Annotation of rpl/lapack/lapack/dorgr2.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DORGR2( 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: * DORGR2 generates an m by n real matrix Q with orthonormal rows,
! 19: * which is defined as the last m rows of a product of k elementary
! 20: * reflectors of order n
! 21: *
! 22: * Q = H(1) H(2) . . . H(k)
! 23: *
! 24: * as returned by DGERQF.
! 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 (m-k+i)-th row must contain the vector which
! 41: * defines the elementary reflector H(i), for i = 1,2,...,k, as
! 42: * returned by DGERQF in the last k rows of its array argument
! 43: * A.
! 44: * On exit, the m by n matrix Q.
! 45: *
! 46: * LDA (input) INTEGER
! 47: * The first dimension of the array A. LDA >= max(1,M).
! 48: *
! 49: * TAU (input) DOUBLE PRECISION array, dimension (K)
! 50: * TAU(i) must contain the scalar factor of the elementary
! 51: * reflector H(i), as returned by DGERQF.
! 52: *
! 53: * WORK (workspace) DOUBLE PRECISION array, dimension (M)
! 54: *
! 55: * INFO (output) INTEGER
! 56: * = 0: successful exit
! 57: * < 0: if INFO = -i, the i-th argument has an illegal value
! 58: *
! 59: * =====================================================================
! 60: *
! 61: * .. Parameters ..
! 62: DOUBLE PRECISION ONE, ZERO
! 63: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 64: * ..
! 65: * .. Local Scalars ..
! 66: INTEGER I, II, J, L
! 67: * ..
! 68: * .. External Subroutines ..
! 69: EXTERNAL DLARF, DSCAL, XERBLA
! 70: * ..
! 71: * .. Intrinsic Functions ..
! 72: INTRINSIC MAX
! 73: * ..
! 74: * .. Executable Statements ..
! 75: *
! 76: * Test the input arguments
! 77: *
! 78: INFO = 0
! 79: IF( M.LT.0 ) THEN
! 80: INFO = -1
! 81: ELSE IF( N.LT.M ) THEN
! 82: INFO = -2
! 83: ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
! 84: INFO = -3
! 85: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
! 86: INFO = -5
! 87: END IF
! 88: IF( INFO.NE.0 ) THEN
! 89: CALL XERBLA( 'DORGR2', -INFO )
! 90: RETURN
! 91: END IF
! 92: *
! 93: * Quick return if possible
! 94: *
! 95: IF( M.LE.0 )
! 96: $ RETURN
! 97: *
! 98: IF( K.LT.M ) THEN
! 99: *
! 100: * Initialise rows 1:m-k to rows of the unit matrix
! 101: *
! 102: DO 20 J = 1, N
! 103: DO 10 L = 1, M - K
! 104: A( L, J ) = ZERO
! 105: 10 CONTINUE
! 106: IF( J.GT.N-M .AND. J.LE.N-K )
! 107: $ A( M-N+J, J ) = ONE
! 108: 20 CONTINUE
! 109: END IF
! 110: *
! 111: DO 40 I = 1, K
! 112: II = M - K + I
! 113: *
! 114: * Apply H(i) to A(1:m-k+i,1:n-k+i) from the right
! 115: *
! 116: A( II, N-M+II ) = ONE
! 117: CALL DLARF( 'Right', II-1, N-M+II, A( II, 1 ), LDA, TAU( I ),
! 118: $ A, LDA, WORK )
! 119: CALL DSCAL( N-M+II-1, -TAU( I ), A( II, 1 ), LDA )
! 120: A( II, N-M+II ) = ONE - TAU( I )
! 121: *
! 122: * Set A(m-k+i,n-k+i+1:n) to zero
! 123: *
! 124: DO 30 L = N - M + II + 1, N
! 125: A( II, L ) = ZERO
! 126: 30 CONTINUE
! 127: 40 CONTINUE
! 128: RETURN
! 129: *
! 130: * End of DORGR2
! 131: *
! 132: END
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