mat_expo.c
/* matexpo.c 2011-06-23 */
/* Copyright 2007-2011 Emmanuel Paradis
/* This file is part of the R-package `ape'. */
/* See the file ../COPYING for licensing issues. */
#include <R.h>
#include <R_ext/Lapack.h>
void mat_expo(double *P, int *nr)
/* This function computes the exponential of a nr x nr matrix */
{
double *U, *vl, *WR, *Uinv, *WI, *work;
int i, j, k, l, info, *ipiv, n = *nr, nc = n*n, lw = nc << 1;
char yes = 'V', no = 'N';
U = (double *)R_alloc(nc, sizeof(double));
vl = (double *)R_alloc(n, sizeof(double));
WR = (double *)R_alloc(n, sizeof(double));
Uinv = (double *)R_alloc(nc, sizeof(double));
WI = (double *)R_alloc(n, sizeof(double));
work = (double *)R_alloc(lw, sizeof(double));
ipiv = (int *)R_alloc(nc, sizeof(int));
/* The matrix is not symmetric, so we use 'dgeev'.
We take the real part of the eigenvalues -> WR
and the right eigenvectors (vr) -> U */
F77_CALL(dgeev)(&no, &yes, &n, P, &n, WR, WI, vl, &n,
U, &n, work, &lw, &info);
/* It is not necessary to sort the eigenvalues...
Copy U -> P */
memcpy(P, U, nc*sizeof(double));
/* For the inversion, we first make Uinv an identity matrix */
memset(Uinv, 0, nc*sizeof(double));
for (i = 0; i < nc; i += n + 1) Uinv[i] = 1;
/* The matrix is not symmetric, so we use 'dgesv'.
This subroutine puts the result in Uinv (B)
(P [= U] is erased) */
F77_CALL(dgesv)(&n, &n, P, &n, ipiv, Uinv, &n, &info);
/* The matrix product of U with the eigenvalues diagonal matrix: */
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
U[j + i*n] *= exp(WR[i]);
/* The second matrix product with U^-1 */
memset(P, 0, nc*sizeof(double));
for (k = 0; k < n; k++) {
for (l = 0; l < n; l++) {
lw = l + k*n;
for (i = 0 + n*k, j = l; j < nc; i++, j += n)
P[lw] += U[j]*Uinv[i];
}
}
}