245 lines
7.0 KiB
FortranFixed
245 lines
7.0 KiB
FortranFixed
SUBROUTINE STZRZF( 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 ..
|
|
REAL A( LDA, * ), TAU( * ), WORK( * )
|
|
* ..
|
|
*
|
|
* Purpose
|
|
* =======
|
|
*
|
|
* STZRZF 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) REAL 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) REAL array, dimension (M)
|
|
* The scalar factors of the elementary reflectors.
|
|
*
|
|
* WORK (workspace/output) REAL 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 ..
|
|
REAL ZERO
|
|
PARAMETER ( ZERO = 0.0E+0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL LQUERY
|
|
INTEGER I, IB, IWS, KI, KK, LDWORK, LWKOPT, M1, MU, NB,
|
|
$ NBMIN, NX
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL SLARZB, SLARZT, SLATRZ, 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, 'SGERQF', ' ', 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( 'STZRZF', -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, 'SGERQF', ' ', 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, 'SGERQF', ' ', 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 SLATRZ( 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 SLARZT( '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 SLARZB( '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 SLATRZ( MU, N, N-M, A, LDA, TAU, WORK )
|
|
*
|
|
WORK( 1 ) = LWKOPT
|
|
*
|
|
RETURN
|
|
*
|
|
* End of STZRZF
|
|
*
|
|
END
|