diff options
Diffstat (limited to 'SRC/dtzrzf.f')
| -rw-r--r-- | SRC/dtzrzf.f | 244 |
1 files changed, 244 insertions, 0 deletions
diff --git a/SRC/dtzrzf.f b/SRC/dtzrzf.f new file mode 100644 index 00000000..378eefe1 --- /dev/null +++ b/SRC/dtzrzf.f @@ -0,0 +1,244 @@ + SUBROUTINE DTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO ) +* +* -- LAPACK routine (version 3.1) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2006 +* +* .. Scalar Arguments .. + INTEGER INFO, LDA, LWORK, M, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) +* .. +* +* Purpose +* ======= +* +* DTZRZF 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. +* +* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) +* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +* +* LWORK (input) INTEGER +* The dimension of the array WORK. LWORK >= max(1,M). +* For optimum performance LWORK >= M*NB, where NB is +* the optimal blocksize. +* +* If LWORK = -1, then a workspace query is assumed; the routine +* only calculates the optimal size of the WORK array, returns +* this value as the first entry of the WORK array, and no error +* message related to LWORK is issued by XERBLA. +* +* INFO (output) INTEGER +* = 0: successful exit +* < 0: if INFO = -i, the i-th argument had an illegal value +* +* 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 ( 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 ZERO + PARAMETER ( ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + LOGICAL LQUERY + INTEGER I, IB, IWS, KI, KK, LDWORK, LWKOPT, M1, MU, NB, + $ NBMIN, NX +* .. +* .. External Subroutines .. + EXTERNAL DLARZB, DLARZT, DLATRZ, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN +* .. +* .. External Functions .. + INTEGER ILAENV + EXTERNAL ILAENV +* .. +* .. Executable Statements .. +* +* Test the input arguments +* + INFO = 0 + LQUERY = ( LWORK.EQ.-1 ) + 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.EQ.0 ) THEN + IF( M.EQ.0 .OR. M.EQ.N ) THEN + LWKOPT = 1 + ELSE +* +* Determine the block size. +* + NB = ILAENV( 1, 'DGERQF', ' ', M, N, -1, -1 ) + LWKOPT = M*NB + END IF + WORK( 1 ) = LWKOPT +* + IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN + INFO = -7 + END IF + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DTZRZF', -INFO ) + RETURN + ELSE IF( LQUERY ) THEN + RETURN + END IF +* +* 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 +* + NBMIN = 2 + NX = 1 + IWS = M + IF( NB.GT.1 .AND. NB.LT.M ) THEN +* +* Determine when to cross over from blocked to unblocked code. +* + NX = MAX( 0, ILAENV( 3, 'DGERQF', ' ', M, N, -1, -1 ) ) + IF( NX.LT.M ) THEN +* +* Determine if workspace is large enough for blocked code. +* + LDWORK = M + IWS = LDWORK*NB + IF( LWORK.LT.IWS ) THEN +* +* Not enough workspace to use optimal NB: reduce NB and +* determine the minimum value of NB. +* + NB = LWORK / LDWORK + NBMIN = MAX( 2, ILAENV( 2, 'DGERQF', ' ', M, N, -1, + $ -1 ) ) + END IF + END IF + END IF +* + IF( NB.GE.NBMIN .AND. NB.LT.M .AND. NX.LT.M ) THEN +* +* Use blocked code initially. +* The last kk rows are handled by the block method. +* + M1 = MIN( M+1, N ) + KI = ( ( M-NX-1 ) / NB )*NB + KK = MIN( M, KI+NB ) +* + DO 20 I = M - KK + KI + 1, M - KK + 1, -NB + IB = MIN( M-I+1, NB ) +* +* Compute the TZ factorization of the current block +* A(i:i+ib-1,i:n) +* + CALL DLATRZ( IB, N-I+1, N-M, A( I, I ), LDA, TAU( I ), + $ WORK ) + IF( I.GT.1 ) THEN +* +* Form the triangular factor of the block reflector +* H = H(i+ib-1) . . . H(i+1) H(i) +* + CALL DLARZT( 'Backward', 'Rowwise', N-M, IB, A( I, M1 ), + $ LDA, TAU( I ), WORK, LDWORK ) +* +* Apply H to A(1:i-1,i:n) from the right +* + CALL DLARZB( 'Right', 'No transpose', 'Backward', + $ 'Rowwise', I-1, N-I+1, IB, N-M, A( I, M1 ), + $ LDA, WORK, LDWORK, A( 1, I ), LDA, + $ WORK( IB+1 ), LDWORK ) + END IF + 20 CONTINUE + MU = I + NB - 1 + ELSE + MU = M + END IF +* +* Use unblocked code to factor the last or only block +* + IF( MU.GT.0 ) + $ CALL DLATRZ( MU, N, N-M, A, LDA, TAU, WORK ) +* + WORK( 1 ) = LWKOPT +* + RETURN +* +* End of DTZRZF +* + END |