cgesvd man page on IRIX

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CGESVD(3F)							    CGESVD(3F)

NAME
     CGESVD - compute the singular value decomposition (SVD) of a complex M-
     by-N matrix A, optionally computing the left and/or right singular
     vectors

SYNOPSIS
     SUBROUTINE CGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK,
			LWORK, RWORK, INFO )

	 CHARACTER	JOBU, JOBVT

	 INTEGER	INFO, LDA, LDU, LDVT, LWORK, M, N

	 REAL		RWORK( * ), S( * )

	 COMPLEX	A( LDA, * ), U( LDU, * ), VT( LDVT, * ), WORK( * )

PURPOSE
     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

	  A = 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.

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**H:
	     = 'A':  all N rows of V**H are returned in the array VT;
	     = 'S':  the first min(m,n) rows of V**H (the right singular
	     vectors) are returned in the array VT; = 'O':  the first min(m,n)
	     rows of V**H (the right singular vectors) are overwritten on the
	     array A; = 'N':  no rows of V**H (no right singular vectors) are
	     computed.

									Page 1

CGESVD(3F)							    CGESVD(3F)

	     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) COMPLEX 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**H (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) COMPLEX 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 unitary 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) COMPLEX array, dimension (LDVT,N)
	     If JOBVT = 'A', VT contains the N-by-N unitary matrix V**H; if
	     JOBVT = 'S', 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.

     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) COMPLEX array, dimension (LWORK)
	     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

     LWORK   (input) INTEGER
	     The dimension of the array WORK. LWORK >= 1.  LWORK >=
	     2*MIN(M,N)+MAX(M,N).  For good performance, LWORK should
	     generally be larger.

									Page 2

CGESVD(3F)							    CGESVD(3F)

     RWORK   (workspace) REAL array, dimension
	     (max(3*min(M,N),5*min(M,N)-4)) On exit, if INFO > 0,
	     RWORK(1:MIN(M,N)-1) 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.

     INFO    (output) INTEGER
	     = 0:  successful exit.
	     < 0:  if INFO = -i, the i-th argument had an illegal value.
	     > 0:  if CBDSQR did not converge, INFO specifies how many
	     superdiagonals of an intermediate bidiagonal form B did not
	     converge to zero. See the description of RWORK above for details.

									Page 3

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