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  • 12/20/2021
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ZGESVD Example Program in C

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Any license * under such intellectual property rights must be express and approved by Intel * in writing. * ******************************************************************************** */ /* ZGESVD Example. ============== Program computes the singular value decomposition of a general rectangular complex matrix A: ( 5.91, -5.69) ( 7.09, 2.72) ( 7.78, -4.06) ( -0.79, -7.21) ( -3.15, -4.08) ( -1.89, 3.27) ( 4.57, -2.07) ( -3.88, -3.30) ( -4.89, 4.20) ( 4.10, -6.70) ( 3.28, -3.84) ( 3.84, 1.19) Description. ============ The routine computes the singular value decomposition (SVD) of a complex m-by-n matrix A, optionally computing the left and/or right singular vectors. The SVD is written as A = U*SIGMA*VH where SIGMA is an m-by-n matrix which is zero except for its min(m,n) diagonal elements, U is an m-by-m unitary matrix and VH (V conjugate transposed) is an n-by-n unitary matrix. The diagonal elements of SIGMA are the singular values of A; they are real and non-negative, and are returned in descending order. The first min(m, n) columns of U and V are the left and right singular vectors of A. Note that the routine returns VH, not V. Example Program Results. ======================== ZGESVD Example Program Results Singular values 17.63 11.61 6.78 Left singular vectors (stored columnwise) ( -0.86, 0.00) ( 0.40, 0.00) ( 0.32, 0.00) ( -0.35, 0.13) ( -0.24, -0.21) ( -0.63, 0.60) ( 0.15, 0.32) ( 0.61, 0.61) ( -0.36, 0.10) Right singular vectors (stored rowwise) ( -0.22, 0.51) ( -0.37, -0.32) ( -0.53, 0.11) ( 0.15, 0.38) ( 0.31, 0.31) ( 0.09, -0.57) ( 0.18, -0.39) ( 0.38, -0.39) ( 0.53, 0.24) ( 0.49, 0.28) ( -0.47, -0.25) ( -0.15, 0.19) */ #include <stdlib.h> #include <stdio.h> /* Complex datatype */ struct _dcomplex { double re, im; }; typedef struct _dcomplex dcomplex; /* ZGESVD prototype */ extern void zgesvd( char* jobu, char* jobvt, int* m, int* n, dcomplex* a, int* lda, double* s, dcomplex* u, int* ldu, dcomplex* vt, int* ldvt, dcomplex* work, int* lwork, double* rwork, int* info ); /* Auxiliary routines prototypes */ extern void print_matrix( char* desc, int m, int n, dcomplex* a, int lda ); extern void print_rmatrix( char* desc, int m, int n, double* a, int lda ); /* Parameters */ #define M 3 #define N 4 #define LDA M #define LDU M #define LDVT N /* Main program */ int main() { /* Locals */ int m = M, n = N, lda = LDA, ldu = LDU, ldvt = LDVT, info, lwork; dcomplex wkopt; dcomplex* work; /* Local arrays */ /* rwork dimension should be at least max( 1, 5*min(m,n) ) */ double s[M], rwork[5*M]; dcomplex u[LDU*M], vt[LDVT*N]; dcomplex a[LDA*N] = { { 5.91, -5.69}, {-3.15, -4.08}, {-4.89, 4.20}, { 7.09, 2.72}, {-1.89, 3.27}, { 4.10, -6.70}, { 7.78, -4.06}, { 4.57, -2.07}, { 3.28, -3.84}, {-0.79, -7.21}, {-3.88, -3.30}, { 3.84, 1.19} }; /* Executable statements */ printf( " ZGESVD Example Program Results\n" ); /* Query and allocate the optimal workspace */ lwork = -1; zgesvd( "All", "All", &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, &wkopt, &lwork, rwork, &info ); lwork = (int)wkopt.re; work = (dcomplex*)malloc( lwork*sizeof(dcomplex) ); /* Compute SVD */ zgesvd( "All", "All", &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work, &lwork, rwork, &info ); /* Check for convergence */ if( info > 0 ) { printf( "The algorithm computing SVD failed to converge.\n" ); exit( 1 ); } /* Print singular values */ print_rmatrix( "Singular values", 1, m, s, 1 ); /* Print left singular vectors */ print_matrix( "Left singular vectors (stored columnwise)", m, m, u, ldu ); /* Print right singular vectors */ print_matrix( "Right singular vectors (stored rowwise)", m, n, vt, ldvt ); /* Free workspace */ free( (void*)work ); exit( 0 ); } /* End of ZGESVD Example */ /* Auxiliary routine: printing a matrix */ void print_matrix( char* desc, int m, int n, dcomplex* a, int lda ) { int i, j; printf( "\n %s\n", desc ); for( i = 0; i < m; i++ ) { for( j = 0; j < n; j++ ) printf( " (%6.2f,%6.2f)", a[i+j*lda].re, a[i+j*lda].im ); printf( "\n" ); } } /* Auxiliary routine: printing a real matrix */ void print_rmatrix( char* desc, int m, int n, double* a, int lda ) { int i, j; printf( "\n %s\n", desc ); for( i = 0; i < m; i++ ) { for( j = 0; j < n; j++ ) printf( " %6.2f", a[i+j*lda] ); printf( "\n" ); } }

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