slaqps.f.html

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      SUBROUTINE <a name="SLAQPS.1"></a><a href="slaqps.f.html#SLAQPS.1">SLAQPS</a>( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1,
     $                   VN2, AUXV, F, LDF )
<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            KB, LDA, LDF, M, N, NB, OFFSET
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            JPVT( * )
      REAL               A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * ),
     $                   VN1( * ), VN2( * )
<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="SLAQPS.20"></a><a href="slaqps.f.html#SLAQPS.1">SLAQPS</a> computes a step of QR factorization with column pivoting
</span><span class="comment">*</span><span class="comment">  of a real M-by-N matrix A by using Blas-3.  It tries to factorize
</span><span class="comment">*</span><span class="comment">  NB columns from A starting from the row OFFSET+1, and updates all
</span><span class="comment">*</span><span class="comment">  of the matrix with Blas-3 xGEMM.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  In some cases, due to catastrophic cancellations, it cannot
</span><span class="comment">*</span><span class="comment">  factorize NB columns.  Hence, the actual number of factorized
</span><span class="comment">*</span><span class="comment">  columns is returned in KB.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
</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">  OFFSET  (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of rows of A that have been factorized in
</span><span class="comment">*</span><span class="comment">          previous steps.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  NB      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of columns to factorize.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  KB      (output) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of columns actually factorized.
</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, block A(OFFSET+1:M,1:KB) is the triangular
</span><span class="comment">*</span><span class="comment">          factor obtained and block A(1:OFFSET,1:N) has been
</span><span class="comment">*</span><span class="comment">          accordingly pivoted, but no factorized.
</span><span class="comment">*</span><span class="comment">          The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has
</span><span class="comment">*</span><span class="comment">          been updated.
</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">          JPVT(I) = K &lt;==&gt; Column K of the full matrix A has been
</span><span class="comment">*</span><span class="comment">          permuted into position I in AP.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TAU     (output) REAL array, dimension (KB)
</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">  VN1     (input/output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">          The vector with the partial column norms.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  VN2     (input/output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">          The vector with the exact column norms.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  AUXV    (input/output) REAL array, dimension (NB)
</span><span class="comment">*</span><span class="comment">          Auxiliar vector.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  F       (input/output) REAL array, dimension (LDF,NB)
</span><span class="comment">*</span><span class="comment">          Matrix F' = L*Y'*A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDF     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array F. LDF &gt;= max(1,N).
</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">    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">  Partial column norm updating strategy modified by
</span><span class="comment">*</span><span class="comment">    Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
</span><span class="comment">*</span><span class="comment">    University of Zagreb, Croatia.
</span><span class="comment">*</span><span class="comment">    June 2006.
</span><span class="comment">*</span><span class="comment">  For more details see LAPACK Working Note 176.
</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>      REAL               ZERO, ONE
      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            ITEMP, J, K, LASTRK, LSTICC, PVT, RK
      REAL               AKK, TEMP, TEMP2, TOL3Z
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           SGEMM, SGEMV, <a name="SLARFG.106"></a><a href="slarfg.f.html#SLARFG.1">SLARFG</a>, SSWAP
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          ABS, MAX, MIN, NINT, REAL, SQRT
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      INTEGER            ISAMAX
      REAL               <a name="SLAMCH.113"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, SNRM2
      EXTERNAL           ISAMAX, <a name="SLAMCH.114"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, SNRM2
<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>      LASTRK = MIN( M, N+OFFSET )
      LSTICC = 0
      K = 0
      TOL3Z = SQRT(<a name="SLAMCH.121"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>(<span class="string">'Epsilon'</span>))
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Beginning of while loop.
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