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46 #include "gromacs/utility/fatalerror.h"
47 #include "gromacs/utility/smalloc.h"
49 #include "gmx_lapack.h"
51 double** alloc_matrix(int n, int m)
56 /* There's always time for more pointer arithmetic! */
57 /* This is necessary in order to be able to work with LAPACK */
60 for (i = 1; (i < n); i++)
62 ptr[i] = ptr[i - 1] + m;
67 void free_matrix(double** a)
74 void matrix_multiply(FILE* fp, int n, int m, double** x, double** y, double** z)
81 fprintf(fp, "Multiplying %d x %d matrix with a %d x %d matrix\n", n, m, m, n);
85 for (i = 0; (i < n); i++)
87 for (j = 0; (j < m); j++)
89 fprintf(fp, " %7g", x[i][j]);
95 for (i = 0; (i < m); i++)
97 for (j = 0; (j < m); j++)
100 for (k = 0; (k < n); k++)
102 z[i][j] += x[k][i] * y[j][k];
108 static void dump_matrix(FILE* fp, const char* title, int n, double** a)
113 fprintf(fp, "%s\n", title);
114 for (i = 0; (i < n); i++)
117 for (j = 0; (j < n); j++)
119 fprintf(fp, " %8.2f", a[i][j]);
123 fprintf(fp, "Prod a[i][i] = %g\n", d);
126 int matrix_invert(FILE* fp, int n, double** a)
128 int i, j, m, lda, *ipiv, lwork, info;
129 double **test = nullptr, **id, *work;
134 fprintf(fp, "Inverting %d square matrix\n", n);
135 test = alloc_matrix(n, n);
136 for (i = 0; (i < n); i++)
138 for (j = 0; (j < n); j++)
140 test[i][j] = a[i][j];
143 dump_matrix(fp, "before inversion", n, a);
151 F77_FUNC(dgetrf, DGETRF)(&n, &m, a[0], &lda, ipiv, &info);
155 dump_matrix(fp, "after dgetrf", n, a);
162 F77_FUNC(dgetri, DGETRI)(&n, a[0], &lda, ipiv, work, &lwork, &info);
166 dump_matrix(fp, "after dgetri", n, a);
177 id = alloc_matrix(n, n);
178 matrix_multiply(fp, n, n, test, a, id);
179 dump_matrix(fp, "And here is the product of A and Ainv", n, id);
190 double multi_regression(FILE* fp, int nrow, double* y, int ncol, double** xx, double* a0)
193 double ax, chi2, **a, **at, **ata, *atx;
195 a = alloc_matrix(nrow, ncol);
196 at = alloc_matrix(ncol, nrow);
197 ata = alloc_matrix(ncol, ncol);
198 for (i = 0; (i < nrow); i++)
200 for (j = 0; (j < ncol); j++)
202 at[j][i] = a[i][j] = xx[j][i];
205 matrix_multiply(fp, nrow, ncol, a, at, ata);
206 if ((row = matrix_invert(fp, ncol, ata)) != 0)
210 "Matrix inversion failed. Incorrect row = %d.\nThis probably indicates that you do "
211 "not have sufficient data points, or that some parameters are linearly dependent.",
216 for (i = 0; (i < ncol); i++)
219 for (j = 0; (j < nrow); j++)
221 atx[i] += at[i][j] * y[j];
224 for (i = 0; (i < ncol); i++)
227 for (j = 0; (j < ncol); j++)
229 a0[i] += ata[i][j] * atx[j];
233 for (j = 0; (j < nrow); j++)
236 for (i = 0; (i < ncol); i++)
238 ax += a0[i] * a[j][i];
240 chi2 += (y[j] - ax) * (y[j] - ax);