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cgesvd(3P)		    Sun Performance Library		    cgesvd(3P)

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

SYNOPSIS
       SUBROUTINE CGESVD(JOBU, JOBVT, M, N, A, LDA, SING, U, LDU, VT, LDVT,
	     WORK, LDWORK, WORK2, INFO)

       CHARACTER * 1 JOBU, JOBVT
       COMPLEX A(LDA,*), U(LDU,*), VT(LDVT,*), WORK(*)
       INTEGER M, N, LDA, LDU, LDVT, LDWORK, INFO
       REAL SING(*), WORK2(*)

       SUBROUTINE CGESVD_64(JOBU, JOBVT, M, N, A, LDA, SING, U, LDU, VT,
	     LDVT, WORK, LDWORK, WORK2, INFO)

       CHARACTER * 1 JOBU, JOBVT
       COMPLEX A(LDA,*), U(LDU,*), VT(LDVT,*), WORK(*)
       INTEGER*8 M, N, LDA, LDU, LDVT, LDWORK, INFO
       REAL SING(*), WORK2(*)

   F95 INTERFACE
       SUBROUTINE GESVD(JOBU, JOBVT, [M], [N], A, [LDA], SING, U, [LDU], VT,
	      [LDVT], [WORK], [LDWORK], [WORK2], [INFO])

       CHARACTER(LEN=1) :: JOBU, JOBVT
       COMPLEX, DIMENSION(:) :: WORK
       COMPLEX, DIMENSION(:,:) :: A, U, VT
       INTEGER :: M, N, LDA, LDU, LDVT, LDWORK, INFO
       REAL, DIMENSION(:) :: SING, WORK2

       SUBROUTINE GESVD_64(JOBU, JOBVT, [M], [N], A, [LDA], SING, U, [LDU],
	      VT, [LDVT], [WORK], [LDWORK], [WORK2], [INFO])

       CHARACTER(LEN=1) :: JOBU, JOBVT
       COMPLEX, DIMENSION(:) :: WORK
       COMPLEX, DIMENSION(:,:) :: A, U, VT
       INTEGER(8) :: M, N, LDA, LDU, LDVT, LDWORK, INFO
       REAL, DIMENSION(:) :: SING, WORK2

   C INTERFACE
       #include <sunperf.h>

       void  cgesvd(char  jobu, char jobvt, int m, int n, complex *a, int lda,
		 float *sing, complex *u, int ldu, complex *vt, int ldvt,  int
		 *info);

       void  cgesvd_64(char jobu, char jobvt, long m, long n, complex *a, long
		 lda, float *sing, complex *u, long  ldu,  complex  *vt,  long
		 ldvt, long *info);

PURPOSE
       cgesvd  computes the singular value decomposition (SVD) of a complex M-
       by-N matrix A, optionally computing the left and/or right singular vec‐
       tors. The SVD is written
	= 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)
		 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	 over‐
		 written on the array A; = 'N':	 no columns of U (no left sin‐
		 gular vectors) are computed.

       JOBVT (input)
		 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 over‐
		 written on the array A; = 'N':	 no rows  of  V**H  (no	 right
		 singular vectors) are computed.

		 JOBVT and JOBU cannot both be 'O'.

       M (input) The number of rows of the input matrix A.  M >= 0.

       N (input) The number of columns of the input matrix A.  N >= 0.

       A (input/output)
		 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)
		 The leading dimension of the array A.	LDA >= max(1,M).

       SING (output)
		 The  singular	values	of  A,	sorted	so  that  SING(i)   >=
		 SING(i+1).

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

       VT (output)
		 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)
		 The leading dimension of the array VT.	 LDVT >= 1; if JOBVT =
		 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N).

       WORK (workspace)
		 On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.

       LDWORK (input)
		 The dimension of the array WORK.  LDWORK  >=  1.   LDWORK  >=
		 2*MIN(M,N)+MAX(M,N)  For good performance, LDWORK should gen‐
		 erally be larger.

		 If LDWORK = -1, then a workspace query is assumed;  the  rou‐
		 tine  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 LDWORK is issued by XERBLA.

       WORK2 (workspace)
		 DIMENSION(5*MIN(M,N)).	    On	  exit,	   if	 INFO	>   0,
		 WORK2(1:MIN(M,N)-1) contains  the  unconverged	 superdiagonal
		 elements of an upper bidiagonal matrix B whose diagonal is in
		 SING (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)
		 = 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  WORK2  above  for
		 details.

				  6 Mar 2009			    cgesvd(3P)
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