/* Main program */
int main() {
/* Locals */
lapack_int m = M, n = N, lda = LDA, ldu = LDU, ldvt = LDVT, info;
double superb[min(M,N)-1];
/* Local arrays */
double s[N], u[LDU*M], vt[LDVT*N];
double a[LDA*N] = {
8.79, 6.11, -9.15, 9.57, -3.49, 9.84,
9.93, 6.91, -7.93, 1.64, 4.02, 0.15,
9.83, 5.04, 4.86, 8.83, 9.80, -8.99,
5.45, -0.27, 4.85, 0.74, 10.00, -6.02,
3.16, 7.98, 3.01, 5.80, 4.27, -5.31
};
/* Executable statements */
printf( "LAPACKE_dgesvd (column-major, high-level) Example Program Results\n" );
/* Compute SVD */
info = LAPACKE_dgesvd( LAPACK_COL_MAJOR, 'A', 'A', m, n, a, lda,
s, u, ldu, vt, ldvt, superb );
/* Check for convergence */
if( info > 0 ) {
printf( "The algorithm computing SVD failed to converge.\n" );
exit( 1 );
}
/* Print singular values */
print_matrix( "Singular values", 1, n, s, 1 );
/* Print left singular vectors */
print_matrix( "Left singular vectors (stored columnwise)", m, n, u, ldu );
/* Print right singular vectors */
print_matrix( "Right singular vectors (stored rowwise)", n, n, vt, ldvt );
return 0;
} /* End of LAPACKE_dgesvd Example */
int phonopy_pinv(double *data_out,
const double *data_in,
const int m,
const int n,
const double cutoff)
{
int i, j, k;
lapack_int info;
double *s, *a, *u, *vt, *superb;
a = (double*)malloc(sizeof(double) * m * n);
s = (double*)malloc(sizeof(double) * min(m,n));
u = (double*)malloc(sizeof(double) * m * m);
vt = (double*)malloc(sizeof(double) * n * n);
superb = (double*)malloc(sizeof(double) * (min(m,n) - 1));
for (i = 0; i < m * n; i++) {
a[i] = data_in[i];
}
info = LAPACKE_dgesvd(LAPACK_ROW_MAJOR,
'A',
'A',
(lapack_int)m,
(lapack_int)n,
a,
(lapack_int)n,
s,
u,
(lapack_int)m,
vt,
(lapack_int)n,
superb);
for (i = 0; i < n * m; i++) {
data_out[i] = 0;
}
for (i = 0; i < m; i++) {
for (j = 0; j < n; j++) {
for (k = 0; k < min(m,n); k++) {
if (s[k] > cutoff) {
data_out[j * m + i] += u[i * m + k] / s[k] * vt[k * n + j];
}
}
}
}
free(a);
free(s);
free(u);
free(vt);
free(superb);
return (int)info;
}
double* HFMatrix<T>::pinv(double *matrix, int rows, int cols)
{
lapack_int m, n, lda, ldu, ldvt, info;
char jobu = 'A';
char jobvt = 'A';
m = rows;
n = cols;
lda = rows;
ldu = rows;
ldvt = cols;
int ssize = HFMath::min(m, n);
double *s = (double*)malloc(sizeof(double)*ssize);
double *u = (double*)malloc(sizeof(double)*m*m);
double *vt = (double*)malloc(sizeof(double)*n*n);
double *sb = (double*)malloc(sizeof(double)*(ssize-1));
info = LAPACKE_dgesvd(LAPACK_COL_MAJOR, jobu, jobvt, m, n,
matrix, lda, s, u, ldu, vt, ldvt, sb);
ASSERT(info == 0);
print_matrix("Singular values", 1, n, s, 1);
print_matrix("Left singular vectors(stored columnwise)", m, n, u, ldu);
print_matrix("Left singular vectors(stored rowwise)", n, n, vt, ldvt);
for(int i = 0; i < n; ++i)
{
for(int j = 0; j < ssize; ++j)
vt[i*n+j] = vt[i*n+j]/s[j];
}
double *result = (double*)malloc(m*n*sizeof(double));
cblas_dgemm(CblasColMajor, CblasTrans, CblasTrans, n, m,
n, 1.0, vt, ldvt, u, ldu, 0, result, n);
free(s);
free(u);
free(vt);
free(sb);
return result;
}
static void bench_gesvd(int size, double *A, double *U, double *VT, double *S, double *superb)
{
int i, iter = 1;
double start, stop;
double gflops, peak;
if ((double) size * (double) size * (double) size <= 1.e12) iter = 2;
if ((double) size * (double) size * (double) size <= 1.e10) iter = 3;
if ((double) size * (double) size * (double) size <= 1.e8) iter = 5;
peak = 0.;
for (i = 0; i < iter; i++) {
start = gettime();
LAPACKE_dgesvd(LAPACK_COL_MAJOR, 'A', 'A', size, size, A, size, S, U, size, VT, size, superb);
stop = gettime();
gflops = getgflops(size, stop - start);
if (peak < gflops) peak = gflops;
}
printf("%4d, %10.3f\n", size, peak);
fflush(stdout);
return;
}
int main()
{
lapack_int m = 3, n = 4;
lapack_int ret;
double *A = new double[m * n];
double *U = new double[m * m];
double *VT = new double[n * n];
double *S = new double[std::min(m, n)];
double *superb = new double[std::min(m, n)];
//setting A matrix
A[0 + 0 * m] = 1; A[0 + 1 * m] = 2; A[0 + 2 * m] = 3; A[0 + 3 * m] = 4;
A[1 + 0 * m] = 5; A[1 + 1 * m] = 6; A[1 + 2 * m] = 7; A[1 + 3 * m] = 8;
A[2 + 0 * m] = 9; A[2 + 1 * m] = 10; A[2 + 2 * m] = 11; A[2 + 3 * m] = 12;
printf("A ="); printmat(m, n, A, m); printf("\n");
ret = LAPACKE_dgesvd(LAPACK_COL_MAJOR, 'A', 'A', m, n, A, m, S, U, m, VT, n, superb);
//print out some results.
printf("#singular values\n");
printf("S ="); printmat(std::min(m, n), 1, S, 1); printf("\n");
printf("#U matrix\n");
printf("U ="); printmat(m, m, U, m); printf("\n");
printf("#V^t matrix\n");
printf("Vt ="); printmat(n, n, VT, n); printf("\n");
printf("#You can check result by octave/matlab by\n");
printf("[u, s, v] = svd (A) \n");
printf("#u*s*v' should be equal to A\n");
printf("u*s*v' \n");
printf("U*diag(S,%d,%d)*Vt \n",m,n);
delete[]superb;
delete[]S;
delete[]VT;
delete[]U;
delete[]A;
}
int svd(int m, int n, scalar* A,scalar* U,scalar* S,scalar* VT,scalar* superb){
return LAPACKE_dgesvd( LAPACK_ROW_MAJOR, 'A','A',m,n,A,n,S,U,m,VT,n,superb);
}