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authorjofret2009-04-28 07:17:00 +0000
committerjofret2009-04-28 07:17:00 +0000
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Moving lapack to right place
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- SUBROUTINE DGEQL2( M, N, A, LDA, TAU, WORK, INFO )
-*
-* -- LAPACK routine (version 3.1) --
-* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
-* November 2006
-*
-* .. Scalar Arguments ..
- INTEGER INFO, LDA, M, N
-* ..
-* .. Array Arguments ..
- DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
-* ..
-*
-* Purpose
-* =======
-*
-* DGEQL2 computes a QL factorization of a real m by n matrix A:
-* A = Q * L.
-*
-* Arguments
-* =========
-*
-* M (input) INTEGER
-* The number of rows of the matrix A. M >= 0.
-*
-* N (input) INTEGER
-* The number of columns of the matrix A. N >= 0.
-*
-* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
-* On entry, the m by n matrix A.
-* On exit, if m >= n, the lower triangle of the subarray
-* A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
-* if m <= n, the elements on and below the (n-m)-th
-* superdiagonal contain the m by n lower trapezoidal matrix L;
-* the remaining elements, with the array TAU, represent the
-* orthogonal matrix Q as a product of elementary reflectors
-* (see Further Details).
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,M).
-*
-* TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
-* The scalar factors of the elementary reflectors (see Further
-* Details).
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension (N)
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-*
-* Further Details
-* ===============
-*
-* The matrix Q is represented as a product of elementary reflectors
-*
-* Q = H(k) . . . H(2) H(1), where k = min(m,n).
-*
-* Each H(i) has the form
-*
-* H(i) = I - tau * v * v'
-*
-* where tau is a real scalar, and v is a real vector with
-* v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
-* A(1:m-k+i-1,n-k+i), and tau in TAU(i).
-*
-* =====================================================================
-*
-* .. Parameters ..
- DOUBLE PRECISION ONE
- PARAMETER ( ONE = 1.0D+0 )
-* ..
-* .. Local Scalars ..
- INTEGER I, K
- DOUBLE PRECISION AII
-* ..
-* .. External Subroutines ..
- EXTERNAL DLARF, DLARFG, XERBLA
-* ..
-* .. Intrinsic Functions ..
- INTRINSIC MAX, MIN
-* ..
-* .. Executable Statements ..
-*
-* Test the input arguments
-*
- INFO = 0
- IF( M.LT.0 ) THEN
- INFO = -1
- ELSE IF( N.LT.0 ) THEN
- INFO = -2
- ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
- INFO = -4
- END IF
- IF( INFO.NE.0 ) THEN
- CALL XERBLA( 'DGEQL2', -INFO )
- RETURN
- END IF
-*
- K = MIN( M, N )
-*
- DO 10 I = K, 1, -1
-*
-* Generate elementary reflector H(i) to annihilate
-* A(1:m-k+i-1,n-k+i)
-*
- CALL DLARFG( M-K+I, A( M-K+I, N-K+I ), A( 1, N-K+I ), 1,
- $ TAU( I ) )
-*
-* Apply H(i) to A(1:m-k+i,1:n-k+i-1) from the left
-*
- AII = A( M-K+I, N-K+I )
- A( M-K+I, N-K+I ) = ONE
- CALL DLARF( 'Left', M-K+I, N-K+I-1, A( 1, N-K+I ), 1, TAU( I ),
- $ A, LDA, WORK )
- A( M-K+I, N-K+I ) = AII
- 10 CONTINUE
- RETURN
-*
-* End of DGEQL2
-*
- END