134 lines
3.5 KiB
Fortran
134 lines
3.5 KiB
Fortran
SUBROUTINE DORGL2( M, N, K, A, LDA, TAU, WORK, INFO )
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*
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* -- LAPACK routine (version 2.0) --
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* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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* Courant Institute, Argonne National Lab, and Rice University
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* February 29, 1992
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*
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* .. Scalar Arguments ..
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INTEGER INFO, K, LDA, M, N
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
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* ..
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*
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* Purpose
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* =======
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*
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* DORGL2 generates an m by n real matrix Q with orthonormal rows,
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* which is defined as the first m rows of a product of k elementary
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* reflectors of order n
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*
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* Q = H(k) . . . H(2) H(1)
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*
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* as returned by DGELQF.
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*
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* Arguments
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* =========
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*
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* M (input) INTEGER
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* The number of rows of the matrix Q. M >= 0.
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*
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* N (input) INTEGER
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* The number of columns of the matrix Q. N >= M.
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*
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* K (input) INTEGER
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* The number of elementary reflectors whose product defines the
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* matrix Q. M >= K >= 0.
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*
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* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
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* On entry, the i-th row must contain the vector which defines
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* the elementary reflector H(i), for i = 1,2,...,k, as returned
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* by DGELQF in the first k rows of its array argument A.
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* On exit, the m-by-n matrix Q.
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*
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* LDA (input) INTEGER
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* The first dimension of the array A. LDA >= max(1,M).
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*
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* TAU (input) DOUBLE PRECISION array, dimension (K)
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* TAU(i) must contain the scalar factor of the elementary
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* reflector H(i), as returned by DGELQF.
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*
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* WORK (workspace) DOUBLE PRECISION array, dimension (M)
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument has an illegal value
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, J, L
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* ..
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* .. External Subroutines ..
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EXTERNAL DLARF, DSCAL, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Executable Statements ..
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*
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* Test the input arguments
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*
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INFO = 0
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IF( M.LT.0 ) THEN
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INFO = -1
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ELSE IF( N.LT.M ) THEN
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INFO = -2
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ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
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INFO = -3
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -5
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DORGL2', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( M.LE.0 )
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$ RETURN
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*
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IF( K.LT.M ) THEN
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*
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* Initialise rows k+1:m to rows of the unit matrix
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*
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DO 20 J = 1, N
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DO 10 L = K + 1, M
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A( L, J ) = ZERO
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10 CONTINUE
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IF( J.GT.K .AND. J.LE.M )
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$ A( J, J ) = ONE
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20 CONTINUE
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END IF
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*
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DO 40 I = K, 1, -1
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*
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* Apply H(i) to A(i:m,i:n) from the right
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*
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IF( I.LT.N ) THEN
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IF( I.LT.M ) THEN
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A( I, I ) = ONE
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CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
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$ TAU( I ), A( I+1, I ), LDA, WORK )
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END IF
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CALL DSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA )
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END IF
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A( I, I ) = ONE - TAU( I )
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*
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* Set A(1:i-1,i) to zero
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*
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DO 30 L = 1, I - 1
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A( I, L ) = ZERO
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30 CONTINUE
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40 CONTINUE
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RETURN
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*
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* End of DORGL2
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*
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END
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