int is_mirror_image(double* X, int X_dim0, int X_dim1, int X_dim1_mem,
double* Y, int Y_dim0, int Y_dim1, int Y_dim1_mem) {
// Check if two configurations X and Y are mirror images
// (i.e. does their optimal superposition involve a reflection?)
//
// Parameters
// ----------
// X : double*, shape=(X_dim0, X_dim1)
// Pointer to the upper left corner of matrix X.
// X_dim0 : int
// The number of rows in matrix X. Should be 3.
// X_dim1 : int
// The number of columns in matrix X. Corresponds to number of atoms
// X_dim1_mem : int
// number of columns of X in memory. corresponds to the number of padded atoms.
// such that the (i,j)-th element of X is accessed at X[i*X_dim1*mem + j]
// Y : double*, shape=(X_dim0, X_dim1)
// Pointer to the upper left corner of matrix X.
// Y_dim0 : int
// The number of rows in matrix Y. Should be 3.
// Y_dim1 : int
// The number of columns in matrix Y. Corresponds to number of atoms
// Y_dim1_mem : int
// number of columns of Y in memory. corresponds to the number of padded atoms.
// such that the (i,j)-th element of Y is accessed at Y[i*Y_dim1*mem + j] //
//
// Returns
// -------
// mirror : int
// = 1 if they are mirror images
// = 0 if they are not mirror images
if ((X_dim0 != Y_dim0) || (X_dim1 != Y_dim1) || (X_dim0 != 3)){
fprintf(stderr, "is_mirror_image called with wrong shape\n");
exit(1);
}
// covariance = np.dot(X, Y.T)
gsl_matrix* covariance = gsl_matrix_alloc(3, 3);
gsl_matrix_view mX = gsl_matrix_view_array_with_tda(X, X_dim0, X_dim1, X_dim1_mem);
gsl_matrix_view mY = gsl_matrix_view_array_with_tda(Y, Y_dim0, Y_dim1, Y_dim1_mem);
gsl_blas_dgemm(CblasNoTrans, CblasTrans, 1.0, &mX.matrix, &mY.matrix, 0.0, covariance);
gsl_matrix* U = gsl_matrix_alloc(3, 3);
gsl_vector* S = gsl_vector_alloc(3);
gsl_vector* work = gsl_vector_alloc(3);
gsl_linalg_SV_decomp(covariance, U, S, work);
double determinant = ddet(covariance->data) * ddet(U->data);
gsl_matrix_free(covariance);
gsl_matrix_free(U);
gsl_vector_free(S);
gsl_vector_free(work);
return determinant < 0;
}
/* Multivariate Normal density */
double dMVN(
double *Y, /* The data */
double *MEAN, /* The parameters */
double **SIG_INV, /* inverse of the covariance matrix */
int dim, /* dimension */
int give_log){ /* 1 if log_scale 0 otherwise */
int j,k;
double value=0.0;
for(j=0;j<dim;j++){
for(k=0;k<j;k++)
value+=2*(Y[k]-MEAN[k])*(Y[j]-MEAN[j])*SIG_INV[j][k];
value+=(Y[j]-MEAN[j])*(Y[j]-MEAN[j])*SIG_INV[j][j];
}
value=-0.5*value-0.5*dim*log(2*M_PI)+0.5*ddet(SIG_INV, dim, 1);
if(give_log)
return(value);
else
return(exp(value));
}
