1CTZRQF(1)                LAPACK routine (version 3.2)                CTZRQF(1)
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NAME

6       CTZRQF - routine i deprecated and has been replaced by routine CTZRZF
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SYNOPSIS

9       SUBROUTINE CTZRQF( M, N, A, LDA, TAU, INFO )
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11           INTEGER        INFO, LDA, M, N
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13           COMPLEX        A( LDA, * ), TAU( * )
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PURPOSE

16       This  routine  is  deprecated  and has been replaced by routine CTZRZF.
17       CTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal  matrix  A
18       to  upper  triangular  form  by  means of unitary transformations.  The
19       upper trapezoidal matrix A is factored as
20          A = ( R  0 ) * Z,
21       where Z is an N-by-N unitary matrix and R is an M-by-M upper triangular
22       matrix.
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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 >= M.
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31       A       (input/output) COMPLEX array, dimension (LDA,N)
32               On  entry,  the  leading  M-by-N  upper trapezoidal part of the
33               array A must contain the matrix to be factorized.  On exit, the
34               leading  M-by-M  upper  triangular part of A contains the upper
35               triangular matrix R, and elements M+1 to N of the first M  rows
36               of  A,  with the array TAU, represent the unitary matrix Z as a
37               product of M elementary reflectors.
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39       LDA     (input) INTEGER
40               The leading dimension of the array A.  LDA >= max(1,M).
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42       TAU     (output) COMPLEX array, dimension (M)
43               The scalar factors of the elementary reflectors.
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45       INFO    (output) INTEGER
46               = 0: successful exit
47               < 0: if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

50       The  factorization is obtained by Householder's method.  The kth trans‐
51       formation  matrix,  Z( k ), whose conjugate transpose is used to intro‐
52       duce zeros into the (m - k + 1)th row of A, is given in the form
53          Z( k ) = ( I     0   ),
54                   ( 0  T( k ) )
55       where
56          T( k ) = I - tau*u( k )*u( k )',   u( k ) = (   1    ),
57                                                      (   0    )
58                                                      ( z( k  )  )  tau  is  a
59       scalar  and  z( k ) is an ( n - m ) element vector.  tau and z( k ) are
60       chosen to annihilate the elements of the kth row of X.
61       The scalar tau is returned in the kth element of TAU and the vector  u(
62       k ) in the kth row of A, such that the elements of z( k ) are in  a( k,
63       m + 1 ), ..., a( k, n ). The elements of R are returned  in  the  upper
64       triangular part of A.
65       Z is given by
66          Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).
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70 LAPACK routine (version 3.2)    November 2008                       CTZRQF(1)