NAME

       sgesvd.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sgesvd (JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, INFO)
            SGESVD computes the singular value decomposition (SVD) for GE matrices

Function/Subroutine Documentation

   subroutine sgesvd (characterJOBU, characterJOBVT, integerM, integerN, real, dimension( lda, *
       )A, integerLDA, real, dimension( * )S, real, dimension( ldu, * )U, integerLDU, real,
       dimension( ldvt, * )VT, integerLDVT, real, dimension( * )WORK, integerLWORK, integerINFO)
        SGESVD computes the singular value decomposition (SVD) for GE matrices

       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:
           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.

           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'.

           M

                     M is INTEGER
                     The number of rows of the input matrix A.  M >= 0.

           N

                     N is INTEGER
                     The number of columns of the input matrix A.  N >= 0.

           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.

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,M).

           S

                     S is REAL array, dimension (min(M,N))
                     The singular values of A, sorted so that S(i) >= S(i+1).

           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.

           LDU

                     LDU is INTEGER
                     The leading dimension of the array U.  LDU >= 1; if
                     JOBU = 'S' or 'A', LDU >= M.

           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.

           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).

           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.

           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.

           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.

       Date:
           April 2012

       Definition at line 211 of file sgesvd.f.

Author

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