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Diffstat (limited to '2.3-1/src/fortran/lapack/zlatrz.f')
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diff --git a/2.3-1/src/fortran/lapack/zlatrz.f b/2.3-1/src/fortran/lapack/zlatrz.f new file mode 100644 index 00000000..c1c7aab3 --- /dev/null +++ b/2.3-1/src/fortran/lapack/zlatrz.f @@ -0,0 +1,133 @@ + SUBROUTINE ZLATRZ( M, N, L, A, LDA, TAU, WORK ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + INTEGER L, LDA, M, N +* .. +* .. Array Arguments .. + COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* ZLATRZ factors the M-by-(M+L) complex upper trapezoidal matrix +* [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means +* of unitary transformations, where Z is an (M+L)-by-(M+L) unitary +* matrix and, R and A1 are M-by-M upper triangular matrices. +* +* 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 >= 0. +* +* L (input) INTEGER +* The number of columns of the matrix A containing the +* meaningful part of the Householder vectors. N-M >= L >= 0. +* +* A (input/output) COMPLEX*16 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 N-L+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*16 array, dimension (M) +* The scalar factors of the elementary reflectors. +* +* WORK (workspace) COMPLEX*16 array, dimension (M) +* +* Further Details +* =============== +* +* Based on contributions by +* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA +* +* The factorization is obtained by Householder's method. The kth +* transformation matrix, Z( k ), which 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 l element vector. tau and z( k ) +* are chosen to annihilate the elements of the kth row of A2. +* +* The scalar tau is returned in the kth element of TAU and the vector +* u( k ) in the kth row of A2, such that the elements of z( k ) are +* in a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in +* the upper triangular part of A1. +* +* Z is given by +* +* Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX*16 ZERO + PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) +* .. +* .. Local Scalars .. + INTEGER I + COMPLEX*16 ALPHA +* .. +* .. External Subroutines .. + EXTERNAL ZLACGV, ZLARFG, ZLARZ +* .. +* .. Intrinsic Functions .. + INTRINSIC DCONJG +* .. +* .. Executable Statements .. +* +* Quick return if possible +* + IF( M.EQ.0 ) THEN + RETURN + ELSE IF( M.EQ.N ) THEN + DO 10 I = 1, N + TAU( I ) = ZERO + 10 CONTINUE + RETURN + END IF +* + DO 20 I = M, 1, -1 +* +* Generate elementary reflector H(i) to annihilate +* [ A(i,i) A(i,n-l+1:n) ] +* + CALL ZLACGV( L, A( I, N-L+1 ), LDA ) + ALPHA = DCONJG( A( I, I ) ) + CALL ZLARFG( L+1, ALPHA, A( I, N-L+1 ), LDA, TAU( I ) ) + TAU( I ) = DCONJG( TAU( I ) ) +* +* Apply H(i) to A(1:i-1,i:n) from the right +* + CALL ZLARZ( 'Right', I-1, N-I+1, L, A( I, N-L+1 ), LDA, + $ DCONJG( TAU( I ) ), A( 1, I ), LDA, WORK ) + A( I, I ) = DCONJG( ALPHA ) +* + 20 CONTINUE +* + RETURN +* +* End of ZLATRZ +* + END |