cgesvd
cgesvd - compute the singular value decomposition (SVD) of a complex M-by-N matrix A, optionally computing the left and/or right singular vectors
SUBROUTINE CGESVD( JOBU, JOBVT, M, N, A, LDA, SING, U, LDU, VT,
* LDVT, WORK, LDWORK, WORK2, INFO)
CHARACTER * 1 JOBU, JOBVT
COMPLEX A(LDA,*), U(LDU,*), VT(LDVT,*), WORK(*)
INTEGER M, N, LDA, LDU, LDVT, LDWORK, INFO
REAL SING(*), WORK2(*)
SUBROUTINE CGESVD_64( JOBU, JOBVT, M, N, A, LDA, SING, U, LDU, VT,
* LDVT, WORK, LDWORK, WORK2, INFO)
CHARACTER * 1 JOBU, JOBVT
COMPLEX A(LDA,*), U(LDU,*), VT(LDVT,*), WORK(*)
INTEGER*8 M, N, LDA, LDU, LDVT, LDWORK, INFO
REAL SING(*), WORK2(*)
SUBROUTINE GESVD( JOBU, JOBVT, [M], [N], A, [LDA], SING, U, [LDU],
* VT, [LDVT], [WORK], [LDWORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: JOBU, JOBVT
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, U, VT
INTEGER :: M, N, LDA, LDU, LDVT, LDWORK, INFO
REAL, DIMENSION(:) :: SING, WORK2
SUBROUTINE GESVD_64( JOBU, JOBVT, [M], [N], A, [LDA], SING, U, [LDU],
* VT, [LDVT], [WORK], [LDWORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: JOBU, JOBVT
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, U, VT
INTEGER(8) :: M, N, LDA, LDU, LDVT, LDWORK, INFO
REAL, DIMENSION(:) :: SING, WORK2
#include <sunperf.h>
void cgesvd(char jobu, char jobvt, int m, int n, complex *a, int lda, float *sing, complex *u, int ldu, complex *vt, int ldvt, int *info);
void cgesvd_64(char jobu, char jobvt, long m, long n, complex *a, long lda, float *sing, complex *u, long ldu, complex *vt, long ldvt, long *info);
cgesvd 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
= U * SIGMA * conjugate-transpose(V)
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
V 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 V**H, not V.
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* JOBU (input)
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Specifies options for computing all or part of the matrix U:
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* JOBVT (input)
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Specifies options for computing all or part of the matrix
V**H:
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* M (input)
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The number of rows of the input matrix A. M >= 0.
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* N (input)
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The number of columns of the input matrix A. N >= 0.
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* A (input/output)
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On entry, the M-by-N matrix A.
On exit,
if JOBU = 'O', A is overwritten with the first min(m,n)
columns of U (the left singular vectors,
stored columnwise);
if JOBVT = 'O', A is overwritten with the first min(m,n)
rows of V**H (the right singular vectors,
stored rowwise);
if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A
are destroyed.
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* LDA (input)
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The leading dimension of the array A. LDA >= max(1,M).
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* SING (output)
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The singular values of A, sorted so that SING(i) >= SING(i+1).
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* U (input)
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(LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'SING'.
If JOBU = 'A', U contains the M-by-M unitary matrix U;
if JOBU = 'SING', U contains the first min(m,n) columns of U
(the left singular vectors, stored columnwise);
if JOBU = 'N' or 'O', U is not referenced.
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* LDU (input)
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The leading dimension of the array U. LDU >= 1; if
JOBU = 'SING' or 'A', LDU >= M.
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* VT (input)
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If JOBVT = 'A', VT contains the N-by-N unitary matrix
V**H;
if JOBVT = 'SING', VT contains the first min(m,n) rows of
V**H (the right singular vectors, stored rowwise);
if JOBVT = 'N' or 'O', VT is not referenced.
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* LDVT (input)
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The leading dimension of the array VT. LDVT >= 1; if
JOBVT = 'A', LDVT >= N; if JOBVT = 'SING', LDVT >= min(M,N).
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* WORK (workspace)
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On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.
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* LDWORK (input)
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The dimension of the array WORK. LDWORK >= 1.
LDWORK >= 2*MIN(M,N)+MAX(M,N)
For good performance, LDWORK should generally be larger.
If LDWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LDWORK is issued by XERBLA.
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* WORK2 (workspace)
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DIMENSION(5*MIN(M,N)). On exit, if INFO > 0, WORK2(1:MIN(M,N)-1) contains the
unconverged superdiagonal elements of an upper bidiagonal
matrix B whose diagonal is in SING (not necessarily sorted).
B satisfies A = U * B * VT, so it has the same singular
values as A, and singular vectors related by U and VT.
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* INFO (output)
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