// Matrix power by squaring: P = A^b (A is garbage on exit)
static void matpow_by_squaring(double *A, int n, int b, double *P)
{
double *TMP;
mateye(n, P);
// Trivial cases
if (b == 0)
return;
if (b == 1)
{
matcopy(n, A, P);
return;
}
// General case
TMP = malloc(n*n*sizeof(double));
while (b)
{
if (b&1)
{
matprod(n, P, A, TMP);
matcopy(n, TMP, P);
}
b >>= 1;
matprod(n, A, A, TMP);
matcopy(n, TMP, A);
}
free(TMP);
}
/*
Generate the transpose of a dynamic Iliffe matrix.
*/
int transpose (dmat A, dmat ATrans)
{
int i,
j,
rowsize,
colsize,
error;
double **a = A.el,
**atrans = ATrans.el,
temp;
dmat TMP;
rowsize = A.ub1 - A.lb1;
colsize = A.ub2 - A.lb2;
if (rowsize < 0 || rowsize != ATrans.ub2 - ATrans.lb2 ||
colsize < 0 || colsize != ATrans.ub1 - ATrans.lb1) {
errno = EDOM;
return (-1);
}
if (A.mat_sto == ATrans.mat_sto
&& A.lb1 == ATrans.lb1
&& A.lb2 == ATrans.lb2) {
for (i = 0; i <= rowsize; i++)
for (j = i + 1; j <= colsize; j++) {
temp = a[A.lb1 + i][A.lb2 + j];
atrans[A.lb1 + i][A.lb2 + j] = a[A.lb1 + j][A.lb2 + i];
atrans[A.lb1 + j][A.lb2 + i] = temp;
}
} else if (A.mat_sto == ATrans.mat_sto) {
TMP = newdmat (ATrans.lb1, ATrans.ub1, ATrans.lb2, ATrans.ub2, &error);
if (error)
return (-2);
for (i = 0; i <= rowsize; i++)
for (j = 0; j <= colsize; j++) {
TMP.el[ATrans.lb1 + j][ATrans.lb2 + i] =
a[A.lb1 + i][A.lb2 + j];
}
matcopy (TMP, ATrans);
freemat (TMP);
} else {
for (i = 0; i <= rowsize; i++)
for (j = 0; j <= colsize; j++)
atrans[ATrans.lb1 + j][ATrans.lb2 + i]
= a[A.lb1 + i][A.lb2 + j];
}
return (0);
}
void mattrans(float a[4][4])
{
float r[4][4];
int i,j;
for(i=0;i<4;i++) {
for(j=0;j<4;j++) {
r[i][j] = a[j][i];
}
}
matcopy(a,r);
}
void matxmat(float out[4][4],float m0[4][4],float m1[4][4])
{
float r[4][4];
int i,j,k;
for(i=0;i<4;i++) {
for(j=0;j<4;j++) {
r[i][j] = 0;
for(k=0;k<4;k++) {
r[i][j] += m0[i][k]*m1[k][j];
}
}
}
matcopy(out,r);
return;
}
void matinv4x4(float A[4][4])
{
float r[4][4];
int i,j;
float det = matadjoint(r,A);
if (det == 0.0) return;
for(i=0;i<4;i++) {
for(j=0;j<4;j++) {
r[i][j] /= det;
}
}
matcopy(A,r);
return;
}
// Condition estimate:
// Return ratio of largest/smallest singular values.
//---------------------------------------------------------
double cond(ZMat& mat)
//---------------------------------------------------------
{
double rcond = 1.;
ZVec work(2*mat.num_cols(), "work");
DVec rwork(2*mat.num_cols(), "rwork");
int info;
ZMat matcopy(mat);
IVec ipiv(mat.num_rows(), "ipiv");
ZGETRF(mat.num_rows(),
mat.num_cols(),
matcopy.data(),
mat.num_rows(),
ipiv.data(),
info);
// fprintf(stdout, "zgetrf: info=%d \n", info);
// must fix this
double anorm = 1.0;
ZGECON('I',
mat.num_cols(),
matcopy.data(),
mat.num_rows(),
anorm,
rcond,
work.data(),
rwork.data(),
info);
// fprintf(stdout, "zgecon: info=%d rcond=%lf\n", info, rcond);
return 1./rcond;
}