123 lines
3.3 KiB
FortranFixed
123 lines
3.3 KiB
FortranFixed
SUBROUTINE DGEQL2( M, N, 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, 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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* DGEQL2 computes a QL factorization of a real m by n matrix A:
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* A = Q * L.
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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 A. M >= 0.
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*
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* N (input) INTEGER
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* The number of columns of the matrix A. N >= 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 m by n matrix A.
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* On exit, if m >= n, the lower triangle of the subarray
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* A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
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* if m <= n, the elements on and below the (n-m)-th
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* superdiagonal contain the m by n lower trapezoidal matrix L;
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* the remaining elements, with the array TAU, represent the
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* orthogonal matrix Q as a product of elementary reflectors
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* (see Further Details).
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A. LDA >= max(1,M).
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*
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* TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
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* The scalar factors of the elementary reflectors (see Further
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* Details).
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*
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* WORK (workspace) DOUBLE PRECISION array, dimension (N)
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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 had an illegal value
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*
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* Further Details
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* ===============
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*
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* The matrix Q is represented as a product of elementary reflectors
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*
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* Q = H(k) . . . H(2) H(1), where k = min(m,n).
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*
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* Each H(i) has the form
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*
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* H(i) = I - tau * v * v'
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*
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* where tau is a real scalar, and v is a real vector with
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* v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
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* A(1:m-k+i-1,n-k+i), and tau in TAU(i).
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE
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PARAMETER ( ONE = 1.0D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, K
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DOUBLE PRECISION AII
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* ..
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* .. External Subroutines ..
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EXTERNAL DLARF, DLARFP, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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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.0 ) THEN
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INFO = -2
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -4
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DGEQL2', -INFO )
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RETURN
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END IF
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*
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K = MIN( M, N )
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*
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DO 10 I = K, 1, -1
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*
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* Generate elementary reflector H(i) to annihilate
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* A(1:m-k+i-1,n-k+i)
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*
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CALL DLARFP( M-K+I, A( M-K+I, N-K+I ), A( 1, N-K+I ), 1,
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$ TAU( I ) )
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*
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* Apply H(i) to A(1:m-k+i,1:n-k+i-1) from the left
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*
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AII = A( M-K+I, N-K+I )
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A( M-K+I, N-K+I ) = ONE
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CALL DLARF( 'Left', M-K+I, N-K+I-1, A( 1, N-K+I ), 1, TAU( I ),
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$ A, LDA, WORK )
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A( M-K+I, N-K+I ) = AII
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10 CONTINUE
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RETURN
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*
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* End of DGEQL2
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*
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END
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