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SUBROUTINE CTZRQF( M, N, A, LDA, TAU, INFO )
*
* -- LAPACK routine (version 3.2.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* June 2010
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, M, N
* ..
* .. Array Arguments ..
COMPLEX A( LDA, * ), TAU( * )
* ..
*
* Purpose
* =======
*
* This routine is deprecated and has been replaced by routine CTZRZF.
*
* CTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
* to upper triangular form by means of unitary transformations.
*
* The upper trapezoidal matrix A is factored as
*
* A = ( R 0 ) * Z,
*
* where Z is an N-by-N unitary matrix and R is an M-by-M upper
* triangular matrix.
*
* Arguments
* =========
*
* M (input) INTEGER
* The number of rows of the matrix A. M >= 0.
*
* N (input) INTEGER
* The number of columns of the matrix A. N >= M.
*
* A (input/output) COMPLEX array, dimension (LDA,N)
* On entry, the leading M-by-N upper trapezoidal part of the
* array A must contain the matrix to be factorized.
* On exit, the leading M-by-M upper triangular part of A
* contains the upper triangular matrix R, and elements M+1 to
* N of the first M rows of A, with the array TAU, represent the
* unitary matrix Z as a product of M elementary reflectors.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,M).
*
* TAU (output) COMPLEX array, dimension (M)
* The scalar factors of the elementary reflectors.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* Further Details
* ===============
*
* The factorization is obtained by Householder's method. The kth
* transformation matrix, Z( k ), whose conjugate transpose is used to
* introduce zeros into the (m - k + 1)th row of A, is given in the form
*
* Z( k ) = ( I 0 ),
* ( 0 T( k ) )
*
* where
*
* T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ),
* ( 0 )
* ( z( k ) )
*
* tau is a scalar and z( k ) is an ( n - m ) element vector.
* tau and z( k ) are chosen to annihilate the elements of the kth row
* of X.
*
* The scalar tau is returned in the kth element of TAU and the vector
* u( k ) in the kth row of A, such that the elements of z( k ) are
* in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
* the upper triangular part of A.
*
* Z is given by
*
* Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
*
* =====================================================================
*
* .. Parameters ..
COMPLEX CONE, CZERO
PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ),
$ CZERO = ( 0.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
INTEGER I, K, M1
COMPLEX ALPHA
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG, MAX, MIN
* ..
* .. External Subroutines ..
EXTERNAL CAXPY, CCOPY, CGEMV, CGERC, CLACGV, CLARFG,
$ XERBLA
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
IF( M.LT.0 ) THEN
INFO = -1
ELSE IF( N.LT.M ) THEN
INFO = -2
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -4
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CTZRQF', -INFO )
RETURN
END IF
*
* Perform the factorization.
*
IF( M.EQ.0 )
$ RETURN
IF( M.EQ.N ) THEN
DO 10 I = 1, N
TAU( I ) = CZERO
10 CONTINUE
ELSE
M1 = MIN( M+1, N )
DO 20 K = M, 1, -1
*
* Use a Householder reflection to zero the kth row of A.
* First set up the reflection.
*
A( K, K ) = CONJG( A( K, K ) )
CALL CLACGV( N-M, A( K, M1 ), LDA )
ALPHA = A( K, K )
CALL CLARFG( N-M+1, ALPHA, A( K, M1 ), LDA, TAU( K ) )
A( K, K ) = ALPHA
TAU( K ) = CONJG( TAU( K ) )
*
IF( TAU( K ).NE.CZERO .AND. K.GT.1 ) THEN
*
* We now perform the operation A := A*P( k )'.
*
* Use the first ( k - 1 ) elements of TAU to store a( k ),
* where a( k ) consists of the first ( k - 1 ) elements of
* the kth column of A. Also let B denote the first
* ( k - 1 ) rows of the last ( n - m ) columns of A.
*
CALL CCOPY( K-1, A( 1, K ), 1, TAU, 1 )
*
* Form w = a( k ) + B*z( k ) in TAU.
*
CALL CGEMV( 'No transpose', K-1, N-M, CONE, A( 1, M1 ),
$ LDA, A( K, M1 ), LDA, CONE, TAU, 1 )
*
* Now form a( k ) := a( k ) - conjg(tau)*w
* and B := B - conjg(tau)*w*z( k )'.
*
CALL CAXPY( K-1, -CONJG( TAU( K ) ), TAU, 1, A( 1, K ),
$ 1 )
CALL CGERC( K-1, N-M, -CONJG( TAU( K ) ), TAU, 1,
$ A( K, M1 ), LDA, A( 1, M1 ), LDA )
END IF
20 CONTINUE
END IF
*
RETURN
*
* End of CTZRQF
*
END
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