Annotation of rpl/lapack/lapack/dorgtr.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DORGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, 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: CHARACTER UPLO
! 10: INTEGER INFO, LDA, LWORK, N
! 11: * ..
! 12: * .. Array Arguments ..
! 13: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
! 14: * ..
! 15: *
! 16: * Purpose
! 17: * =======
! 18: *
! 19: * DORGTR generates a real orthogonal matrix Q which is defined as the
! 20: * product of n-1 elementary reflectors of order N, as returned by
! 21: * DSYTRD:
! 22: *
! 23: * if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
! 24: *
! 25: * if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
! 26: *
! 27: * Arguments
! 28: * =========
! 29: *
! 30: * UPLO (input) CHARACTER*1
! 31: * = 'U': Upper triangle of A contains elementary reflectors
! 32: * from DSYTRD;
! 33: * = 'L': Lower triangle of A contains elementary reflectors
! 34: * from DSYTRD.
! 35: *
! 36: * N (input) INTEGER
! 37: * The order of the matrix Q. N >= 0.
! 38: *
! 39: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
! 40: * On entry, the vectors which define the elementary reflectors,
! 41: * as returned by DSYTRD.
! 42: * On exit, the N-by-N orthogonal matrix Q.
! 43: *
! 44: * LDA (input) INTEGER
! 45: * The leading dimension of the array A. LDA >= max(1,N).
! 46: *
! 47: * TAU (input) DOUBLE PRECISION array, dimension (N-1)
! 48: * TAU(i) must contain the scalar factor of the elementary
! 49: * reflector H(i), as returned by DSYTRD.
! 50: *
! 51: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 52: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 53: *
! 54: * LWORK (input) INTEGER
! 55: * The dimension of the array WORK. LWORK >= max(1,N-1).
! 56: * For optimum performance LWORK >= (N-1)*NB, where NB is
! 57: * the optimal blocksize.
! 58: *
! 59: * If LWORK = -1, then a workspace query is assumed; the routine
! 60: * only calculates the optimal size of the WORK array, returns
! 61: * this value as the first entry of the WORK array, and no error
! 62: * message related to LWORK is issued by XERBLA.
! 63: *
! 64: * INFO (output) INTEGER
! 65: * = 0: successful exit
! 66: * < 0: if INFO = -i, the i-th argument had an illegal value
! 67: *
! 68: * =====================================================================
! 69: *
! 70: * .. Parameters ..
! 71: DOUBLE PRECISION ZERO, ONE
! 72: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 73: * ..
! 74: * .. Local Scalars ..
! 75: LOGICAL LQUERY, UPPER
! 76: INTEGER I, IINFO, J, LWKOPT, NB
! 77: * ..
! 78: * .. External Functions ..
! 79: LOGICAL LSAME
! 80: INTEGER ILAENV
! 81: EXTERNAL LSAME, ILAENV
! 82: * ..
! 83: * .. External Subroutines ..
! 84: EXTERNAL DORGQL, DORGQR, XERBLA
! 85: * ..
! 86: * .. Intrinsic Functions ..
! 87: INTRINSIC MAX
! 88: * ..
! 89: * .. Executable Statements ..
! 90: *
! 91: * Test the input arguments
! 92: *
! 93: INFO = 0
! 94: LQUERY = ( LWORK.EQ.-1 )
! 95: UPPER = LSAME( UPLO, 'U' )
! 96: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
! 97: INFO = -1
! 98: ELSE IF( N.LT.0 ) THEN
! 99: INFO = -2
! 100: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
! 101: INFO = -4
! 102: ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN
! 103: INFO = -7
! 104: END IF
! 105: *
! 106: IF( INFO.EQ.0 ) THEN
! 107: IF( UPPER ) THEN
! 108: NB = ILAENV( 1, 'DORGQL', ' ', N-1, N-1, N-1, -1 )
! 109: ELSE
! 110: NB = ILAENV( 1, 'DORGQR', ' ', N-1, N-1, N-1, -1 )
! 111: END IF
! 112: LWKOPT = MAX( 1, N-1 )*NB
! 113: WORK( 1 ) = LWKOPT
! 114: END IF
! 115: *
! 116: IF( INFO.NE.0 ) THEN
! 117: CALL XERBLA( 'DORGTR', -INFO )
! 118: RETURN
! 119: ELSE IF( LQUERY ) THEN
! 120: RETURN
! 121: END IF
! 122: *
! 123: * Quick return if possible
! 124: *
! 125: IF( N.EQ.0 ) THEN
! 126: WORK( 1 ) = 1
! 127: RETURN
! 128: END IF
! 129: *
! 130: IF( UPPER ) THEN
! 131: *
! 132: * Q was determined by a call to DSYTRD with UPLO = 'U'
! 133: *
! 134: * Shift the vectors which define the elementary reflectors one
! 135: * column to the left, and set the last row and column of Q to
! 136: * those of the unit matrix
! 137: *
! 138: DO 20 J = 1, N - 1
! 139: DO 10 I = 1, J - 1
! 140: A( I, J ) = A( I, J+1 )
! 141: 10 CONTINUE
! 142: A( N, J ) = ZERO
! 143: 20 CONTINUE
! 144: DO 30 I = 1, N - 1
! 145: A( I, N ) = ZERO
! 146: 30 CONTINUE
! 147: A( N, N ) = ONE
! 148: *
! 149: * Generate Q(1:n-1,1:n-1)
! 150: *
! 151: CALL DORGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO )
! 152: *
! 153: ELSE
! 154: *
! 155: * Q was determined by a call to DSYTRD with UPLO = 'L'.
! 156: *
! 157: * Shift the vectors which define the elementary reflectors one
! 158: * column to the right, and set the first row and column of Q to
! 159: * those of the unit matrix
! 160: *
! 161: DO 50 J = N, 2, -1
! 162: A( 1, J ) = ZERO
! 163: DO 40 I = J + 1, N
! 164: A( I, J ) = A( I, J-1 )
! 165: 40 CONTINUE
! 166: 50 CONTINUE
! 167: A( 1, 1 ) = ONE
! 168: DO 60 I = 2, N
! 169: A( I, 1 ) = ZERO
! 170: 60 CONTINUE
! 171: IF( N.GT.1 ) THEN
! 172: *
! 173: * Generate Q(2:n,2:n)
! 174: *
! 175: CALL DORGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
! 176: $ LWORK, IINFO )
! 177: END IF
! 178: END IF
! 179: WORK( 1 ) = LWKOPT
! 180: RETURN
! 181: *
! 182: * End of DORGTR
! 183: *
! 184: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dorgtr.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack