sgesvd()

subroutine sgesvd	(	character	jobu,
		character	jobvt,
		integer	m,
		integer	n,
		real, dimension( lda, * )	a,
		integer	lda,
		real, dimension( * )	s,
		real, dimension( ldu, * )	u,
		integer	ldu,
		real, dimension( ldvt, * )	vt,
		integer	ldvt,
		real, dimension( * )	work,
		integer	lwork,
		integer	info )

SGESVD computes the singular value decomposition (SVD) for GE matrices

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Purpose:

!>
!> SGESVD computes the singular value decomposition (SVD) of a real
!> M-by-N matrix A, optionally computing the left and/or right singular
!> vectors. The SVD is written
!>
!>      A = U * SIGMA * 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 orthogonal matrix, and
!> V is an N-by-N orthogonal 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**T, not V.
!> 

Parameters

[in]	JOBU	!> JOBU is CHARACTER*1 !> Specifies options for computing all or part of the matrix U: !> = 'A': all M columns of U are returned in array U: !> = 'S': the first min(m,n) columns of U (the left singular !> vectors) are returned in the array U; !> = 'O': the first min(m,n) columns of U (the left singular !> vectors) are overwritten on the array A; !> = 'N': no columns of U (no left singular vectors) are !> computed. !>
[in]	JOBVT	!> JOBVT is CHARACTER*1 !> Specifies options for computing all or part of the matrix !> V**T: !> = 'A': all N rows of V**T are returned in the array VT; !> = 'S': the first min(m,n) rows of V**T (the right singular !> vectors) are returned in the array VT; !> = 'O': the first min(m,n) rows of V**T (the right singular !> vectors) are overwritten on the array A; !> = 'N': no rows of V**T (no right singular vectors) are !> computed. !> !> JOBVT and JOBU cannot both be 'O'. !>
[in]	M	!> M is INTEGER !> The number of rows of the input matrix A. M >= 0. !>
[in]	N	!> N is INTEGER !> The number of columns of the input matrix A. N >= 0. !>
[in,out]	A	!> A is REAL array, dimension (LDA,N) !> 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**T (the right singular vectors, !> stored rowwise); !> if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A !> are destroyed. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !>
[out]	S	!> S is REAL array, dimension (min(M,N)) !> The singular values of A, sorted so that S(i) >= S(i+1). !>
[out]	U	!> U is REAL array, dimension (LDU,UCOL) !> (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. !> If JOBU = 'A', U contains the M-by-M orthogonal matrix U; !> if JOBU = 'S', 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. !>
[in]	LDU	!> LDU is INTEGER !> The leading dimension of the array U. LDU >= 1; if !> JOBU = 'S' or 'A', LDU >= M. !>
[out]	VT	!> VT is REAL array, dimension (LDVT,N) !> If JOBVT = 'A', VT contains the N-by-N orthogonal matrix !> V**T; !> if JOBVT = 'S', VT contains the first min(m,n) rows of !> V**T (the right singular vectors, stored rowwise); !> if JOBVT = 'N' or 'O', VT is not referenced. !>
[in]	LDVT	!> LDVT is INTEGER !> The leading dimension of the array VT. LDVT >= 1; if !> JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N). !>
[out]	WORK	!> WORK is REAL array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK; !> if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged !> superdiagonal elements of an upper bidiagonal matrix B !> whose diagonal is in S (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. !>
[in]	LWORK	!> LWORK is INTEGER !> The dimension of the array WORK. !> LWORK >= MAX(1,5*MIN(M,N)) for the paths (see comments inside code): !> - PATH 1 (M much larger than N, JOBU='N') !> - PATH 1t (N much larger than M, JOBVT='N') !> LWORK >= MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(M,N)) for the other paths !> For good performance, LWORK should generally be larger. !> !> If LWORK = -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 LWORK is issued by XERBLA. !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit. !> < 0: if INFO = -i, the i-th argument had an illegal value. !> > 0: if SBDSQR did not converge, INFO specifies how many !> superdiagonals of an intermediate bidiagonal form B !> did not converge to zero. See the description of WORK !> above for details. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.