Annotation of rpl/lapack/lapack/dorgl2.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DORGL2( M, N, K, 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, K, LDA, M, N
! 10: * ..
! 11: * .. Array Arguments ..
! 12: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
! 13: * ..
! 14: *
! 15: * Purpose
! 16: * =======
! 17: *
! 18: * DORGL2 generates an m by n real matrix Q with orthonormal rows,
! 19: * which is defined as the first m rows of a product of k elementary
! 20: * reflectors of order n
! 21: *
! 22: * Q = H(k) . . . H(2) H(1)
! 23: *
! 24: * as returned by DGELQF.
! 25: *
! 26: * Arguments
! 27: * =========
! 28: *
! 29: * M (input) INTEGER
! 30: * The number of rows of the matrix Q. M >= 0.
! 31: *
! 32: * N (input) INTEGER
! 33: * The number of columns of the matrix Q. N >= M.
! 34: *
! 35: * K (input) INTEGER
! 36: * The number of elementary reflectors whose product defines the
! 37: * matrix Q. M >= K >= 0.
! 38: *
! 39: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
! 40: * On entry, the i-th row must contain the vector which defines
! 41: * the elementary reflector H(i), for i = 1,2,...,k, as returned
! 42: * by DGELQF in the first k rows of its array argument A.
! 43: * On exit, the m-by-n matrix Q.
! 44: *
! 45: * LDA (input) INTEGER
! 46: * The first dimension of the array A. LDA >= max(1,M).
! 47: *
! 48: * TAU (input) DOUBLE PRECISION array, dimension (K)
! 49: * TAU(i) must contain the scalar factor of the elementary
! 50: * reflector H(i), as returned by DGELQF.
! 51: *
! 52: * WORK (workspace) DOUBLE PRECISION array, dimension (M)
! 53: *
! 54: * INFO (output) INTEGER
! 55: * = 0: successful exit
! 56: * < 0: if INFO = -i, the i-th argument has an illegal value
! 57: *
! 58: * =====================================================================
! 59: *
! 60: * .. Parameters ..
! 61: DOUBLE PRECISION ONE, ZERO
! 62: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 63: * ..
! 64: * .. Local Scalars ..
! 65: INTEGER I, J, L
! 66: * ..
! 67: * .. External Subroutines ..
! 68: EXTERNAL DLARF, DSCAL, XERBLA
! 69: * ..
! 70: * .. Intrinsic Functions ..
! 71: INTRINSIC MAX
! 72: * ..
! 73: * .. Executable Statements ..
! 74: *
! 75: * Test the input arguments
! 76: *
! 77: INFO = 0
! 78: IF( M.LT.0 ) THEN
! 79: INFO = -1
! 80: ELSE IF( N.LT.M ) THEN
! 81: INFO = -2
! 82: ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
! 83: INFO = -3
! 84: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 85: INFO = -5
! 86: END IF
! 87: IF( INFO.NE.0 ) THEN
! 88: CALL XERBLA( 'DORGL2', -INFO )
! 89: RETURN
! 90: END IF
! 91: *
! 92: * Quick return if possible
! 93: *
! 94: IF( M.LE.0 )
! 95: $ RETURN
! 96: *
! 97: IF( K.LT.M ) THEN
! 98: *
! 99: * Initialise rows k+1:m to rows of the unit matrix
! 100: *
! 101: DO 20 J = 1, N
! 102: DO 10 L = K + 1, M
! 103: A( L, J ) = ZERO
! 104: 10 CONTINUE
! 105: IF( J.GT.K .AND. J.LE.M )
! 106: $ A( J, J ) = ONE
! 107: 20 CONTINUE
! 108: END IF
! 109: *
! 110: DO 40 I = K, 1, -1
! 111: *
! 112: * Apply H(i) to A(i:m,i:n) from the right
! 113: *
! 114: IF( I.LT.N ) THEN
! 115: IF( I.LT.M ) THEN
! 116: A( I, I ) = ONE
! 117: CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
! 118: $ TAU( I ), A( I+1, I ), LDA, WORK )
! 119: END IF
! 120: CALL DSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA )
! 121: END IF
! 122: A( I, I ) = ONE - TAU( I )
! 123: *
! 124: * Set A(i,1:i-1) to zero
! 125: *
! 126: DO 30 L = 1, I - 1
! 127: A( I, L ) = ZERO
! 128: 30 CONTINUE
! 129: 40 CONTINUE
! 130: RETURN
! 131: *
! 132: * End of DORGL2
! 133: *
! 134: END
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