174 lines
5.2 KiB
FortranFixed
174 lines
5.2 KiB
FortranFixed
SUBROUTINE ZTZRQF( M, N, A, LDA, TAU, INFO )
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*
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* -- LAPACK routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, M, N
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* ..
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* .. Array Arguments ..
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COMPLEX*16 A( LDA, * ), TAU( * )
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* ..
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*
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* Purpose
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* =======
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*
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* This routine is deprecated and has been replaced by routine ZTZRZF.
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*
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* ZTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
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* to upper triangular form by means of unitary transformations.
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*
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* The upper trapezoidal matrix A is factored as
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*
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* A = ( R 0 ) * Z,
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*
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* where Z is an N-by-N unitary matrix and R is an M-by-M upper
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* triangular matrix.
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*
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* Arguments
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* =========
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*
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* M (input) INTEGER
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* The number of rows of the matrix A. M >= 0.
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*
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* N (input) INTEGER
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* The number of columns of the matrix A. N >= M.
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*
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* A (input/output) COMPLEX*16 array, dimension (LDA,N)
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* On entry, the leading M-by-N upper trapezoidal part of the
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* array A must contain the matrix to be factorized.
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* On exit, the leading M-by-M upper triangular part of A
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* contains the upper triangular matrix R, and elements M+1 to
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* N of the first M rows of A, with the array TAU, represent the
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* unitary matrix Z as a product of M elementary reflectors.
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A. LDA >= max(1,M).
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*
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* TAU (output) COMPLEX*16 array, dimension (M)
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* The scalar factors of the elementary reflectors.
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument had an illegal value
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*
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* Further Details
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* ===============
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*
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* The factorization is obtained by Householder's method. The kth
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* transformation matrix, Z( k ), whose conjugate transpose is used to
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* introduce zeros into the (m - k + 1)th row of A, is given in the form
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*
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* Z( k ) = ( I 0 ),
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* ( 0 T( k ) )
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*
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* where
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*
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* T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ),
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* ( 0 )
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* ( z( k ) )
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*
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* tau is a scalar and z( k ) is an ( n - m ) element vector.
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* tau and z( k ) are chosen to annihilate the elements of the kth row
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* of X.
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*
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* The scalar tau is returned in the kth element of TAU and the vector
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* u( k ) in the kth row of A, such that the elements of z( k ) are
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* in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
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* the upper triangular part of A.
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*
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* Z is given by
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*
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* Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
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*
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* =====================================================================
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*
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* .. Parameters ..
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COMPLEX*16 CONE, CZERO
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PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ),
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$ CZERO = ( 0.0D+0, 0.0D+0 ) )
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* ..
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* .. Local Scalars ..
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INTEGER I, K, M1
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COMPLEX*16 ALPHA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DCONJG, MAX, MIN
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* ..
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* .. External Subroutines ..
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EXTERNAL XERBLA, ZAXPY, ZCOPY, ZGEMV, ZGERC, ZLACGV,
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$ ZLARFP
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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IF( M.LT.0 ) THEN
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INFO = -1
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ELSE IF( N.LT.M ) THEN
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INFO = -2
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -4
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZTZRQF', -INFO )
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RETURN
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END IF
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*
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* Perform the factorization.
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*
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IF( M.EQ.0 )
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$ RETURN
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IF( M.EQ.N ) THEN
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DO 10 I = 1, N
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TAU( I ) = CZERO
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10 CONTINUE
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ELSE
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M1 = MIN( M+1, N )
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DO 20 K = M, 1, -1
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*
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* Use a Householder reflection to zero the kth row of A.
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* First set up the reflection.
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*
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A( K, K ) = DCONJG( A( K, K ) )
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CALL ZLACGV( N-M, A( K, M1 ), LDA )
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ALPHA = A( K, K )
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CALL ZLARFP( N-M+1, ALPHA, A( K, M1 ), LDA, TAU( K ) )
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A( K, K ) = ALPHA
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TAU( K ) = DCONJG( TAU( K ) )
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*
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IF( TAU( K ).NE.CZERO .AND. K.GT.1 ) THEN
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*
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* We now perform the operation A := A*P( k )'.
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*
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* Use the first ( k - 1 ) elements of TAU to store a( k ),
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* where a( k ) consists of the first ( k - 1 ) elements of
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* the kth column of A. Also let B denote the first
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* ( k - 1 ) rows of the last ( n - m ) columns of A.
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*
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CALL ZCOPY( K-1, A( 1, K ), 1, TAU, 1 )
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*
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* Form w = a( k ) + B*z( k ) in TAU.
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*
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CALL ZGEMV( 'No transpose', K-1, N-M, CONE, A( 1, M1 ),
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$ LDA, A( K, M1 ), LDA, CONE, TAU, 1 )
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*
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* Now form a( k ) := a( k ) - conjg(tau)*w
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* and B := B - conjg(tau)*w*z( k )'.
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*
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CALL ZAXPY( K-1, -DCONJG( TAU( K ) ), TAU, 1, A( 1, K ),
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$ 1 )
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CALL ZGERC( K-1, N-M, -DCONJG( TAU( K ) ), TAU, 1,
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$ A( K, M1 ), LDA, A( 1, M1 ), LDA )
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END IF
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20 CONTINUE
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END IF
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*
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RETURN
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*
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* End of ZTZRQF
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*
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END
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