438 lines
12 KiB
Fortran
438 lines
12 KiB
Fortran
SUBROUTINE MB04NY( M, N, V, INCV, TAU, A, LDA, B, LDB, DWORK )
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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 apply a real elementary reflector H to a real m-by-(n+1)
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C matrix C = [ A B ], from the right, where A has one column. H is
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C represented in the form
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C ( 1 )
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C H = I - tau * u *u', u = ( ),
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C ( v )
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C where tau is a real scalar and v is a real n-vector.
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C
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C If tau = 0, then H is taken to be the unit matrix.
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C
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C In-line code is used if H has order < 11.
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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 M (input) INTEGER
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C The number of rows of the matrices A and B. M >= 0.
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C
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C N (input) INTEGER
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C The number of columns of the matrix B. N >= 0.
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C
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C V (input) DOUBLE PRECISION array, dimension
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C (1+(N-1)*ABS( INCV ))
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C The vector v in the representation of H.
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C
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C INCV (input) INTEGER
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C The increment between the elements of v. INCV <> 0.
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C
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C TAU (input) DOUBLE PRECISION
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C The scalar factor of the elementary reflector H.
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C
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C A (input/output) DOUBLE PRECISION array, dimension (LDA,1)
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C On entry, the leading M-by-1 part of this array must
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C contain the matrix A.
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C On exit, the leading M-by-1 part of this array contains
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C the updated matrix A (the first column of C * H).
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C
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C LDA INTEGER
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C The leading dimension of array A. LDA >= MAX(1,M).
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C
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C B (input/output) DOUBLE PRECISION array, dimension (LDB,N)
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C On entry, the leading M-by-N part of this array must
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C contain the matrix B.
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C On exit, the leading M-by-N part of this array contains
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C the updated matrix B (the last n columns of C * H).
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C
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C LDB INTEGER
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C The leading dimension of array B. LDB >= MAX(1,M).
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C
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C Workspace
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C
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C DWORK DOUBLE PRECISION array, dimension (M)
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C DWORK is not referenced if H has order less than 11.
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C
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C METHOD
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C
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C The routine applies the elementary reflector H, taking the special
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C structure of C into account.
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C
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C NUMERICAL ASPECTS
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C
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C The algorithm is backward stable.
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C
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C CONTRIBUTORS
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C
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C V. Sima, Katholieke Univ. Leuven, Belgium, Apr. 1998.
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C Based on LAPACK routines DLARFX and DLATZM.
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C
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C REVISIONS
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C
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C -
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C
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C KEYWORDS
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C
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C Elementary matrix operations, elementary reflector, orthogonal
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C transformation.
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C
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C ******************************************************************
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C
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C .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
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C .. Scalar Arguments ..
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INTEGER INCV, LDA, LDB, M, N
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DOUBLE PRECISION TAU
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C .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), B( LDB, * ), DWORK( * ), V( * )
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C .. Local Scalars ..
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INTEGER IV, J
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DOUBLE PRECISION SUM, T1, T2, T3, T4, T5, T6, T7, T8, T9, V1, V2,
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$ V3, V4, V5, V6, V7, V8, V9
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C .. External Subroutines ..
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EXTERNAL DAXPY, DCOPY, DGEMV, DGER
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C
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C .. Executable Statements ..
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C
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IF( TAU.EQ.ZERO )
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$ RETURN
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C
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C Form C * H, where H has order n+1.
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C
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GO TO ( 10, 30, 50, 70, 90, 110, 130, 150,
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$ 170, 190 ) N+1
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C
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C Code for general N. Compute
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C
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C w := C*u, C := C - tau * w * u'.
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C
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CALL DCOPY( M, A, 1, DWORK, 1 )
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CALL DGEMV( 'No transpose', M, N, ONE, B, LDB, V, INCV, ONE,
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$ DWORK, 1 )
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CALL DAXPY( M, -TAU, DWORK, 1, A, 1 )
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CALL DGER( M, N, -TAU, DWORK, 1, V, INCV, B, LDB )
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GO TO 210
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10 CONTINUE
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C
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C Special code for 1 x 1 Householder
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C
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T1 = ONE - TAU
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DO 20 J = 1, M
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A( J, 1 ) = T1*A( J, 1 )
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20 CONTINUE
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GO TO 210
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30 CONTINUE
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C
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C Special code for 2 x 2 Householder
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C
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IV = 1
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IF( INCV.LT.0 )
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$ IV = (-N+1)*INCV + 1
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V1 = V( IV )
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T1 = TAU*V1
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DO 40 J = 1, M
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SUM = A( J, 1 ) + V1*B( J, 1 )
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A( J, 1 ) = A( J, 1 ) - SUM*TAU
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B( J, 1 ) = B( J, 1 ) - SUM*T1
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40 CONTINUE
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GO TO 210
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50 CONTINUE
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C
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C Special code for 3 x 3 Householder
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C
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IV = 1
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IF( INCV.LT.0 )
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$ IV = (-N+1)*INCV + 1
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V1 = V( IV )
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T1 = TAU*V1
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IV = IV + INCV
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V2 = V( IV )
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T2 = TAU*V2
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DO 60 J = 1, M
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SUM = A( J, 1 ) + V1*B( J, 1 ) + V2*B( J, 2 )
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A( J, 1 ) = A( J, 1 ) - SUM*TAU
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B( J, 1 ) = B( J, 1 ) - SUM*T1
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B( J, 2 ) = B( J, 2 ) - SUM*T2
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60 CONTINUE
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GO TO 210
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70 CONTINUE
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C
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C Special code for 4 x 4 Householder
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C
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IV = 1
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IF( INCV.LT.0 )
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$ IV = (-N+1)*INCV + 1
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V1 = V( IV )
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T1 = TAU*V1
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IV = IV + INCV
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V2 = V( IV )
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T2 = TAU*V2
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IV = IV + INCV
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V3 = V( IV )
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T3 = TAU*V3
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DO 80 J = 1, M
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SUM = A( J, 1 ) + V1*B( J, 1 ) + V2*B( J, 2 ) + V3*B( J, 3 )
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A( J, 1 ) = A( J, 1 ) - SUM*TAU
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B( J, 1 ) = B( J, 1 ) - SUM*T1
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B( J, 2 ) = B( J, 2 ) - SUM*T2
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B( J, 3 ) = B( J, 3 ) - SUM*T3
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80 CONTINUE
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GO TO 210
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90 CONTINUE
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C
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C Special code for 5 x 5 Householder
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C
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IV = 1
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IF( INCV.LT.0 )
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$ IV = (-N+1)*INCV + 1
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V1 = V( IV )
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T1 = TAU*V1
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IV = IV + INCV
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V2 = V( IV )
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T2 = TAU*V2
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IV = IV + INCV
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V3 = V( IV )
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T3 = TAU*V3
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IV = IV + INCV
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V4 = V( IV )
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T4 = TAU*V4
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DO 100 J = 1, M
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SUM = A( J, 1 ) + V1*B( J, 1 ) + V2*B( J, 2 ) + V3*B( J, 3 ) +
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$ V4*B( J, 4 )
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A( J, 1 ) = A( J, 1 ) - SUM*TAU
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B( J, 1 ) = B( J, 1 ) - SUM*T1
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B( J, 2 ) = B( J, 2 ) - SUM*T2
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B( J, 3 ) = B( J, 3 ) - SUM*T3
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B( J, 4 ) = B( J, 4 ) - SUM*T4
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100 CONTINUE
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GO TO 210
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110 CONTINUE
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C
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C Special code for 6 x 6 Householder
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C
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IV = 1
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IF( INCV.LT.0 )
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$ IV = (-N+1)*INCV + 1
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V1 = V( IV )
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T1 = TAU*V1
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IV = IV + INCV
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V2 = V( IV )
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T2 = TAU*V2
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IV = IV + INCV
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V3 = V( IV )
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T3 = TAU*V3
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IV = IV + INCV
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V4 = V( IV )
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T4 = TAU*V4
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IV = IV + INCV
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V5 = V( IV )
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T5 = TAU*V5
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DO 120 J = 1, M
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SUM = A( J, 1 ) + V1*B( J, 1 ) + V2*B( J, 2 ) + V3*B( J, 3 ) +
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$ V4*B( J, 4 ) + V5*B( J, 5 )
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A( J, 1 ) = A( J, 1 ) - SUM*TAU
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B( J, 1 ) = B( J, 1 ) - SUM*T1
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B( J, 2 ) = B( J, 2 ) - SUM*T2
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B( J, 3 ) = B( J, 3 ) - SUM*T3
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B( J, 4 ) = B( J, 4 ) - SUM*T4
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B( J, 5 ) = B( J, 5 ) - SUM*T5
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120 CONTINUE
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GO TO 210
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130 CONTINUE
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C
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C Special code for 7 x 7 Householder
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C
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IV = 1
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IF( INCV.LT.0 )
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$ IV = (-N+1)*INCV + 1
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V1 = V( IV )
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T1 = TAU*V1
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IV = IV + INCV
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V2 = V( IV )
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T2 = TAU*V2
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IV = IV + INCV
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V3 = V( IV )
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T3 = TAU*V3
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IV = IV + INCV
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V4 = V( IV )
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T4 = TAU*V4
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IV = IV + INCV
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V5 = V( IV )
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T5 = TAU*V5
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IV = IV + INCV
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V6 = V( IV )
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T6 = TAU*V6
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DO 140 J = 1, M
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SUM = A( J, 1 ) + V1*B( J, 1 ) + V2*B( J, 2 ) + V3*B( J, 3 ) +
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$ V4*B( J, 4 ) + V5*B( J, 5 ) + V6*B( J, 6 )
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A( J, 1 ) = A( J, 1 ) - SUM*TAU
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B( J, 1 ) = B( J, 1 ) - SUM*T1
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B( J, 2 ) = B( J, 2 ) - SUM*T2
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B( J, 3 ) = B( J, 3 ) - SUM*T3
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B( J, 4 ) = B( J, 4 ) - SUM*T4
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B( J, 5 ) = B( J, 5 ) - SUM*T5
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B( J, 6 ) = B( J, 6 ) - SUM*T6
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140 CONTINUE
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GO TO 210
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150 CONTINUE
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C
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C Special code for 8 x 8 Householder
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C
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IV = 1
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IF( INCV.LT.0 )
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$ IV = (-N+1)*INCV + 1
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V1 = V( IV )
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T1 = TAU*V1
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IV = IV + INCV
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V2 = V( IV )
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T2 = TAU*V2
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IV = IV + INCV
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V3 = V( IV )
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T3 = TAU*V3
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IV = IV + INCV
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V4 = V( IV )
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T4 = TAU*V4
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IV = IV + INCV
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V5 = V( IV )
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T5 = TAU*V5
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IV = IV + INCV
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V6 = V( IV )
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T6 = TAU*V6
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IV = IV + INCV
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V7 = V( IV )
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T7 = TAU*V7
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DO 160 J = 1, M
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SUM = A( J, 1 ) + V1*B( J, 1 ) + V2*B( J, 2 ) + V3*B( J, 3 ) +
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$ V4*B( J, 4 ) + V5*B( J, 5 ) + V6*B( J, 6 ) +
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$ V7*B( J, 7 )
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A( J, 1 ) = A( J, 1 ) - SUM*TAU
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B( J, 1 ) = B( J, 1 ) - SUM*T1
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B( J, 2 ) = B( J, 2 ) - SUM*T2
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B( J, 3 ) = B( J, 3 ) - SUM*T3
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B( J, 4 ) = B( J, 4 ) - SUM*T4
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B( J, 5 ) = B( J, 5 ) - SUM*T5
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B( J, 6 ) = B( J, 6 ) - SUM*T6
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B( J, 7 ) = B( J, 7 ) - SUM*T7
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160 CONTINUE
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GO TO 210
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170 CONTINUE
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C
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C Special code for 9 x 9 Householder
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C
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IV = 1
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IF( INCV.LT.0 )
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$ IV = (-N+1)*INCV + 1
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V1 = V( IV )
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T1 = TAU*V1
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IV = IV + INCV
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V2 = V( IV )
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T2 = TAU*V2
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IV = IV + INCV
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V3 = V( IV )
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T3 = TAU*V3
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IV = IV + INCV
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V4 = V( IV )
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T4 = TAU*V4
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IV = IV + INCV
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V5 = V( IV )
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T5 = TAU*V5
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IV = IV + INCV
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V6 = V( IV )
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T6 = TAU*V6
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IV = IV + INCV
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V7 = V( IV )
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T7 = TAU*V7
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IV = IV + INCV
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V8 = V( IV )
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T8 = TAU*V8
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DO 180 J = 1, M
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SUM = A( J, 1 ) + V1*B( J, 1 ) + V2*B( J, 2 ) + V3*B( J, 3 ) +
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$ V4*B( J, 4 ) + V5*B( J, 5 ) + V6*B( J, 6 ) +
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$ V7*B( J, 7 ) + V8*B( J, 8 )
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A( J, 1 ) = A( J, 1 ) - SUM*TAU
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B( J, 1 ) = B( J, 1 ) - SUM*T1
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B( J, 2 ) = B( J, 2 ) - SUM*T2
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B( J, 3 ) = B( J, 3 ) - SUM*T3
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B( J, 4 ) = B( J, 4 ) - SUM*T4
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B( J, 5 ) = B( J, 5 ) - SUM*T5
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B( J, 6 ) = B( J, 6 ) - SUM*T6
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B( J, 7 ) = B( J, 7 ) - SUM*T7
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B( J, 8 ) = B( J, 8 ) - SUM*T8
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180 CONTINUE
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GO TO 210
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190 CONTINUE
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C
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C Special code for 10 x 10 Householder
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C
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IV = 1
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IF( INCV.LT.0 )
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$ IV = (-N+1)*INCV + 1
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V1 = V( IV )
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T1 = TAU*V1
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IV = IV + INCV
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V2 = V( IV )
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T2 = TAU*V2
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IV = IV + INCV
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V3 = V( IV )
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T3 = TAU*V3
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IV = IV + INCV
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V4 = V( IV )
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T4 = TAU*V4
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IV = IV + INCV
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V5 = V( IV )
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T5 = TAU*V5
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IV = IV + INCV
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V6 = V( IV )
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T6 = TAU*V6
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IV = IV + INCV
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V7 = V( IV )
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T7 = TAU*V7
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IV = IV + INCV
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V8 = V( IV )
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T8 = TAU*V8
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IV = IV + INCV
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V9 = V( IV )
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T9 = TAU*V9
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DO 200 J = 1, M
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SUM = A( J, 1 ) + V1*B( J, 1 ) + V2*B( J, 2 ) + V3*B( J, 3 ) +
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$ V4*B( J, 4 ) + V5*B( J, 5 ) + V6*B( J, 6 ) +
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$ V7*B( J, 7 ) + V8*B( J, 8 ) + V9*B( J, 9 )
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A( J, 1 ) = A( J, 1 ) - SUM*TAU
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B( J, 1 ) = B( J, 1 ) - SUM*T1
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B( J, 2 ) = B( J, 2 ) - SUM*T2
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B( J, 3 ) = B( J, 3 ) - SUM*T3
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B( J, 4 ) = B( J, 4 ) - SUM*T4
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B( J, 5 ) = B( J, 5 ) - SUM*T5
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B( J, 6 ) = B( J, 6 ) - SUM*T6
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B( J, 7 ) = B( J, 7 ) - SUM*T7
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B( J, 8 ) = B( J, 8 ) - SUM*T8
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B( J, 9 ) = B( J, 9 ) - SUM*T9
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200 CONTINUE
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210 CONTINUE
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RETURN
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C *** Last line of MB04NY ***
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END
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