sgesdd.f(3)							      LAPACK							       sgesdd.f(3)

NAME

       sgesdd.f -

SYNOPSIS

   Functions/Subroutines
       subroutine sgesdd (JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, IWORK, INFO)
	   SGESDD

Function/Subroutine Documentation
   subroutine sgesdd (characterJOBZ, integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )S, real, dimension( ldu, *
       )U, integerLDU, real, dimension( ldvt, * )VT, integerLDVT, real, dimension( * )WORK, integerLWORK, integer, dimension( * )IWORK,
       integerINFO)
       SGESDD

       Purpose:

	    SGESDD computes the singular value decomposition (SVD) of a real
	    M-by-N matrix A, optionally computing the left and right singular
	    vectors.  If singular vectors are desired, it uses a
	    divide-and-conquer algorithm.

	    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 VT = V**T, not V.

	    The divide and conquer algorithm makes very mild assumptions about
	    floating point arithmetic. It will work on machines with a guard
	    digit in add/subtract, or on those binary machines without guard
	    digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
	    Cray-2. It could conceivably fail on hexadecimal or decimal machines
	    without guard digits, but we know of none.

       Parameters:
	   JOBZ

		     JOBZ is CHARACTER*1
		     Specifies options for computing all or part of the matrix U:
		     = 'A':  all M columns of U and all N rows of V**T are
			     returned in the arrays U and VT;
		     = 'S':  the first min(M,N) columns of U and the first
			     min(M,N) rows of V**T are returned in the arrays U
			     and VT;
		     = 'O':  If M >= N, the first N columns of U are overwritten
			     on the array A and all rows of V**T are returned in
			     the array VT;
			     otherwise, all columns of U are returned in the
			     array U and the first M rows of V**T are overwritten
			     in the array A;
		     = 'N':  no columns of U or rows of V**T are computed.

	   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 JOBZ = 'O',  A is overwritten with the first N columns
				     of U (the left singular vectors, stored
				     columnwise) if M >= N;
				     A is overwritten with the first M rows
				     of V**T (the right singular vectors, stored
				     rowwise) otherwise.
		     if JOBZ .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)
		     UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
		     UCOL = min(M,N) if JOBZ = 'S'.
		     If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
		     orthogonal matrix U;
		     if JOBZ = 'S', U contains the first min(M,N) columns of U
		     (the left singular vectors, stored columnwise);
		     if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.

	   LDU

		     LDU is INTEGER
		     The leading dimension of the array U.  LDU >= 1; if
		     JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.

	   VT

		     VT is REAL array, dimension (LDVT,N)
		     If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the
		     N-by-N orthogonal matrix V**T;
		     if JOBZ = 'S', VT contains the first min(M,N) rows of
		     V**T (the right singular vectors, stored rowwise);
		     if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.

	   LDVT

		     LDVT is INTEGER
		     The leading dimension of the array VT.  LDVT >= 1; if
		     JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N;
		     if JOBZ = '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;

	   LWORK

		     LWORK is INTEGER
		     The dimension of the array WORK. LWORK >= 1.
		     If JOBZ = 'N',
		       LWORK >= 3*min(M,N) + max(max(M,N),6*min(M,N)).
		     If JOBZ = 'O',
		       LWORK >= 3*min(M,N) +
				max(max(M,N),5*min(M,N)*min(M,N)+4*min(M,N)).
		     If JOBZ = 'S' or 'A'
		       LWORK >= 3*min(M,N) +
				max(max(M,N),4*min(M,N)*min(M,N)+4*min(M,N)).
		     For good performance, LWORK should generally be larger.
		     If LWORK = -1 but other input arguments are legal, WORK(1)
		     returns the optimal LWORK.

	   IWORK

		     IWORK is INTEGER array, dimension (8*min(M,N))

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit.
		     < 0:  if INFO = -i, the i-th argument had an illegal value.
		     > 0:  SBDSDC did not converge, updating process failed.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Contributors:
	   Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

       Definition at line 217 of file sgesdd.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       sgesdd.f(3)