cgeqpf.f.html

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      SUBROUTINE <a name="CGEQPF.1"></a><a href="cgeqpf.f.html#CGEQPF.1">CGEQPF</a>( M, N, A, LDA, JPVT, TAU, WORK, RWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK deprecated driver 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, M, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            JPVT( * )
      REAL               RWORK( * )
      COMPLEX            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">  This routine is deprecated and has been replaced by routine <a name="CGEQP3.19"></a><a href="cgeqp3.f.html#CGEQP3.1">CGEQP3</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="CGEQPF.21"></a><a href="cgeqpf.f.html#CGEQPF.1">CGEQPF</a> computes a QR factorization with column pivoting of a
</span><span class="comment">*</span><span class="comment">  complex M-by-N matrix A: A*P = Q*R.
</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) COMPLEX 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 triangular matrix R; the elements
</span><span class="comment">*</span><span class="comment">          below the diagonal, together with the array TAU,
</span><span class="comment">*</span><span class="comment">          represent the unitary matrix Q as a product of
</span><span class="comment">*</span><span class="comment">          min(m,n) elementary 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(i) .ne. 0, the i-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(i) = 0,
</span><span class="comment">*</span><span class="comment">          the i-th column of A is a free column.
</span><span class="comment">*</span><span class="comment">          On exit, if JPVT(i) = k, then the i-th column of A*P
</span><span class="comment">*</span><span class="comment">          was the k-th column of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TAU     (output) COMPLEX 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) COMPLEX array, dimension (N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  RWORK   (workspace) REAL array, dimension (2*N)
</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(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 - tau * v * v'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  where tau is a complex scalar, and v is a complex vector with
</span><span class="comment">*</span><span class="comment">  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The matrix P is represented in jpvt as follows: If
</span><span class="comment">*</span><span class="comment">     jpvt(j) = i
</span><span class="comment">*</span><span class="comment">  then the jth column of P is the ith canonical unit vector.
</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">
</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            I, ITEMP, J, MA, MN, PVT
      REAL               TEMP, TEMP2, TOL3Z
      COMPLEX            AII
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="CGEQR2.98"></a><a href="cgeqr2.f.html#CGEQR2.1">CGEQR2</a>, <a name="CLARF.98"></a><a href="clarf.f.html#CLARF.1">CLARF</a>, <a name="CLARFG.98"></a><a href="clarfg.f.html#CLARFG.1">CLARFG</a>, CSWAP, <a name="CUNM2R.98"></a><a href="cunm2r.f.html#CUNM2R.1">CUNM2R</a>, <a name="XERBLA.98"></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          ABS, CMPLX, CONJG, MAX, MIN, SQRT
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      INTEGER            ISAMAX
      REAL               SCNRM2, <a name="SLAMCH.105"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
      EXTERNAL           ISAMAX, SCNRM2, <a name="SLAMCH.106"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>
<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><span class="comment">*</span><span class="comment">     Test the input arguments
</span><span class="comment">*</span><span class="comment">
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