stepan
/
dynare
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
dynare/mex/sources/libslicot/MB04ID.f

279 lines
9.1 KiB
Fortran
Raw Blame History

SUBROUTINE MB04ID( N, M, P, L, A, LDA, B, LDB, TAU, DWORK, LDWORK,
$ INFO )
C
C SLICOT RELEASE 5.0.
C
C Copyright (c) 2002-2009 NICONET e.V.
C
C This program is free software: you can redistribute it and/or
C modify it under the terms of the GNU General Public License as
C published by the Free Software Foundation, either version 2 of
C the License, or (at your option) any later version.
C
C This program is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
C GNU General Public License for more details.
C
C You should have received a copy of the GNU General Public License
C along with this program. If not, see
C <http://www.gnu.org/licenses/>.
C
C PURPOSE
C
C To compute a QR factorization of an n-by-m matrix A (A = Q * R),
C having a p-by-min(p,m) zero triangle in the lower left-hand side
C corner, as shown below, for n = 8, m = 7, and p = 2:
C
C [ x x x x x x x ]
C [ x x x x x x x ]
C [ x x x x x x x ]
C [ x x x x x x x ]
C A = [ x x x x x x x ],
C [ x x x x x x x ]
C [ 0 x x x x x x ]
C [ 0 0 x x x x x ]
C
C and optionally apply the transformations to an n-by-l matrix B
C (from the left). The problem structure is exploited. This
C computation is useful, for instance, in combined measurement and
C time update of one iteration of the time-invariant Kalman filter
C (square root information filter).
C
C ARGUMENTS
C
C Input/Output Parameters
C
C N (input) INTEGER
C The number of rows of the matrix A. N >= 0.
C
C M (input) INTEGER
C The number of columns of the matrix A. M >= 0.
C
C P (input) INTEGER
C The order of the zero triagle. P >= 0.
C
C L (input) INTEGER
C The number of columns of the matrix B. L >= 0.
C
C A (input/output) DOUBLE PRECISION array, dimension (LDA,M)
C On entry, the leading N-by-M part of this array must
C contain the matrix A. The elements corresponding to the
C zero P-by-MIN(P,M) lower trapezoidal/triangular part
C (if P > 0) are not referenced.
C On exit, the elements on and above the diagonal of this
C array contain the MIN(N,M)-by-M upper trapezoidal matrix
C R (R is upper triangular, if N >= M) of the QR
C factorization, and the relevant elements below the
C diagonal contain the trailing components (the vectors v,
C see Method) of the elementary reflectors used in the
C factorization.
C
C LDA INTEGER
C The leading dimension of array A. LDA >= MAX(1,N).
C
C B (input/output) DOUBLE PRECISION array, dimension (LDB,L)
C On entry, the leading N-by-L part of this array must
C contain the matrix B.
C On exit, the leading N-by-L part of this array contains
C the updated matrix B.
C If L = 0, this array is not referenced.
C
C LDB INTEGER
C The leading dimension of array B.
C LDB >= MAX(1,N) if L > 0;
C LDB >= 1 if L = 0.
C
C TAU (output) DOUBLE PRECISION array, dimension MIN(N,M)
C The scalar factors of the elementary reflectors used.
C
C Workspace
C
C DWORK DOUBLE PRECISION array, dimension (LDWORK)
C On exit, if INFO = 0, DWORK(1) returns the optimal value
C of LDWORK.
C
C LDWORK The length of the array DWORK.
C LDWORK >= MAX(1,M-1,M-P,L).
C For optimum performance LDWORK should be larger.
C
C If LDWORK = -1, then a workspace query is assumed;
C the routine only calculates the optimal size of the
C DWORK array, returns this value as the first entry of
C the DWORK array, and no error message related to LDWORK
C is issued by XERBLA.
C
C Error Indicator
C
C INFO INTEGER
C = 0: successful exit;
C < 0: if INFO = -i, the i-th argument had an illegal
C value.
C
C METHOD
C
C The routine uses min(N,M) Householder transformations exploiting
C the zero pattern of the matrix. A Householder matrix has the form
C
C ( 1 ),
C H = I - tau *u *u', u = ( v )
C i i i i i ( i)
C
C where v is an (N-P+I-2)-vector. The components of v are stored
C i i
C in the i-th column of A, beginning from the location i+1, and
C tau is stored in TAU(i).
C i
C
C NUMERICAL ASPECTS
C
C The algorithm is backward stable.
C
C CONTRIBUTORS
C
C V. Sima, Katholieke Univ. Leuven, Belgium, Feb. 1997.
C
C REVISIONS
C
C V. Sima, Research Institute for Informatics, Bucharest, Jan. 2009,
C Apr. 2009.
C
C KEYWORDS
C
C Elementary reflector, QR factorization, orthogonal transformation.
C
C ******************************************************************
C
C .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
C .. Scalar Arguments ..
INTEGER INFO, L, LDA, LDB, LDWORK, M, N, P
C .. Array Arguments ..
DOUBLE PRECISION A(LDA,*), B(LDB,*), DWORK(*), TAU(*)
C .. Local Scalars ..
LOGICAL LQUERY
INTEGER I, NB, WRKOPT
DOUBLE PRECISION FIRST
C .. External Functions ..
INTEGER ILAENV
EXTERNAL ILAENV
C .. External Subroutines ..
EXTERNAL DGEQRF, DLARF, DLARFG, DORMQR, XERBLA
C .. Intrinsic Functions ..
INTRINSIC INT, MAX, MIN
C .. Executable Statements ..
C
C Test the input scalar arguments.
C
INFO = 0
LQUERY = ( LDWORK.EQ.-1 )
IF( N.LT.0 ) THEN
INFO = -1
ELSE IF( M.LT.0 ) THEN
INFO = -2
ELSE IF( P.LT.0 ) THEN
INFO = -3
ELSE IF( L.LT.0 ) THEN
INFO = -4
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -6
ELSE IF( LDB.LT.1 .OR. ( L.GT.0 .AND. LDB.LT.N ) ) THEN
INFO = -8
ELSE
I = MAX( 1, M - 1, M - P, L )
IF( LQUERY ) THEN
IF( M.GT.P ) THEN
NB = ILAENV( 1, 'DGEQRF', ' ', N-P, M-P, -1, -1 )
WRKOPT = MAX( I, ( M - P )*NB )
IF ( L.GT.0 ) THEN
NB = MIN( 64, ILAENV( 1, 'DORMQR', 'LT', N-P, L,
$ MIN(N,M)-P, -1 ) )
WRKOPT = MAX( WRKOPT, MAX( 1, L )*NB )
END IF
END IF
ELSE IF( LDWORK.LT.I ) THEN
INFO = -11
END IF
END IF
C
IF( INFO.NE.0 ) THEN
C
C Error return.
C
CALL XERBLA( 'MB04ID', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
DWORK(1) = WRKOPT
RETURN
END IF
C
C Quick return if possible.
C
IF( MIN( M, N ).EQ.0 ) THEN
DWORK(1) = ONE
RETURN
ELSE IF( N.LE.P+1 ) THEN
DO 5 I = 1, MIN( N, M )
TAU(I) = ZERO
5 CONTINUE
DWORK(1) = ONE
RETURN
END IF
C
C Annihilate the subdiagonal elements of A and apply the
C transformations to B, if L > 0.
C Workspace: need MAX(M-1,L).
C
C (Note: Comments in the code beginning "Workspace:" describe the
C minimal amount of real workspace needed at that point in the
C code, as well as the preferred amount for good performance.
C NB refers to the optimal block size for the immediately
C following subroutine, as returned by ILAENV.)
C
DO 10 I = 1, MIN( P, M )
C
C Exploit the structure of the I-th column of A.
C
CALL DLARFG( N-P, A(I,I), A(I+1,I), 1, TAU(I) )
IF( TAU(I).NE.ZERO ) THEN
C
FIRST = A(I,I)
A(I,I) = ONE
C
IF ( I.LT.M ) CALL DLARF( 'Left', N-P, M-I, A(I,I), 1,
$ TAU(I), A(I,I+1), LDA, DWORK )
IF ( L.GT.0 ) CALL DLARF( 'Left', N-P, L, A(I,I), 1, TAU(I),
$ B(I,1), LDB, DWORK )
C
A(I,I) = FIRST
END IF
10 CONTINUE
C
WRKOPT = MAX( 1, M - 1, L )
C
C Fast QR factorization of the remaining right submatrix, if any.
C Workspace: need M-P; prefer (M-P)*NB.
C
IF( M.GT.P ) THEN
CALL DGEQRF( N-P, M-P, A(P+1,P+1), LDA, TAU(P+1), DWORK,
$ LDWORK, INFO )
WRKOPT = MAX( WRKOPT, INT( DWORK(1) ) )
C
IF ( L.GT.0 ) THEN
C
C Apply the transformations to B.
C Workspace: need L; prefer L*NB.
C
CALL DORMQR( 'Left', 'Transpose', N-P, L, MIN(N,M)-P,
$ A(P+1,P+1), LDA, TAU(P+1), B(P+1,1), LDB,
$ DWORK, LDWORK, INFO )
WRKOPT = MAX( WRKOPT, INT( DWORK(1) ) )
END IF
END IF
C
DWORK(1) = WRKOPT
RETURN
C *** Last line of MB04ID ***
END
Reference in New Issue View Git Blame Copy Permalink