132 lines
3.4 KiB
FortranFixed
132 lines
3.4 KiB
FortranFixed
SUBROUTINE SORGR2( M, N, K, A, LDA, TAU, WORK, INFO )
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*
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* -- LAPACK routine (version 3.1) --
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* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
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* November 2006
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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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REAL 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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* SORGR2 generates an m by n real matrix Q with orthonormal rows,
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* which is defined as the last 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(1) H(2) . . . H(k)
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*
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* as returned by SGERQF.
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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) REAL array, dimension (LDA,N)
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* On entry, the (m-k+i)-th row must contain the vector which
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* defines the elementary reflector H(i), for i = 1,2,...,k, as
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* returned by SGERQF in the last k rows of its array argument
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* 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) REAL 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 SGERQF.
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*
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* WORK (workspace) REAL 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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REAL ONE, ZERO
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PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, II, J, L
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* ..
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* .. External Subroutines ..
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EXTERNAL SLARF, SSCAL, 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( 'SORGR2', -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 1:m-k 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 = 1, M - K
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A( L, J ) = ZERO
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10 CONTINUE
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IF( J.GT.N-M .AND. J.LE.N-K )
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$ A( M-N+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 = 1, K
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II = M - K + I
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*
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* Apply H(i) to A(1:m-k+i,1:n-k+i) from the right
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*
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A( II, N-M+II ) = ONE
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CALL SLARF( 'Right', II-1, N-M+II, A( II, 1 ), LDA, TAU( I ),
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$ A, LDA, WORK )
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CALL SSCAL( N-M+II-1, -TAU( I ), A( II, 1 ), LDA )
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A( II, N-M+II ) = ONE - TAU( I )
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*
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* Set A(m-k+i,n-k+i+1:n) to zero
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*
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DO 30 L = N - M + II + 1, N
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A( II, 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 SORGR2
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*
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END
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