sgeqp3.f.html

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      SUBROUTINE <a name="SGEQP3.1"></a><a href="sgeqp3.f.html#SGEQP3.1">SGEQP3</a>( M, N, A, LDA, JPVT, 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>      INTEGER            INFO, LDA, LWORK, M, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            JPVT( * )
      REAL               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="SGEQP3.18"></a><a href="sgeqp3.f.html#SGEQP3.1">SGEQP3</a> computes a QR factorization with column pivoting of a
</span><span class="comment">*</span><span class="comment">  matrix A:  A*P = Q*R  using Level 3 BLAS.
</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">  M       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of rows of the 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 matrix A.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input/output) REAL 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, the upper triangle of the array contains the
</span><span class="comment">*</span><span class="comment">          min(M,N)-by-N upper trapezoidal matrix R; the elements below
</span><span class="comment">*</span><span class="comment">          the diagonal, together with the array TAU, represent the
</span><span class="comment">*</span><span class="comment">          orthogonal matrix Q as a product of min(M,N) elementary
</span><span class="comment">*</span><span class="comment">          reflectors.
</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">  JPVT    (input/output) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment">          On entry, if JPVT(J).ne.0, the J-th column of A is permuted
</span><span class="comment">*</span><span class="comment">          to the front of A*P (a leading column); if JPVT(J)=0,
</span><span class="comment">*</span><span class="comment">          the J-th column of A is a free column.
</span><span class="comment">*</span><span class="comment">          On exit, if JPVT(J)=K, then the J-th column of A*P was the
</span><span class="comment">*</span><span class="comment">          the K-th column of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TAU     (output) REAL array, dimension (min(M,N))
</span><span class="comment">*</span><span class="comment">          The scalar factors of the elementary reflectors.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace/output) REAL 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;= 3*N+1.
</span><span class="comment">*</span><span class="comment">          For optimal performance LWORK &gt;= 2*N+( N+1 )*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.62"></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">  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">  The matrix Q is represented as a product of elementary reflectors
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Q = H(1) H(2) . . . H(k), where k = min(m,n).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Each H(i) has the form
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     H(i) = I - tau * v * v'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  where tau is a real/complex scalar, and v is a real/complex vector
</span><span class="comment">*</span><span class="comment">  with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
</span><span class="comment">*</span><span class="comment">  A(i+1:m,i), and tau in TAU(i).
</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">    G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
</span><span class="comment">*</span><span class="comment">    X. Sun, Computer Science Dept., Duke University, 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">     .. Parameters ..
</span>      INTEGER            INB, INBMIN, IXOVER
      PARAMETER          ( INB = 1, INBMIN = 2, IXOVER = 3 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            LQUERY
      INTEGER            FJB, IWS, J, JB, LWKOPT, MINMN, MINWS, NA, NB,
     $                   NBMIN, NFXD, NX, SM, SMINMN, SN, TOPBMN
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="SGEQRF.99"></a><a href="sgeqrf.f.html#SGEQRF.1">SGEQRF</a>, <a name="SLAQP2.99"></a><a href="slaqp2.f.html#SLAQP2.1">SLAQP2</a>, <a name="SLAQPS.99"></a><a href="slaqps.f.html#SLAQPS.1">SLAQPS</a>, <a name="SORMQR.99"></a><a href="sormqr.f.html#SORMQR.1">SORMQR</a>, SSWAP, <a name="XERBLA.99"></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">     .. External Functions ..
</span>      INTEGER            <a name="ILAENV.102"></a><a href="hfy-index.html#ILAENV">ILAENV</a>
      REAL               SNRM2
      EXTERNAL           <a name="ILAENV.104"></a><a href="hfy-index.html#ILAENV">ILAENV</a>, SNRM2
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          INT, MAX, MIN
<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>      INFO = 0
      LQUERY = ( LWORK.EQ.-1 )
      IF( M.LT.0 ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
         INFO = -4
      END IF
<span class="comment">*</span><span class="comment">
</span>      IF( INFO.EQ.0 ) THEN
         MINMN = MIN( M, N )
         IF( MINMN.EQ.0 ) THEN
            IWS = 1
            LWKOPT = 1
         ELSE
            IWS = 3*N + 1
            NB = <a name="ILAENV.128"></a><a href="hfy-index.html#ILAENV">ILAENV</a>( INB, <span class="string">'<a name="SGEQRF.128"></a><a href="sgeqrf.f.html#SGEQRF.1">SGEQRF</a>'</span>, <span class="string">' '</span>, M, N, -1, -1 )
            LWKOPT = 2*N + ( N + 1 )*NB
         END IF
         WORK( 1 ) = LWKOPT
<span class="comment">*</span><span class="comment">
</span>         IF( ( LWORK.LT.IWS ) .AND. .NOT.LQUERY ) THEN
            INFO = -8
         END IF
      END IF
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