107 lines
3.4 KiB
Fortran
107 lines
3.4 KiB
Fortran
SUBROUTINE MB04OX( N, A, LDA, X, INCX )
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C
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C SLICOT RELEASE 5.0.
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C
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C Copyright (c) 2002-2009 NICONET e.V.
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C
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C This program is free software: you can redistribute it and/or
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C modify it under the terms of the GNU General Public License as
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C published by the Free Software Foundation, either version 2 of
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C the License, or (at your option) any later version.
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C
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C This program is distributed in the hope that it will be useful,
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C but WITHOUT ANY WARRANTY; without even the implied warranty of
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C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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C GNU General Public License for more details.
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C
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C You should have received a copy of the GNU General Public License
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C along with this program. If not, see
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C <http://www.gnu.org/licenses/>.
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C
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C PURPOSE
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C
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C To perform the QR factorization
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C
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C (U ) = Q*(R),
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C (x') (0)
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C
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C where U and R are n-by-n upper triangular matrices, x is an
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C n element vector and Q is an (n+1)-by-(n+1) orthogonal matrix.
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C
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C U must be supplied in the n-by-n upper triangular part of the
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C array A and this is overwritten by R.
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C
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C ARGUMENTS
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C
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C Input/Output Parameters
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C
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C N (input) INTEGER
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C The number of elements of X and the order of the square
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C matrix A. N >= 0.
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C
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C A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
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C On entry, the leading N-by-N upper triangular part of this
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C array must contain the upper triangular matrix U.
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C On exit, the leading N-by-N upper triangular part of this
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C array contains the upper triangular matrix R.
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C The strict lower triangle of A is not referenced.
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C
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C LDA INTEGER
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C The leading dimension of the array A. LDA >= max(1,N).
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C
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C X (input/output) DOUBLE PRECISION array, dimension
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C (1+(N-1)*INCX)
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C On entry, the incremented array X must contain the
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C vector x. On exit, the content of X is changed.
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C
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C INCX (input) INTEGER.
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C Specifies the increment for the elements of X. INCX > 0.
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C
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C METHOD
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C
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C The matrix Q is formed as a sequence of plane rotations in planes
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C (1, n+1), (2, n+1), ..., (n, n+1), the rotation in the (j, n+1)th
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C plane, Q(j), being chosen to annihilate the jth element of x.
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C
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C CONTRIBUTOR
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C
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C A. Varga, German Aerospace Center,
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C DLR Oberpfaffenhofen, July 1998.
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C Based on the RASP routine DUTUPD.
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C
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C REVISIONS
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C
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C Nov. 1998, V. Sima, Research Institute for Informatics, Bucharest.
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C
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C ******************************************************************
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C
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C .. Scalar Arguments ..
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INTEGER INCX, LDA, N
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C .. Array Arguments ..
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DOUBLE PRECISION A(LDA,*), X(*)
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C .. Local Scalars ..
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DOUBLE PRECISION CI, SI, TEMP
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INTEGER I, IX
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C .. External Subroutines ..
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EXTERNAL DLARTG, DROT
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C
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C .. Executable Statements ..
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C
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C For efficiency reasons, the parameters are not checked.
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C
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IX = 1
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C
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DO 20 I = 1, N - 1
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CALL DLARTG( A(I,I), X(IX), CI, SI, TEMP )
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A(I,I) = TEMP
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IX = IX + INCX
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CALL DROT( N-I, A(I,I+1), LDA, X(IX), INCX, CI, SI )
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20 CONTINUE
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C
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CALL DLARTG( A(N,N), X(IX), CI, SI, TEMP )
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A(N,N) = TEMP
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C
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RETURN
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C *** Last line of MB04OX ***
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END
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