SYNOPSIS
 SUBROUTINE SGESVD(
 JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, INFO )
 CHARACTER JOBU, JOBVT
 INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N
 REAL A( LDA, * ), S( * ), U( LDU, * ), VT( LDVT, * ), WORK( * )
PURPOSE
SGESVD computes the singular value decomposition (SVD) of a real MbyN matrix A, optionally computing the left and/or right singular vectors. The SVD is writtenA = U * SIGMA * transpose(V)
where SIGMA is an MbyN matrix which is zero except for its min(m,n) diagonal elements, U is an MbyM orthogonal matrix, and V is an NbyN orthogonal matrix. The diagonal elements of SIGMA are the singular values of A; they are real and nonnegative, 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.
ARGUMENTS
 JOBU (input) 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.  JOBVT (input) 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'.  M (input) INTEGER
 The number of rows of the input matrix A. M >= 0.
 N (input) INTEGER
 The number of columns of the input matrix A. N >= 0.
 A (input/output) REAL array, dimension (LDA,N)
 On entry, the MbyN 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.
 LDA (input) INTEGER
 The leading dimension of the array A. LDA >= max(1,M).
 S (output) REAL array, dimension (min(M,N))
 The singular values of A, sorted so that S(i) >= S(i+1).
 U (output) REAL array, dimension (LDU,UCOL)
 (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. If JOBU = 'A', U contains the MbyM 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.
 LDU (input) INTEGER
 The leading dimension of the array U. LDU >= 1; if JOBU = 'S' or 'A', LDU >= M.
 VT (output) REAL array, dimension (LDVT,N)
 If JOBVT = 'A', VT contains the NbyN 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.
 LDVT (input) INTEGER
 The leading dimension of the array VT. LDVT >= 1; if JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N).
 WORK (workspace/output) 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.
 LWORK (input) INTEGER
 The dimension of the array WORK. LWORK >= MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(M,N)). 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.
 INFO (output) INTEGER

= 0: successful exit.
< 0: if INFO = i, the ith 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.