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SUBROUTINE <a name="DORMBR.1"></a><a href="dormbr.f.html#DORMBR.1">DORMBR</a>( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C,
$ LDC, WORK, LWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK 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 SIDE, TRANS, VECT
INTEGER INFO, K, LDA, LDC, 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, * ), C( LDC, * ), TAU( * ), 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"> If VECT = 'Q', <a name="DORMBR.19"></a><a href="dormbr.f.html#DORMBR.1">DORMBR</a> overwrites the general real M-by-N matrix C
</span><span class="comment">*</span><span class="comment"> with
</span><span class="comment">*</span><span class="comment"> SIDE = 'L' SIDE = 'R'
</span><span class="comment">*</span><span class="comment"> TRANS = 'N': Q * C C * Q
</span><span class="comment">*</span><span class="comment"> TRANS = 'T': Q**T * C C * Q**T
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If VECT = 'P', <a name="DORMBR.25"></a><a href="dormbr.f.html#DORMBR.1">DORMBR</a> overwrites the general real M-by-N matrix C
</span><span class="comment">*</span><span class="comment"> with
</span><span class="comment">*</span><span class="comment"> SIDE = 'L' SIDE = 'R'
</span><span class="comment">*</span><span class="comment"> TRANS = 'N': P * C C * P
</span><span class="comment">*</span><span class="comment"> TRANS = 'T': P**T * C C * P**T
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Here Q and P**T are the orthogonal matrices determined by <a name="DGEBRD.31"></a><a href="dgebrd.f.html#DGEBRD.1">DGEBRD</a> when
</span><span class="comment">*</span><span class="comment"> reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
</span><span class="comment">*</span><span class="comment"> P**T are defined as products of elementary reflectors H(i) and G(i)
</span><span class="comment">*</span><span class="comment"> respectively.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
</span><span class="comment">*</span><span class="comment"> order of the orthogonal matrix Q or P**T that is applied.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
</span><span class="comment">*</span><span class="comment"> if nq >= k, Q = H(1) H(2) . . . H(k);
</span><span class="comment">*</span><span class="comment"> if nq < k, Q = H(1) H(2) . . . H(nq-1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
</span><span class="comment">*</span><span class="comment"> if k < nq, P = G(1) G(2) . . . G(k);
</span><span class="comment">*</span><span class="comment"> if k >= nq, P = G(1) G(2) . . . G(nq-1).
</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"> VECT (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'Q': apply Q or Q**T;
</span><span class="comment">*</span><span class="comment"> = 'P': apply P or P**T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> SIDE (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'L': apply Q, Q**T, P or P**T from the Left;
</span><span class="comment">*</span><span class="comment"> = 'R': apply Q, Q**T, P or P**T from the Right.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TRANS (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'N': No transpose, apply Q or P;
</span><span class="comment">*</span><span class="comment"> = 'T': Transpose, apply Q**T or P**T.
</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 matrix C. 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 matrix C. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> K (input) INTEGER
</span><span class="comment">*</span><span class="comment"> If VECT = 'Q', the number of columns in the original
</span><span class="comment">*</span><span class="comment"> matrix reduced by <a name="DGEBRD.70"></a><a href="dgebrd.f.html#DGEBRD.1">DGEBRD</a>.
</span><span class="comment">*</span><span class="comment"> If VECT = 'P', the number of rows in the original
</span><span class="comment">*</span><span class="comment"> matrix reduced by <a name="DGEBRD.72"></a><a href="dgebrd.f.html#DGEBRD.1">DGEBRD</a>.
</span><span class="comment">*</span><span class="comment"> K >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A (input) DOUBLE PRECISION array, dimension
</span><span class="comment">*</span><span class="comment"> (LDA,min(nq,K)) if VECT = 'Q'
</span><span class="comment">*</span><span class="comment"> (LDA,nq) if VECT = 'P'
</span><span class="comment">*</span><span class="comment"> The vectors which define the elementary reflectors H(i) and
</span><span class="comment">*</span><span class="comment"> G(i), whose products determine the matrices Q and P, as
</span><span class="comment">*</span><span class="comment"> returned by <a name="DGEBRD.80"></a><a href="dgebrd.f.html#DGEBRD.1">DGEBRD</a>.
</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.
</span><span class="comment">*</span><span class="comment"> If VECT = 'Q', LDA >= max(1,nq);
</span><span class="comment">*</span><span class="comment"> if VECT = 'P', LDA >= max(1,min(nq,K)).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TAU (input) DOUBLE PRECISION array, dimension (min(nq,K))
</span><span class="comment">*</span><span class="comment"> TAU(i) must contain the scalar factor of the elementary
</span><span class="comment">*</span><span class="comment"> reflector H(i) or G(i) which determines Q or P, as returned
</span><span class="comment">*</span><span class="comment"> by <a name="DGEBRD.90"></a><a href="dgebrd.f.html#DGEBRD.1">DGEBRD</a> in the array argument TAUQ or TAUP.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
</span><span class="comment">*</span><span class="comment"> On entry, the M-by-N matrix C.
</span><span class="comment">*</span><span class="comment"> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q
</span><span class="comment">*</span><span class="comment"> or P*C or P**T*C or C*P or C*P**T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDC (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array C. LDC >= max(1,M).
</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">
</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.
</span><span class="comment">*</span><span class="comment"> If SIDE = 'L', LWORK >= max(1,N);
</span><span class="comment">*</span><span class="comment"> if SIDE = 'R', LWORK >= max(1,M).
</span><span class="comment">*</span><span class="comment"> For optimum performance LWORK >= N*NB if SIDE = 'L', and
</span><span class="comment">*</span><span class="comment"> LWORK >= M*NB if SIDE = 'R', where NB is the optimal
</span><span class="comment">*</span><span class="comment"> blocksize.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment"> only calculates the optimal size of the WORK array, returns
</span><span class="comment">*</span><span class="comment"> this value as the first entry of the WORK array, and no error
</span><span class="comment">*</span><span class="comment"> message related to LWORK is issued by <a name="XERBLA.114"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</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"> < 0: if INFO = -i, the i-th argument had an illegal value
</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> LOGICAL APPLYQ, LEFT, LQUERY, NOTRAN
CHARACTER TRANST
INTEGER I1, I2, IINFO, LWKOPT, MI, NB, NI, NQ, NW
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.128"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
INTEGER <a name="ILAENV.129"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
EXTERNAL <a name="LSAME.130"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="ILAENV.130"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="DORMLQ.133"></a><a href="dormlq.f.html#DORMLQ.1">DORMLQ</a>, <a name="DORMQR.133"></a><a href="dormqr.f.html#DORMQR.1">DORMQR</a>, <a name="XERBLA.133"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
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