1DGEQPF(1)       LAPACK deprecated driver routine (version 3.1)       DGEQPF(1)
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NAME

6       DGEQPF - i deprecated and has been replaced by routine DGEQP3
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SYNOPSIS

9       SUBROUTINE DGEQPF( M, N, A, LDA, JPVT, TAU, WORK, INFO )
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11           INTEGER        INFO, LDA, M, N
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13           INTEGER        JPVT( * )
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15           DOUBLE         PRECISION A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

18       This routine is deprecated and has been replaced by routine DGEQP3.
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20       DGEQPF computes a QR factorization with column pivoting of a real M-by-
21       N matrix A: A*P = Q*R.
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ARGUMENTS

25       M       (input) INTEGER
26               The number of rows of the matrix A. M >= 0.
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28       N       (input) INTEGER
29               The number of columns of the matrix A. N >= 0
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31       A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
32               On entry, the M-by-N matrix A.  On exit, the upper triangle  of
33               the array contains the min(M,N)-by-N upper triangular matrix R;
34               the elements below the diagonal, together with the  array  TAU,
35               represent the orthogonal matrix Q as a product of min(m,n) ele‐
36               mentary reflectors.
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38       LDA     (input) INTEGER
39               The leading dimension of the array A. LDA >= max(1,M).
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41       JPVT    (input/output) INTEGER array, dimension (N)
42               On entry, if JPVT(i) .ne. 0, the i-th column of A  is  permuted
43               to  the front of A*P (a leading column); if JPVT(i) = 0, the i-
44               th column of A is a free column.  On exit, if JPVT(i) = k, then
45               the i-th column of A*P was the k-th column of A.
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47       TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))
48               The scalar factors of the elementary reflectors.
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50       WORK    (workspace) DOUBLE PRECISION array, dimension (3*N)
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52       INFO    (output) INTEGER
53               = 0:  successful exit
54               < 0:  if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

57       The matrix Q is represented as a product of elementary reflectors
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59          Q = H(1) H(2) . . . H(n)
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61       Each H(i) has the form
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63          H = I - tau * v * v'
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65       where tau is a real scalar, and v is a real vector with
66       v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i).
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68       The matrix P is represented in jpvt as follows: If
69          jpvt(j) = i
70       then the jth column of P is the ith canonical unit vector.
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72       Partial column norm updating strategy modified by
73         Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
74         University of Zagreb, Croatia.
75         June 2006.
76       For more details see LAPACK Working Note 176.
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81 LAPACK deprecated driver routineN(ovveermsbieorn230.016)                      DGEQPF(1)