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SUBROUTINE <a name="CGESDD.1"></a><a href="cgesdd.f.html#CGESDD.1">CGESDD</a>( JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT,
$ WORK, LWORK, RWORK, IWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK driver routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment"> 8-15-00: Improve consistency of WS calculations (eca)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER JOBZ
INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER IWORK( * )
REAL RWORK( * ), S( * )
COMPLEX A( LDA, * ), U( LDU, * ), VT( LDVT, * ),
$ WORK( * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="CGESDD.23"></a><a href="cgesdd.f.html#CGESDD.1">CGESDD</a> computes the singular value decomposition (SVD) of a complex
</span><span class="comment">*</span><span class="comment"> M-by-N matrix A, optionally computing the left and/or right singular
</span><span class="comment">*</span><span class="comment"> vectors, by using divide-and-conquer method. The SVD is written
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A = U * SIGMA * conjugate-transpose(V)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> where SIGMA is an M-by-N matrix which is zero except for its
</span><span class="comment">*</span><span class="comment"> min(m,n) diagonal elements, U is an M-by-M unitary matrix, and
</span><span class="comment">*</span><span class="comment"> V is an N-by-N unitary matrix. The diagonal elements of SIGMA
</span><span class="comment">*</span><span class="comment"> are the singular values of A; they are real and non-negative, and
</span><span class="comment">*</span><span class="comment"> are returned in descending order. The first min(m,n) columns of
</span><span class="comment">*</span><span class="comment"> U and V are the left and right singular vectors of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Note that the routine returns VT = V**H, not V.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The divide and conquer algorithm makes very mild assumptions about
</span><span class="comment">*</span><span class="comment"> floating point arithmetic. It will work on machines with a guard
</span><span class="comment">*</span><span class="comment"> digit in add/subtract, or on those binary machines without guard
</span><span class="comment">*</span><span class="comment"> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
</span><span class="comment">*</span><span class="comment"> Cray-2. It could conceivably fail on hexadecimal or decimal machines
</span><span class="comment">*</span><span class="comment"> without guard digits, but we know of none.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> JOBZ (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Specifies options for computing all or part of the matrix U:
</span><span class="comment">*</span><span class="comment"> = 'A': all M columns of U and all N rows of V**H are
</span><span class="comment">*</span><span class="comment"> returned in the arrays U and VT;
</span><span class="comment">*</span><span class="comment"> = 'S': the first min(M,N) columns of U and the first
</span><span class="comment">*</span><span class="comment"> min(M,N) rows of V**H are returned in the arrays U
</span><span class="comment">*</span><span class="comment"> and VT;
</span><span class="comment">*</span><span class="comment"> = 'O': If M >= N, the first N columns of U are overwritten
</span><span class="comment">*</span><span class="comment"> in the array A and all rows of V**H are returned in
</span><span class="comment">*</span><span class="comment"> the array VT;
</span><span class="comment">*</span><span class="comment"> otherwise, all columns of U are returned in the
</span><span class="comment">*</span><span class="comment"> array U and the first M rows of V**H are overwritten
</span><span class="comment">*</span><span class="comment"> in the array A;
</span><span class="comment">*</span><span class="comment"> = 'N': no columns of U or rows of V**H are computed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> M (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of rows of the input matrix A. M >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of columns of the input matrix A. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A (input/output) COMPLEX array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment"> On entry, the M-by-N matrix A.
</span><span class="comment">*</span><span class="comment"> On exit,
</span><span class="comment">*</span><span class="comment"> if JOBZ = 'O', A is overwritten with the first N columns
</span><span class="comment">*</span><span class="comment"> of U (the left singular vectors, stored
</span><span class="comment">*</span><span class="comment"> columnwise) if M >= N;
</span><span class="comment">*</span><span class="comment"> A is overwritten with the first M rows
</span><span class="comment">*</span><span class="comment"> of V**H (the right singular vectors, stored
</span><span class="comment">*</span><span class="comment"> rowwise) otherwise.
</span><span class="comment">*</span><span class="comment"> if JOBZ .ne. 'O', the contents of A are destroyed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDA (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array A. LDA >= max(1,M).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> S (output) REAL array, dimension (min(M,N))
</span><span class="comment">*</span><span class="comment"> The singular values of A, sorted so that S(i) >= S(i+1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> U (output) COMPLEX array, dimension (LDU,UCOL)
</span><span class="comment">*</span><span class="comment"> UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
</span><span class="comment">*</span><span class="comment"> UCOL = min(M,N) if JOBZ = 'S'.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
</span><span class="comment">*</span><span class="comment"> unitary matrix U;
</span><span class="comment">*</span><span class="comment"> if JOBZ = 'S', U contains the first min(M,N) columns of U
</span><span class="comment">*</span><span class="comment"> (the left singular vectors, stored columnwise);
</span><span class="comment">*</span><span class="comment"> if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDU (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array U. LDU >= 1; if
</span><span class="comment">*</span><span class="comment"> JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> VT (output) COMPLEX array, dimension (LDVT,N)
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the
</span><span class="comment">*</span><span class="comment"> N-by-N unitary matrix V**H;
</span><span class="comment">*</span><span class="comment"> if JOBZ = 'S', VT contains the first min(M,N) rows of
</span><span class="comment">*</span><span class="comment"> V**H (the right singular vectors, stored rowwise);
</span><span class="comment">*</span><span class="comment"> if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDVT (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array VT. LDVT >= 1; if
</span><span class="comment">*</span><span class="comment"> JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N;
</span><span class="comment">*</span><span class="comment"> if JOBZ = 'S', LDVT >= min(M,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LWORK (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The dimension of the array WORK. LWORK >= 1.
</span><span class="comment">*</span><span class="comment"> if JOBZ = 'N', LWORK >= 2*min(M,N)+max(M,N).
</span><span class="comment">*</span><span class="comment"> if JOBZ = 'O',
</span><span class="comment">*</span><span class="comment"> LWORK >= 2*min(M,N)*min(M,N)+2*min(M,N)+max(M,N).
</span><span class="comment">*</span><span class="comment"> if JOBZ = 'S' or 'A',
</span><span class="comment">*</span><span class="comment"> LWORK >= min(M,N)*min(M,N)+2*min(M,N)+max(M,N).
</span><span class="comment">*</span><span class="comment"> For good performance, LWORK should generally be larger.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If LWORK = -1, a workspace query is assumed. The optimal
</span><span class="comment">*</span><span class="comment"> size for the WORK array is calculated and stored in WORK(1),
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