
+	aCb_dot_c = aCb.u*csx + aCb.v*csy + aCb.w*csz;
+
+	rh_reciprocal = aCb_dot_c > 0.0;
+
+	if ( cell_get_cartesian(cell, &asx, &asy, &asz,
+	                              &bsx, &bsy, &bsz,
+	                              &csx, &csy, &csz) ) {
+		ERROR("Couldn't get direct cell.\n");
+		return 0;
+	}
+
+	/* "a" cross "b" */
+	aCb.u = asy*bsz - asz*bsy;
+	aCb.v = - (asx*bsz - asz*bsx);
+	aCb.w = asx*bsy - asy*bsx;
+
+	/* "a cross b" dot "c" */
+	aCb_dot_c = aCb.u*csx + aCb.v*csy + aCb.w*csz;
+
+	rh_direct = aCb_dot_c > 0.0;
+
+	assert(rh_reciprocal == rh_direct);
+
+	return rh_direct;
+}
+
+
+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;
+	LatticeType lt;
+	char cen;
+
+	lt = cell_get_lattice_type(cell);
+	cen = cell_get_centering(cell);
+
+	STATUS("%s %c", str_lattice(lt), cen);
+
+	if ( (lt==L_MONOCLINIC) || (lt==L_TETRAGONAL) || ( lt==L_HEXAGONAL)
+	  || ( (lt==L_ORTHORHOMBIC) && (cen=='A') )
+	  || ( (lt==L_ORTHORHOMBIC) && (cen=='B') )
+	  || ( (lt==L_ORTHORHOMBIC) && (cen=='C') ) )
+	{
+		STATUS(", unique axis %c", cell_get_unique_axis(cell));
+	}
+
+	if ( right_handed(cell) ) {
+		STATUS(", right handed");
+	} else {
+		STATUS(", left handed");
+	}
+
+	STATUS(", point group '%s'.\n", cell_get_pointgroup(cell));
+
+	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("Cell representation is %s.\n", cell_rep(cell));
+}
+
+
+int bravais_lattice(UnitCell *cell)
+{
+	LatticeType lattice = cell_get_lattice_type(cell);
+	char centering = cell_get_centering(cell);
+	char ua = cell_get_unique_axis(cell);
+
+	switch ( centering )
+	{
+		case 'P' :
+		return 1;
+
+		case 'A' :
+		case 'B' :
+		case 'C' :
+		if ( lattice == L_MONOCLINIC ) {
+			if ( (ua=='a') && (centering=='A') ) return 1;
+			if ( (ua=='b') && (centering=='B') ) return 1;
+			if ( (ua=='c') && (centering=='C') ) return 1;
+		} else if ( lattice == L_ORTHORHOMBIC) {
+			return 1;
+		}
+		return 0;
+
+		case 'I' :
+		if ( (lattice == L_ORTHORHOMBIC)
+		  || (lattice == L_TETRAGONAL)
+		  || (lattice == L_CUBIC) )
+		{
+			return 1;
+		}
+		return 0;
+
+		case 'F' :
+		if ( (lattice == L_ORTHORHOMBIC) || (lattice == L_CUBIC) ) {
+			return 1;
+		}
+		return 0;
+
+		case 'H' :
+		/* "Hexagonal H" is not a Bravais lattice, but rather something
+		 * invented by the PDB to make life difficult for programmers.
+		 * Accepting it as Bravais seems to be the least painful way to
+		 * handle it correctly. Yuk. */
+		if ( ua != 'c' ) return 0;
+		if ( lattice == L_HEXAGONAL ) return 1;
+		return 0;
+
+		case 'R' :
+		if ( lattice == L_RHOMBOHEDRAL ) return 1;
+		return 0;
+
+		default :
+		return 0;
+	}
+}
+
+
+static UnitCellTransformation *uncentering_transformation(UnitCell *in,
+                                                          char *new_centering,
+                                                          LatticeType *new_latt)
+{
+	UnitCellTransformation *t;
+	const double OT = 1.0/3.0;
+	const double TT = 2.0/3.0;
+	const double H = 0.5;
+	LatticeType lt;
+	char ua, cen;
+
+	lt = cell_get_lattice_type(in);
+	ua = cell_get_unique_axis(in);
+	cen = cell_get_centering(in);
+
+	t = tfn_identity();
+	if ( t == NULL ) return NULL;
+
+	if ( ua == 'a' ) {
+		tfn_combine(t, tfn_vector(0,0,1),
+		               tfn_vector(0,1,0),
+		               tfn_vector(-1,0,0));
+	}
+
+	if ( ua == 'b' ) {
+		tfn_combine(t, tfn_vector(1,0,0),
+		               tfn_vector(0,0,1),
+		               tfn_vector(0,-1,0));
+	}
+
+	switch ( cen ) {
+
+		case 'P' :
+		*new_latt = lt;
+		*new_centering = 'P';
+		break;
+
+		case 'R' :
+		*new_latt = L_RHOMBOHEDRAL;
+		*new_centering = 'R';
+		break;
+
+		case 'I' :
+		tfn_combine(t, tfn_vector(-H,H,H),
+		               tfn_vector(H,-H,H),
+		               tfn_vector(H,H,-H));
+		if ( lt == L_CUBIC ) {
+			*new_latt = L_RHOMBOHEDRAL;
+			*new_centering = 'R';
+		} else {
+			/* Tetragonal or orthorhombic */
+			*new_latt = L_TRICLINIC;
+			*new_centering = 'P';
+		}
+		break;
+
+		case 'F' :
+		tfn_combine(t, tfn_vector(0,H,H),
+		               tfn_vector(H,0,H),
+		               tfn_vector(H,H,0));
+		if ( lt == L_CUBIC ) {
+			*new_latt = L_RHOMBOHEDRAL;
+			*new_centering = 'R';
+		} else {
+			assert(lt == L_ORTHORHOMBIC);
+			*new_latt = L_TRICLINIC;
+			*new_centering = 'P';
+		}
+		break;
+
+		case 'A' :
+		case 'B' :
+		case 'C' :
+		tfn_combine(t, tfn_vector(H,H,0),
+		               tfn_vector(-H,H,0),
+		               tfn_vector(0,0,1));
+		*new_latt = L_MONOCLINIC;
+		*new_centering = 'P';
+		break;
+
+		case 'H' :
+		/* Obverse setting */
+		tfn_combine(t, tfn_vector(TT,OT,OT),
+		               tfn_vector(-OT,OT,OT),
+		               tfn_vector(-OT,-TT,OT));
+		assert(lt == L_HEXAGONAL);
+		*new_latt = L_RHOMBOHEDRAL;
+		*new_centering = 'R';
+		break;
+
+		default :
+		ERROR("Invalid centering '%c'\n", cell_get_centering(in));
+		return NULL;
+
+	}
+
+	/* Reverse the axis permutation, but only if this was not an H->R
+	 * transformation */
+	if ( !((cen=='H') && (*new_latt == L_RHOMBOHEDRAL)) ) {
+		if ( ua == 'a' ) {
+			tfn_combine(t, tfn_vector(0,0,-1),
+				       tfn_vector(0,1,0),
+				       tfn_vector(1,0,0));
+		}
+
+		if ( ua == 'b' ) {
+			tfn_combine(t, tfn_vector(1,0,0),
+				       tfn_vector(0,0,-1),
+				       tfn_vector(0,1,0));
+		}
+	}
+
+	return t;
+}
+
+
+/**
+ * uncenter_cell:
+ * @in: A %UnitCell
+ * @t: Location at which to store the transformation which was used.
+ *
+ * Turns any cell into a primitive one, e.g. for comparison purposes.  The
+ * transformation which was used is stored at @t, which can be NULL if the
+ * transformation is not required.
+ *
+ * Returns: a primitive version of @in in a conventional (unique axis c)
+ * setting.
+ *
+ */
+UnitCell *uncenter_cell(UnitCell *in, UnitCellTransformation **t)
+{
+	UnitCellTransformation *tt;
+	char new_centering;
+	LatticeType new_latt;
+	UnitCell *out;
+
+	if ( !bravais_lattice(in) ) {
+		ERROR("Cannot uncenter: not a Bravais lattice.\n");
+		cell_print(in);
+		return NULL;
+	}
+
+	tt = uncentering_transformation(in, &new_centering, &new_latt);
+	if ( tt == NULL ) return NULL;
+
+	if ( t != NULL ) *t = tt;
+
+	out = cell_transform(in, tt);
+	if ( out == NULL ) return NULL;
+
+	cell_set_lattice_type(out, new_latt);
+	cell_set_centering(out, new_centering);
+
+	return out;
+}
+
+
+#define MAX_CAND (1024)
+
+static int right_handed_vec(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_in, UnitCell *template_in, int verbose,
+                     const float *tols, 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 angtol = deg2rad(tols[3]);
+	UnitCell *cell;
+	UnitCell *template;
+	UnitCellTransformation *uncentering;
+	UnitCell *new_cell_trans;
+
+	/* "Un-center" the template unit cell to make the comparison easier */
+	template = uncenter_cell(template_in, &uncentering);
+
+	/* The candidate cell is also uncentered, because it might be centered
+	 * if it came from (e.g.) MOSFLM */
+	cell = uncenter_cell(cell_in, NULL);
+
+	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,
+				                       tols[i]) )
+				{
+					continue;
+				}
+
+				if ( ncand[i] == MAX_CAND ) {
+					ERROR("Too many cell candidates - ");
+					ERROR("consider tightening the unit ");
+					ERROR("cell tolerances.\n");
+				} else {
+
+					double fom;
+
+					fom = fabs(lengths[i] - tlen);
+
+					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 = fom;
+
+					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_vec(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]);
+
+	/* Reverse the de-centering transformation */
+	new_cell_trans = cell_transform_inverse(new_cell, uncentering);
+	cell_free(new_cell);
+	cell_set_lattice_type(new_cell, cell_get_lattice_type(template_in));
+	cell_set_centering(new_cell, cell_get_centering(template_in));
+	cell_set_unique_axis(new_cell, cell_get_unique_axis(template_in));
+
+	return new_cell_trans;
+}
+
+
+UnitCell *match_cell_ab(UnitCell *cell_in, UnitCell *template_in)
+{
+	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;
+	float ltl = 5.0;     /* percent */
+	int have_real_a;
+	int have_real_b;
+	int have_real_c;
+	UnitCell *cell;
+	UnitCell *template;
+	UnitCellTransformation *to_given_cell;
+	UnitCell *new_cell;
+	UnitCell *new_cell_trans;
+
+	/* "Un-center" the template unit cell to make the comparison easier */
+	template = uncenter_cell(template_in, &to_given_cell);
+
+	/* The candidate cell is also uncentered, because it might be centered
+	 * if it came from (e.g.) MOSFLM */
+	cell = uncenter_cell(cell_in, NULL);
+
+	/* 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);
+
+	/* 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_vec(real_a, real_b, real_c) ) {
+		real_c.u = -real_c.u;
+		real_c.v = -real_c.v;
+		real_c.w = -real_c.w;
+	}
+
+	new_cell = cell_new_from_direct_axes(real_a, real_b, real_c);
+
+	 /* Reverse the de-centering transformation */
+	new_cell_trans = cell_transform_inverse(new_cell, to_given_cell);
+	cell_free(new_cell);
+	cell_set_lattice_type(new_cell, cell_get_lattice_type(template_in));
+	cell_set_centering(new_cell, cell_get_centering(template_in));
+	cell_set_unique_axis(new_cell, cell_get_unique_axis(template_in));
+
+	return new_cell_trans;
+}
+
+
+/* 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 determine_lattice(UnitCell *cell,
+                              const char *as, const char *bs, const char *cs,
+                              const char *als, const char *bes, const char *gas)
+{
+	int n_right;
+
+	/* Rhombohedral or cubic? */
+	if ( (strcmp(as, bs) == 0) && (strcmp(as, cs) == 0) ) {
+
+		if ( (strcmp(als, "  90.00") == 0)
+		  && (strcmp(bes, "  90.00") == 0)
+		  && (strcmp(gas, "  90.00") == 0) )
+		{
+			/* Cubic.  Unique axis irrelevant. */
+			cell_set_lattice_type(cell, L_CUBIC);
+			return;
+		}
+
+		if ( (strcmp(als, bes) == 0) && (strcmp(als, gas) == 0) ) {
+			/* Rhombohedral.  Unique axis irrelevant. */
+			cell_set_lattice_type(cell, L_RHOMBOHEDRAL);
+			return;
+		}
+
+	}
+
+	if ( (strcmp(als, "  90.00") == 0)
+	  && (strcmp(bes, "  90.00") == 0)
+	  && (strcmp(gas, "  90.00") == 0) )
+	{
+		if ( strcmp(bs, cs) == 0 ) {
+			/* Tetragonal, unique axis a */
+			cell_set_lattice_type(cell, L_TETRAGONAL);
+			cell_set_unique_axis(cell, 'a');
+			return;
+		}
+
+		if ( strcmp(as, cs) == 0 ) {
+			/* Tetragonal, unique axis b */
+			cell_set_lattice_type(cell, L_TETRAGONAL);
+			cell_set_unique_axis(cell, 'b');
+			return;
+		}
+
+		if ( strcmp(as, bs) == 0 ) {
+			/* Tetragonal, unique axis c */
+			cell_set_lattice_type(cell, L_TETRAGONAL);
+			cell_set_unique_axis(cell, 'c');
+			return;
+		}
+
+		/* Orthorhombic.  Unique axis irrelevant, but point group
+		 * can have different orientations. */
+		cell_set_lattice_type(cell, L_ORTHORHOMBIC);
+		return;
+	}
+
+	n_right = 0;
+	if ( strcmp(als, "  90.00") == 0 ) n_right++;
+	if ( strcmp(bes, "  90.00") == 0 ) n_right++;
+	if ( strcmp(gas, "  90.00") == 0 ) n_right++;
+
+	/* Hexgonal or monoclinic? */
+	if ( n_right == 2 ) {
+
+		if ( (strcmp(als, " 120.00") == 0)
+		  && (strcmp(bs, cs) == 0) )
+		{
+			/* Hexagonal, unique axis a */
+			cell_set_lattice_type(cell, L_HEXAGONAL);
+			cell_set_unique_axis(cell, 'a');
+			return;
+		}
+
+		if ( (strcmp(bes, " 120.00") == 0)
+		  && (strcmp(as, cs) == 0) )
+		{
+			/* Hexagonal, unique axis b */
+			cell_set_lattice_type(cell, L_HEXAGONAL);
+			cell_set_unique_axis(cell, 'b');
+			return;
+		}
+
+		if ( (strcmp(gas, " 120.00") == 0)
+		  && (strcmp(as, bs) == 0) )
+		{
+			/* Hexagonal, unique axis c */
+			cell_set_lattice_type(cell, L_HEXAGONAL);
+			cell_set_unique_axis(cell, 'c');
+			return;
+		}
+
+		if ( strcmp(als, "  90.00") != 0 ) {
+			/* Monoclinic, unique axis a */
+			cell_set_lattice_type(cell, L_MONOCLINIC);
+			cell_set_unique_axis(cell, 'a');
+			return;
+		}
+
+		if ( strcmp(bes, "  90.00") != 0 ) {
+			/* Monoclinic, unique axis b */
+			cell_set_lattice_type(cell, L_MONOCLINIC);
+			cell_set_unique_axis(cell, 'b');
+			return;
+		}
+
+		if ( strcmp(gas, "  90.00") != 0 ) {
+			/* Monoclinic, unique axis c */
+			cell_set_lattice_type(cell, L_MONOCLINIC);
+			cell_set_unique_axis(cell, 'c');
+			return;
+		}
+	}
+
+	/* Triclinic, unique axis irrelevant. */
+	cell_set_lattice_type(cell, L_TRICLINIC);
+}
+
+
+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];
+			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));
+
+			determine_lattice(cell, as, bs, cs, als, bes, gas);
+
+			if ( strlen(line) > 65 ) {
+				cell_set_centering(cell, line[55]);
+			} else {
+				cell_set_pointgroup(cell, "1");
+				ERROR("CRYST1 line without centering.\n");
+			}
+
+			break;  /* Done */
+		}
+
+	} while ( rval != NULL );
+
+	fclose(fh);
+
+	validate_cell(cell);
+
+	return cell;
+}
+
+
+/* Force the linker to bring in CBLAS to make GSL happy */
+void cell_fudge_gslcblas()
+{
+        STATUS("%p\n", cblas_sgemm);
+}
+
+
+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;
+}
+
+
+/**
+ * validate_cell:
+ * @cell: A %UnitCell to validate
+ *
+ * Perform some checks for crystallographic validity @cell, such as that the
+ * lattice is a conventional Bravais lattice.
+ * Warnings are printied if any of the checks are failed.
+ *
+ * Returns: true if cell is invalid.
+ *
+ */
+int validate_cell(UnitCell *cell)
+{
+	int err = 0;
+	char cen, ua;
+
+	if ( !cell_is_sensible(cell) ) {
+		ERROR("Warning: Unit cell parameters are not sensible.\n");
+		err = 1;
+	}
+
+	if ( !bravais_lattice(cell) ) {
+		ERROR("Warning: Unit cell is not a conventional Bravais"
+		      " lattice.\n");
+		err = 1;
+	}
+
+	if ( !right_handed(cell) ) {
+		ERROR("Warning: Unit cell is not right handed.\n");
+		err = 1;
+	}
+
+	cen = cell_get_centering(cell);
+	ua = cell_get_unique_axis(cell);
+	if ( (cen == 'A') && (ua != 'a') ) {
+		ERROR("Warning: centering doesn't match unique axis.\n");
+		err = 1;
+	}
+	if ( (cen == 'B') && (ua != 'b') ) {
+		ERROR("Warning: centering doesn't match unique axis.\n");
+		err = 1;
+	}
+	if ( (cen == 'C') && (ua != 'c') ) {
+		ERROR("Warning: centering doesn't match unique axis.\n");
+		err = 1;
+	}
+
+	return err;
+}
+
+
+/**
+ * forbidden_reflection:
+ * @cell: A %UnitCell
+ * @h: h index to check
+ * @k: k index to check
+ * @l: l index to check
+ *
+ * Returns: true if this reflection is forbidden.
+ *
+ */
+int forbidden_reflection(UnitCell *cell,
+                         signed int h, signed int k, signed int l)
+{
+	char cen;
+
+	cen = cell_get_centering(cell);
+
+	/* Reflection conditions here must match the transformation matrices
+	 * in uncentering_transformation().  tests/centering_check verifies
+	 * this (amongst other things). */
+
+	if ( cen == 'P' ) return 0;
+	if ( cen == 'R' ) return 0;
+
+	if ( cen == 'A' ) return (k+l) % 2;
+	if ( cen == 'B' ) return (h+l) % 2;
+	if ( cen == 'C' ) return (h+k) % 2;
+
+	if ( cen == 'I' ) return (h+k+l) % 2;
+	if ( cen == 'F' ) return ((h+k) % 2) || ((h+l) % 2) || ((k+l) % 2);
+
+	/* Obverse setting */
+	if ( cen == 'H' ) return (-h+k+l) % 3;
+
+	return 0;
+}