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      SUBROUTINE <a name="DGESVD.1"></a><a href="dgesvd.f.html#DGESVD.1">DGESVD</a>( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT,
     $                   WORK, LWORK, 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">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          JOBU, JOBVT
      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>      DOUBLE PRECISION   A( LDA, * ), S( * ), 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="DGESVD.20"></a><a href="dgesvd.f.html#DGESVD.1">DGESVD</a> computes the singular value decomposition (SVD) of a real
</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. The SVD is written
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">       A = U * SIGMA * 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 orthogonal matrix, and
</span><span class="comment">*</span><span class="comment">  V is an N-by-N orthogonal 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 V**T, not V.
</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">  JOBU    (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 are returned in array U:
</span><span class="comment">*</span><span class="comment">          = 'S':  the first min(m,n) columns of U (the left singular
</span><span class="comment">*</span><span class="comment">                  vectors) are returned in the array U;
</span><span class="comment">*</span><span class="comment">          = 'O':  the first min(m,n) columns of U (the left singular
</span><span class="comment">*</span><span class="comment">                  vectors) are overwritten on the array A;
</span><span class="comment">*</span><span class="comment">          = 'N':  no columns of U (no left singular vectors) are
</span><span class="comment">*</span><span class="comment">                  computed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  JOBVT   (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies options for computing all or part of the matrix
</span><span class="comment">*</span><span class="comment">          V**T:
</span><span class="comment">*</span><span class="comment">          = 'A':  all N rows of V**T are returned in the array VT;
</span><span class="comment">*</span><span class="comment">          = 'S':  the first min(m,n) rows of V**T (the right singular
</span><span class="comment">*</span><span class="comment">                  vectors) are returned in the array VT;
</span><span class="comment">*</span><span class="comment">          = 'O':  the first min(m,n) rows of V**T (the right singular
</span><span class="comment">*</span><span class="comment">                  vectors) are overwritten on the array A;
</span><span class="comment">*</span><span class="comment">          = 'N':  no rows of V**T (no right singular vectors) are
</span><span class="comment">*</span><span class="comment">                  computed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          JOBVT and JOBU cannot both be 'O'.
</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 &gt;= 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 &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input/output) DOUBLE PRECISION 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 JOBU = 'O',  A is overwritten with the first min(m,n)
</span><span class="comment">*</span><span class="comment">                          columns of U (the left singular vectors,
</span><span class="comment">*</span><span class="comment">                          stored columnwise);
</span><span class="comment">*</span><span class="comment">          if JOBVT = 'O', A is overwritten with the first min(m,n)
</span><span class="comment">*</span><span class="comment">                          rows of V**T (the right singular vectors,
</span><span class="comment">*</span><span class="comment">                          stored rowwise);
</span><span class="comment">*</span><span class="comment">          if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A
</span><span class="comment">*</span><span class="comment">                          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 &gt;= max(1,M).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  S       (output) DOUBLE PRECISION array, dimension (min(M,N))
</span><span class="comment">*</span><span class="comment">          The singular values of A, sorted so that S(i) &gt;= S(i+1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  U       (output) DOUBLE PRECISION array, dimension (LDU,UCOL)
</span><span class="comment">*</span><span class="comment">          (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'.
</span><span class="comment">*</span><span class="comment">          If JOBU = 'A', U contains the M-by-M orthogonal matrix U;
</span><span class="comment">*</span><span class="comment">          if JOBU = '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 JOBU = 'N' or 'O', 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 &gt;= 1; if
</span><span class="comment">*</span><span class="comment">          JOBU = 'S' or 'A', LDU &gt;= M.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  VT      (output) DOUBLE PRECISION array, dimension (LDVT,N)
</span><span class="comment">*</span><span class="comment">          If JOBVT = 'A', VT contains the N-by-N orthogonal matrix
</span><span class="comment">*</span><span class="comment">          V**T;
</span><span class="comment">*</span><span class="comment">          if JOBVT = 'S', VT contains the first min(m,n) rows of
</span><span class="comment">*</span><span class="comment">          V**T (the right singular vectors, stored rowwise);
</span><span class="comment">*</span><span class="comment">          if JOBVT = 'N' or 'O', 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 &gt;= 1; if
</span><span class="comment">*</span><span class="comment">          JOBVT = 'A', LDVT &gt;= N; if JOBVT = 'S', LDVT &gt;= min(M,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace/output) DOUBLE PRECISION 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">          if INFO &gt; 0, WORK(2:MIN(M,N)) contains the unconverged
</span><span class="comment">*</span><span class="comment">          superdiagonal elements of an upper bidiagonal matrix B
</span><span class="comment">*</span><span class="comment">          whose diagonal is in S (not necessarily sorted). B
</span><span class="comment">*</span><span class="comment">          satisfies A = U * B * VT, so it has the same singular values
</span><span class="comment">*</span><span class="comment">          as A, and singular vectors related by U and VT.
</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.
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