slasd0.f.html

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      SUBROUTINE <a name="SLASD0.1"></a><a href="slasd0.f.html#SLASD0.1">SLASD0</a>( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK,
     $                   WORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK auxiliary 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>      INTEGER            INFO, LDU, LDVT, N, SMLSIZ, SQRE
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            IWORK( * )
      REAL               D( * ), E( * ), 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">  Using a divide and conquer approach, <a name="SLASD0.20"></a><a href="slasd0.f.html#SLASD0.1">SLASD0</a> computes the singular
</span><span class="comment">*</span><span class="comment">  value decomposition (SVD) of a real upper bidiagonal N-by-M
</span><span class="comment">*</span><span class="comment">  matrix B with diagonal D and offdiagonal E, where M = N + SQRE.
</span><span class="comment">*</span><span class="comment">  The algorithm computes orthogonal matrices U and VT such that
</span><span class="comment">*</span><span class="comment">  B = U * S * VT. The singular values S are overwritten on D.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A related subroutine, <a name="SLASDA.26"></a><a href="slasda.f.html#SLASDA.1">SLASDA</a>, computes only the singular values,
</span><span class="comment">*</span><span class="comment">  and optionally, the singular vectors in compact form.
</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">  N      (input) INTEGER
</span><span class="comment">*</span><span class="comment">         On entry, the row dimension of the upper bidiagonal matrix.
</span><span class="comment">*</span><span class="comment">         This is also the dimension of the main diagonal array D.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SQRE   (input) INTEGER
</span><span class="comment">*</span><span class="comment">         Specifies the column dimension of the bidiagonal matrix.
</span><span class="comment">*</span><span class="comment">         = 0: The bidiagonal matrix has column dimension M = N;
</span><span class="comment">*</span><span class="comment">         = 1: The bidiagonal matrix has column dimension M = N+1;
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  D      (input/output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">         On entry D contains the main diagonal of the bidiagonal
</span><span class="comment">*</span><span class="comment">         matrix.
</span><span class="comment">*</span><span class="comment">         On exit D, if INFO = 0, contains its singular values.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  E      (input) REAL array, dimension (M-1)
</span><span class="comment">*</span><span class="comment">         Contains the subdiagonal entries of the bidiagonal matrix.
</span><span class="comment">*</span><span class="comment">         On exit, E has been destroyed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  U      (output) REAL array, dimension at least (LDQ, N)
</span><span class="comment">*</span><span class="comment">         On exit, U contains the left singular vectors.
</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">         On entry, leading dimension of U.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  VT     (output) REAL array, dimension at least (LDVT, M)
</span><span class="comment">*</span><span class="comment">         On exit, VT' contains the right singular vectors.
</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">         On entry, leading dimension of VT.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SMLSIZ (input) INTEGER
</span><span class="comment">*</span><span class="comment">         On entry, maximum size of the subproblems at the
</span><span class="comment">*</span><span class="comment">         bottom of the computation tree.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IWORK  (workspace) INTEGER array, dimension (8*N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK   (workspace) REAL array, dimension (3*M**2+2*M)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO   (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit.
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value.
</span><span class="comment">*</span><span class="comment">          &gt; 0:  if INFO = 1, an singular value did not converge
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further Details
</span><span class="comment">*</span><span class="comment">  ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Based on contributions by
</span><span class="comment">*</span><span class="comment">     Ming Gu and Huan Ren, Computer Science Division, University of
</span><span class="comment">*</span><span class="comment">     California at Berkeley, USA
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I, I1, IC, IDXQ, IDXQC, IM1, INODE, ITEMP, IWK,
     $                   J, LF, LL, LVL, M, NCC, ND, NDB1, NDIML, NDIMR,
     $                   NL, NLF, NLP1, NLVL, NR, NRF, NRP1, SQREI
      REAL               ALPHA, BETA
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="SLASD1.91"></a><a href="slasd1.f.html#SLASD1.1">SLASD1</a>, <a name="SLASDQ.91"></a><a href="slasdq.f.html#SLASDQ.1">SLASDQ</a>, <a name="SLASDT.91"></a><a href="slasdt.f.html#SLASDT.1">SLASDT</a>, <a name="XERBLA.91"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
<span class="comment">*</span><span class="comment">
</span>      IF( N.LT.0 ) THEN
         INFO = -1
      ELSE IF( ( SQRE.LT.0 ) .OR. ( SQRE.GT.1 ) ) THEN
         INFO = -2
      END IF
<span class="comment">*</span><span class="comment">
</span>      M = N + SQRE
<span class="comment">*</span><span class="comment">
</span>      IF( LDU.LT.N ) THEN
         INFO = -6
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