Annotation of rpl/lapack/lapack/dgelq2.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DGELQ2( 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: * DGELQ2 computes an LQ factorization of a real m by n matrix A:
! 19: * A = L * Q.
! 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, the elements on and below the diagonal of the array
! 33: * contain the m by min(m,n) lower trapezoidal matrix L (L is
! 34: * lower triangular if m <= n); the elements above the diagonal,
! 35: * with the array TAU, represent the orthogonal matrix Q as a
! 36: * product of elementary reflectors (see Further Details).
! 37: *
! 38: * LDA (input) INTEGER
! 39: * The leading dimension of the array A. LDA >= max(1,M).
! 40: *
! 41: * TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
! 42: * The scalar factors of the elementary reflectors (see Further
! 43: * Details).
! 44: *
! 45: * WORK (workspace) DOUBLE PRECISION array, dimension (M)
! 46: *
! 47: * INFO (output) INTEGER
! 48: * = 0: successful exit
! 49: * < 0: if INFO = -i, the i-th argument had an illegal value
! 50: *
! 51: * Further Details
! 52: * ===============
! 53: *
! 54: * The matrix Q is represented as a product of elementary reflectors
! 55: *
! 56: * Q = H(k) . . . H(2) H(1), where k = min(m,n).
! 57: *
! 58: * Each H(i) has the form
! 59: *
! 60: * H(i) = I - tau * v * v'
! 61: *
! 62: * where tau is a real scalar, and v is a real vector with
! 63: * v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
! 64: * and tau in TAU(i).
! 65: *
! 66: * =====================================================================
! 67: *
! 68: * .. Parameters ..
! 69: DOUBLE PRECISION ONE
! 70: PARAMETER ( ONE = 1.0D+0 )
! 71: * ..
! 72: * .. Local Scalars ..
! 73: INTEGER I, K
! 74: DOUBLE PRECISION AII
! 75: * ..
! 76: * .. External Subroutines ..
! 77: EXTERNAL DLARF, DLARFP, XERBLA
! 78: * ..
! 79: * .. Intrinsic Functions ..
! 80: INTRINSIC MAX, MIN
! 81: * ..
! 82: * .. Executable Statements ..
! 83: *
! 84: * Test the input arguments
! 85: *
! 86: INFO = 0
! 87: IF( M.LT.0 ) THEN
! 88: INFO = -1
! 89: ELSE IF( N.LT.0 ) THEN
! 90: INFO = -2
! 91: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 92: INFO = -4
! 93: END IF
! 94: IF( INFO.NE.0 ) THEN
! 95: CALL XERBLA( 'DGELQ2', -INFO )
! 96: RETURN
! 97: END IF
! 98: *
! 99: K = MIN( M, N )
! 100: *
! 101: DO 10 I = 1, K
! 102: *
! 103: * Generate elementary reflector H(i) to annihilate A(i,i+1:n)
! 104: *
! 105: CALL DLARFP( N-I+1, A( I, I ), A( I, MIN( I+1, N ) ), LDA,
! 106: $ TAU( I ) )
! 107: IF( I.LT.M ) THEN
! 108: *
! 109: * Apply H(i) to A(i+1:m,i:n) from the right
! 110: *
! 111: AII = A( I, I )
! 112: A( I, I ) = ONE
! 113: CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, TAU( I ),
! 114: $ A( I+1, I ), LDA, WORK )
! 115: A( I, I ) = AII
! 116: END IF
! 117: 10 CONTINUE
! 118: RETURN
! 119: *
! 120: * End of DGELQ2
! 121: *
! 122: END
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