Annotation of rpl/lapack/lapack/dgeql2.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DGEQL2( M, N, A, LDA, TAU, WORK, INFO )
! 2: *
! 3: * -- LAPACK routine (version 3.2) --
! 4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 6: * November 2006
! 7: *
! 8: * .. Scalar Arguments ..
! 9: INTEGER INFO, LDA, M, N
! 10: * ..
! 11: * .. Array Arguments ..
! 12: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
! 13: * ..
! 14: *
! 15: * Purpose
! 16: * =======
! 17: *
! 18: * DGEQL2 computes a QL factorization of a real m by n matrix A:
! 19: * A = Q * L.
! 20: *
! 21: * Arguments
! 22: * =========
! 23: *
! 24: * M (input) INTEGER
! 25: * The number of rows of the matrix A. M >= 0.
! 26: *
! 27: * N (input) INTEGER
! 28: * The number of columns of the matrix A. N >= 0.
! 29: *
! 30: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
! 31: * On entry, the m by n matrix A.
! 32: * On exit, if m >= n, the lower triangle of the subarray
! 33: * A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
! 34: * if m <= n, the elements on and below the (n-m)-th
! 35: * superdiagonal contain the m by n lower trapezoidal matrix L;
! 36: * the remaining elements, with the array TAU, represent the
! 37: * orthogonal matrix Q as a product of elementary reflectors
! 38: * (see Further Details).
! 39: *
! 40: * LDA (input) INTEGER
! 41: * The leading dimension of the array A. LDA >= max(1,M).
! 42: *
! 43: * TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
! 44: * The scalar factors of the elementary reflectors (see Further
! 45: * Details).
! 46: *
! 47: * WORK (workspace) DOUBLE PRECISION array, dimension (N)
! 48: *
! 49: * INFO (output) INTEGER
! 50: * = 0: successful exit
! 51: * < 0: if INFO = -i, the i-th argument had an illegal value
! 52: *
! 53: * Further Details
! 54: * ===============
! 55: *
! 56: * The matrix Q is represented as a product of elementary reflectors
! 57: *
! 58: * Q = H(k) . . . H(2) H(1), where k = min(m,n).
! 59: *
! 60: * Each H(i) has the form
! 61: *
! 62: * H(i) = I - tau * v * v'
! 63: *
! 64: * where tau is a real scalar, and v is a real vector with
! 65: * v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
! 66: * A(1:m-k+i-1,n-k+i), and tau in TAU(i).
! 67: *
! 68: * =====================================================================
! 69: *
! 70: * .. Parameters ..
! 71: DOUBLE PRECISION ONE
! 72: PARAMETER ( ONE = 1.0D+0 )
! 73: * ..
! 74: * .. Local Scalars ..
! 75: INTEGER I, K
! 76: DOUBLE PRECISION AII
! 77: * ..
! 78: * .. External Subroutines ..
! 79: EXTERNAL DLARF, DLARFP, XERBLA
! 80: * ..
! 81: * .. Intrinsic Functions ..
! 82: INTRINSIC MAX, MIN
! 83: * ..
! 84: * .. Executable Statements ..
! 85: *
! 86: * Test the input arguments
! 87: *
! 88: INFO = 0
! 89: IF( M.LT.0 ) THEN
! 90: INFO = -1
! 91: ELSE IF( N.LT.0 ) THEN
! 92: INFO = -2
! 93: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 94: INFO = -4
! 95: END IF
! 96: IF( INFO.NE.0 ) THEN
! 97: CALL XERBLA( 'DGEQL2', -INFO )
! 98: RETURN
! 99: END IF
! 100: *
! 101: K = MIN( M, N )
! 102: *
! 103: DO 10 I = K, 1, -1
! 104: *
! 105: * Generate elementary reflector H(i) to annihilate
! 106: * A(1:m-k+i-1,n-k+i)
! 107: *
! 108: CALL DLARFP( M-K+I, A( M-K+I, N-K+I ), A( 1, N-K+I ), 1,
! 109: $ TAU( I ) )
! 110: *
! 111: * Apply H(i) to A(1:m-k+i,1:n-k+i-1) from the left
! 112: *
! 113: AII = A( M-K+I, N-K+I )
! 114: A( M-K+I, N-K+I ) = ONE
! 115: CALL DLARF( 'Left', M-K+I, N-K+I-1, A( 1, N-K+I ), 1, TAU( I ),
! 116: $ A, LDA, WORK )
! 117: A( M-K+I, N-K+I ) = AII
! 118: 10 CONTINUE
! 119: RETURN
! 120: *
! 121: * End of DGEQL2
! 122: *
! 123: END
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