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SUBROUTINE <a name="DLASDA.1"></a><a href="dlasda.f.html#DLASDA.1">DLASDA</a>( ICOMPQ, SMLSIZ, N, SQRE, D, E, U, LDU, VT, K,
$ DIFL, DIFR, Z, POLES, GIVPTR, GIVCOL, LDGCOL,
$ PERM, GIVNUM, C, S, WORK, IWORK, 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 ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ),
$ K( * ), PERM( LDGCOL, * )
DOUBLE PRECISION C( * ), D( * ), DIFL( LDU, * ), DIFR( LDU, * ),
$ E( * ), GIVNUM( LDU, * ), POLES( LDU, * ),
$ S( * ), U( LDU, * ), VT( LDU, * ), WORK( * ),
$ Z( LDU, * )
<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="DLASDA.24"></a><a href="dlasda.f.html#DLASDA.1">DLASDA</a> computes the singular
</span><span class="comment">*</span><span class="comment"> value decomposition (SVD) of a real upper bidiagonal N-by-M matrix
</span><span class="comment">*</span><span class="comment"> B with diagonal D and offdiagonal E, where M = N + SQRE. The
</span><span class="comment">*</span><span class="comment"> algorithm computes the singular values in the SVD B = U * S * VT.
</span><span class="comment">*</span><span class="comment"> The orthogonal matrices U and VT are optionally computed in
</span><span class="comment">*</span><span class="comment"> compact form.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A related subroutine, <a name="DLASD0.31"></a><a href="dlasd0.f.html#DLASD0.1">DLASD0</a>, computes the singular values and
</span><span class="comment">*</span><span class="comment"> the singular vectors in explicit 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"> ICOMPQ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> Specifies whether singular vectors are to be computed
</span><span class="comment">*</span><span class="comment"> in compact form, as follows
</span><span class="comment">*</span><span class="comment"> = 0: Compute singular values only.
</span><span class="comment">*</span><span class="comment"> = 1: Compute singular vectors of upper bidiagonal
</span><span class="comment">*</span><span class="comment"> matrix in compact form.
</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"> The maximum size of the subproblems at the bottom of the
</span><span class="comment">*</span><span class="comment"> computation tree.
</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 row dimension of the upper bidiagonal matrix. This is
</span><span class="comment">*</span><span class="comment"> 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) DOUBLE PRECISION 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. 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) DOUBLE PRECISION 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) DOUBLE PRECISION array,
</span><span class="comment">*</span><span class="comment"> dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced
</span><span class="comment">*</span><span class="comment"> if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left
</span><span class="comment">*</span><span class="comment"> singular vector matrices of all subproblems at the bottom
</span><span class="comment">*</span><span class="comment"> level.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDU (input) INTEGER, LDU = > N.
</span><span class="comment">*</span><span class="comment"> The leading dimension of arrays U, VT, DIFL, DIFR, POLES,
</span><span class="comment">*</span><span class="comment"> GIVNUM, and Z.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> VT (output) DOUBLE PRECISION array,
</span><span class="comment">*</span><span class="comment"> dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced
</span><span class="comment">*</span><span class="comment"> if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT' contains the right
</span><span class="comment">*</span><span class="comment"> singular vector matrices of all subproblems at the bottom
</span><span class="comment">*</span><span class="comment"> level.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> K (output) INTEGER array,
</span><span class="comment">*</span><span class="comment"> dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0.
</span><span class="comment">*</span><span class="comment"> If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th
</span><span class="comment">*</span><span class="comment"> secular equation on the computation tree.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> DIFL (output) DOUBLE PRECISION array, dimension ( LDU, NLVL ),
</span><span class="comment">*</span><span class="comment"> where NLVL = floor(log_2 (N/SMLSIZ))).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> DIFR (output) DOUBLE PRECISION array,
</span><span class="comment">*</span><span class="comment"> dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and
</span><span class="comment">*</span><span class="comment"> dimension ( N ) if ICOMPQ = 0.
</span><span class="comment">*</span><span class="comment"> If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1)
</span><span class="comment">*</span><span class="comment"> record distances between singular values on the I-th
</span><span class="comment">*</span><span class="comment"> level and singular values on the (I -1)-th level, and
</span><span class="comment">*</span><span class="comment"> DIFR(1:N, 2 * I ) contains the normalizing factors for
</span><span class="comment">*</span><span class="comment"> the right singular vector matrix. See <a name="DLASD8.96"></a><a href="dlasd8.f.html#DLASD8.1">DLASD8</a> for details.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Z (output) DOUBLE PRECISION array,
</span><span class="comment">*</span><span class="comment"> dimension ( LDU, NLVL ) if ICOMPQ = 1 and
</span><span class="comment">*</span><span class="comment"> dimension ( N ) if ICOMPQ = 0.
</span><span class="comment">*</span><span class="comment"> The first K elements of Z(1, I) contain the components of
</span><span class="comment">*</span><span class="comment"> the deflation-adjusted updating row vector for subproblems
</span><span class="comment">*</span><span class="comment"> on the I-th level.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> POLES (output) DOUBLE PRECISION array,
</span><span class="comment">*</span><span class="comment"> dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced
</span><span class="comment">*</span><span class="comment"> if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and
</span><span class="comment">*</span><span class="comment"> POLES(1, 2*I) contain the new and old singular values
</span><span class="comment">*</span><span class="comment"> involved in the secular equations on the I-th level.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> GIVPTR (output) INTEGER array,
</span><span class="comment">*</span><span class="comment"> dimension ( N ) if ICOMPQ = 1, and not referenced if
</span><span class="comment">*</span><span class="comment"> ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records
</span><span class="comment">*</span><span class="comment"> the number of Givens rotations performed on the I-th
</span><span class="comment">*</span><span class="comment"> problem on the computation tree.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> GIVCOL (output) INTEGER array,
</span><span class="comment">*</span><span class="comment"> dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not
</span><span class="comment">*</span><span class="comment"> referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
</span><span class="comment">*</span><span class="comment"> GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations
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