dorgbr.f.html

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      SUBROUTINE <a name="DORGBR.1"></a><a href="dorgbr.f.html#DORGBR.1">DORGBR</a>( VECT, M, N, K, A, LDA, TAU, 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          VECT
      INTEGER            INFO, K, LDA, 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, * ), 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">  <a name="DORGBR.18"></a><a href="dorgbr.f.html#DORGBR.1">DORGBR</a> generates one of the real orthogonal matrices Q or P**T
</span><span class="comment">*</span><span class="comment">  determined by <a name="DGEBRD.19"></a><a href="dgebrd.f.html#DGEBRD.1">DGEBRD</a> when reducing a real matrix A to bidiagonal
</span><span class="comment">*</span><span class="comment">  form: A = Q * B * P**T.  Q and P**T are defined as products of
</span><span class="comment">*</span><span class="comment">  elementary reflectors H(i) or G(i) respectively.
</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 M-by-K matrix, and Q
</span><span class="comment">*</span><span class="comment">  is of order M:
</span><span class="comment">*</span><span class="comment">  if m &gt;= k, Q = H(1) H(2) . . . H(k) and <a name="DORGBR.25"></a><a href="dorgbr.f.html#DORGBR.1">DORGBR</a> returns the first n
</span><span class="comment">*</span><span class="comment">  columns of Q, where m &gt;= n &gt;= k;
</span><span class="comment">*</span><span class="comment">  if m &lt; k, Q = H(1) H(2) . . . H(m-1) and <a name="DORGBR.27"></a><a href="dorgbr.f.html#DORGBR.1">DORGBR</a> returns Q as an
</span><span class="comment">*</span><span class="comment">  M-by-M matrix.
</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-N matrix, and P**T
</span><span class="comment">*</span><span class="comment">  is of order N:
</span><span class="comment">*</span><span class="comment">  if k &lt; n, P**T = G(k) . . . G(2) G(1) and <a name="DORGBR.32"></a><a href="dorgbr.f.html#DORGBR.1">DORGBR</a> returns the first m
</span><span class="comment">*</span><span class="comment">  rows of P**T, where n &gt;= m &gt;= k;
</span><span class="comment">*</span><span class="comment">  if k &gt;= n, P**T = G(n-1) . . . G(2) G(1) and <a name="DORGBR.34"></a><a href="dorgbr.f.html#DORGBR.1">DORGBR</a> returns P**T as
</span><span class="comment">*</span><span class="comment">  an N-by-N matrix.
</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">          Specifies whether the matrix Q or the matrix P**T is
</span><span class="comment">*</span><span class="comment">          required, as defined in the transformation applied by <a name="DGEBRD.42"></a><a href="dgebrd.f.html#DGEBRD.1">DGEBRD</a>:
</span><span class="comment">*</span><span class="comment">          = 'Q':  generate Q;
</span><span class="comment">*</span><span class="comment">          = 'P':  generate 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 Q or P**T to be returned.
</span><span class="comment">*</span><span class="comment">          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 matrix Q or P**T to be returned.
</span><span class="comment">*</span><span class="comment">          N &gt;= 0.
</span><span class="comment">*</span><span class="comment">          If VECT = 'Q', M &gt;= N &gt;= min(M,K);
</span><span class="comment">*</span><span class="comment">          if VECT = 'P', N &gt;= M &gt;= min(N,K).
</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 M-by-K
</span><span class="comment">*</span><span class="comment">          matrix reduced by <a name="DGEBRD.58"></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 K-by-N
</span><span class="comment">*</span><span class="comment">          matrix reduced by <a name="DGEBRD.60"></a><a href="dgebrd.f.html#DGEBRD.1">DGEBRD</a>.
</span><span class="comment">*</span><span class="comment">          K &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 vectors which define the elementary reflectors,
</span><span class="comment">*</span><span class="comment">          as returned by <a name="DGEBRD.65"></a><a href="dgebrd.f.html#DGEBRD.1">DGEBRD</a>.
</span><span class="comment">*</span><span class="comment">          On exit, the M-by-N matrix Q or P**T.
</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">  TAU     (input) DOUBLE PRECISION array, dimension
</span><span class="comment">*</span><span class="comment">                                (min(M,K)) if VECT = 'Q'
</span><span class="comment">*</span><span class="comment">                                (min(N,K)) if VECT = 'P'
</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**T, as
</span><span class="comment">*</span><span class="comment">          returned by <a name="DGEBRD.76"></a><a href="dgebrd.f.html#DGEBRD.1">DGEBRD</a> in its array argument TAUQ or TAUP.
</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. LWORK &gt;= max(1,min(M,N)).
</span><span class="comment">*</span><span class="comment">          For optimum performance LWORK &gt;= min(M,N)*NB, where NB
</span><span class="comment">*</span><span class="comment">          is the optimal 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.89"></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">          &lt; 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">     .. Parameters ..
</span>      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            LQUERY, WANTQ
      INTEGER            I, IINFO, J, LWKOPT, MN, NB
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.106"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      INTEGER            <a name="ILAENV.107"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
      EXTERNAL           <a name="LSAME.108"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="ILAENV.108"></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="DORGLQ.111"></a><a href="dorglq.f.html#DORGLQ.1">DORGLQ</a>, <a name="DORGQR.111"></a><a href="dorgqr.f.html#DORGQR.1">DORGQR</a>, <a name="XERBLA.111"></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">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX, MIN
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
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