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SUBROUTINE <a name="SGEQPF.1"></a><a href="sgeqpf.f.html#SGEQPF.1">SGEQPF</a>( M, N, A, LDA, JPVT, TAU, WORK, 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 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 This routine is deprecated and has been replaced by routine 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="SGEQP3.18"></a><a href="sgeqp3.f.html#SGEQP3.1">SGEQP3</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="SGEQPF.20"></a><a href="sgeqpf.f.html#SGEQPF.1">SGEQPF</a> computes a QR factorization with column pivoting of a
</span><span class="comment">*</span><span class="comment"> real 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 >= 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 >= 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 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 orthogonal 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 >= 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) 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) REAL array, dimension (3*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"> < 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 real scalar, and v is a real 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 AII, TEMP, TEMP2, TOL3Z
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="SGEQR2.94"></a><a href="sgeqr2.f.html#SGEQR2.1">SGEQR2</a>, <a name="SLARF.94"></a><a href="slarf.f.html#SLARF.1">SLARF</a>, <a name="SLARFG.94"></a><a href="slarfg.f.html#SLARFG.1">SLARFG</a>, <a name="SORM2R.94"></a><a href="sorm2r.f.html#SORM2R.1">SORM2R</a>, SSWAP, <a name="XERBLA.94"></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, MAX, MIN, 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.101"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, SNRM2
EXTERNAL ISAMAX, <a name="SLAMCH.102"></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><span class="comment">*</span><span class="comment"> Test the input arguments
</span><span class="comment">*</span><span class="comment">
</span> INFO = 0
IF( M.LT.0 ) THEN
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