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Diffstat (limited to '2.3-1/src/fortran/lapack/dtzrqf.f')
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diff --git a/2.3-1/src/fortran/lapack/dtzrqf.f b/2.3-1/src/fortran/lapack/dtzrqf.f new file mode 100644 index 00000000..5555df38 --- /dev/null +++ b/2.3-1/src/fortran/lapack/dtzrqf.f @@ -0,0 +1,164 @@ + SUBROUTINE DTZRQF( M, N, A, LDA, TAU, INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + INTEGER INFO, LDA, M, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ), TAU( * ) +* .. +* +* Purpose +* ======= +* +* This routine is deprecated and has been replaced by routine DTZRZF. +* +* DTZRQF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A +* to upper triangular form by means of orthogonal transformations. +* +* The upper trapezoidal matrix A is factored as +* +* A = ( R 0 ) * Z, +* +* where Z is an N-by-N orthogonal 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) DOUBLE PRECISION 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 +* orthogonal 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) DOUBLE PRECISION 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 ), 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 ( 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 .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER I, K, M1 +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN +* .. +* .. External Subroutines .. + EXTERNAL DAXPY, DCOPY, DGEMV, DGER, DLARFG, 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( 'DTZRQF', -INFO ) + RETURN + END IF +* +* Perform the factorization. +* + IF( M.EQ.0 ) + $ RETURN + IF( M.EQ.N ) THEN + DO 10 I = 1, N + TAU( I ) = ZERO + 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. +* + CALL DLARFG( N-M+1, A( K, K ), A( K, M1 ), LDA, TAU( K ) ) +* + IF( ( TAU( K ).NE.ZERO ) .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 DCOPY( K-1, A( 1, K ), 1, TAU, 1 ) +* +* Form w = a( k ) + B*z( k ) in TAU. +* + CALL DGEMV( 'No transpose', K-1, N-M, ONE, A( 1, M1 ), + $ LDA, A( K, M1 ), LDA, ONE, TAU, 1 ) +* +* Now form a( k ) := a( k ) - tau*w +* and B := B - tau*w*z( k )'. +* + CALL DAXPY( K-1, -TAU( K ), TAU, 1, A( 1, K ), 1 ) + CALL DGER( K-1, N-M, -TAU( K ), TAU, 1, A( K, M1 ), LDA, + $ A( 1, M1 ), LDA ) + END IF + 20 CONTINUE + END IF +* + RETURN +* +* End of DTZRQF +* + END |