Annotation of rpl/lapack/lapack/dgtcon.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
! 2: $ WORK, IWORK, INFO )
! 3: *
! 4: * -- LAPACK routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * November 2006
! 8: *
! 9: * Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH.
! 10: *
! 11: * .. Scalar Arguments ..
! 12: CHARACTER NORM
! 13: INTEGER INFO, N
! 14: DOUBLE PRECISION ANORM, RCOND
! 15: * ..
! 16: * .. Array Arguments ..
! 17: INTEGER IPIV( * ), IWORK( * )
! 18: DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
! 19: * ..
! 20: *
! 21: * Purpose
! 22: * =======
! 23: *
! 24: * DGTCON estimates the reciprocal of the condition number of a real
! 25: * tridiagonal matrix A using the LU factorization as computed by
! 26: * DGTTRF.
! 27: *
! 28: * An estimate is obtained for norm(inv(A)), and the reciprocal of the
! 29: * condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
! 30: *
! 31: * Arguments
! 32: * =========
! 33: *
! 34: * NORM (input) CHARACTER*1
! 35: * Specifies whether the 1-norm condition number or the
! 36: * infinity-norm condition number is required:
! 37: * = '1' or 'O': 1-norm;
! 38: * = 'I': Infinity-norm.
! 39: *
! 40: * N (input) INTEGER
! 41: * The order of the matrix A. N >= 0.
! 42: *
! 43: * DL (input) DOUBLE PRECISION array, dimension (N-1)
! 44: * The (n-1) multipliers that define the matrix L from the
! 45: * LU factorization of A as computed by DGTTRF.
! 46: *
! 47: * D (input) DOUBLE PRECISION array, dimension (N)
! 48: * The n diagonal elements of the upper triangular matrix U from
! 49: * the LU factorization of A.
! 50: *
! 51: * DU (input) DOUBLE PRECISION array, dimension (N-1)
! 52: * The (n-1) elements of the first superdiagonal of U.
! 53: *
! 54: * DU2 (input) DOUBLE PRECISION array, dimension (N-2)
! 55: * The (n-2) elements of the second superdiagonal of U.
! 56: *
! 57: * IPIV (input) INTEGER array, dimension (N)
! 58: * The pivot indices; for 1 <= i <= n, row i of the matrix was
! 59: * interchanged with row IPIV(i). IPIV(i) will always be either
! 60: * i or i+1; IPIV(i) = i indicates a row interchange was not
! 61: * required.
! 62: *
! 63: * ANORM (input) DOUBLE PRECISION
! 64: * If NORM = '1' or 'O', the 1-norm of the original matrix A.
! 65: * If NORM = 'I', the infinity-norm of the original matrix A.
! 66: *
! 67: * RCOND (output) DOUBLE PRECISION
! 68: * The reciprocal of the condition number of the matrix A,
! 69: * computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
! 70: * estimate of the 1-norm of inv(A) computed in this routine.
! 71: *
! 72: * WORK (workspace) DOUBLE PRECISION array, dimension (2*N)
! 73: *
! 74: * IWORK (workspace) INTEGER array, dimension (N)
! 75: *
! 76: * INFO (output) INTEGER
! 77: * = 0: successful exit
! 78: * < 0: if INFO = -i, the i-th argument had an illegal value
! 79: *
! 80: * =====================================================================
! 81: *
! 82: * .. Parameters ..
! 83: DOUBLE PRECISION ONE, ZERO
! 84: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
! 85: * ..
! 86: * .. Local Scalars ..
! 87: LOGICAL ONENRM
! 88: INTEGER I, KASE, KASE1
! 89: DOUBLE PRECISION AINVNM
! 90: * ..
! 91: * .. Local Arrays ..
! 92: INTEGER ISAVE( 3 )
! 93: * ..
! 94: * .. External Functions ..
! 95: LOGICAL LSAME
! 96: EXTERNAL LSAME
! 97: * ..
! 98: * .. External Subroutines ..
! 99: EXTERNAL DGTTRS, DLACN2, XERBLA
! 100: * ..
! 101: * .. Executable Statements ..
! 102: *
! 103: * Test the input arguments.
! 104: *
! 105: INFO = 0
! 106: ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
! 107: IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
! 108: INFO = -1
! 109: ELSE IF( N.LT.0 ) THEN
! 110: INFO = -2
! 111: ELSE IF( ANORM.LT.ZERO ) THEN
! 112: INFO = -8
! 113: END IF
! 114: IF( INFO.NE.0 ) THEN
! 115: CALL XERBLA( 'DGTCON', -INFO )
! 116: RETURN
! 117: END IF
! 118: *
! 119: * Quick return if possible
! 120: *
! 121: RCOND = ZERO
! 122: IF( N.EQ.0 ) THEN
! 123: RCOND = ONE
! 124: RETURN
! 125: ELSE IF( ANORM.EQ.ZERO ) THEN
! 126: RETURN
! 127: END IF
! 128: *
! 129: * Check that D(1:N) is non-zero.
! 130: *
! 131: DO 10 I = 1, N
! 132: IF( D( I ).EQ.ZERO )
! 133: $ RETURN
! 134: 10 CONTINUE
! 135: *
! 136: AINVNM = ZERO
! 137: IF( ONENRM ) THEN
! 138: KASE1 = 1
! 139: ELSE
! 140: KASE1 = 2
! 141: END IF
! 142: KASE = 0
! 143: 20 CONTINUE
! 144: CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
! 145: IF( KASE.NE.0 ) THEN
! 146: IF( KASE.EQ.KASE1 ) THEN
! 147: *
! 148: * Multiply by inv(U)*inv(L).
! 149: *
! 150: CALL DGTTRS( 'No transpose', N, 1, DL, D, DU, DU2, IPIV,
! 151: $ WORK, N, INFO )
! 152: ELSE
! 153: *
! 154: * Multiply by inv(L')*inv(U').
! 155: *
! 156: CALL DGTTRS( 'Transpose', N, 1, DL, D, DU, DU2, IPIV, WORK,
! 157: $ N, INFO )
! 158: END IF
! 159: GO TO 20
! 160: END IF
! 161: *
! 162: * Compute the estimate of the reciprocal condition number.
! 163: *
! 164: IF( AINVNM.NE.ZERO )
! 165: $ RCOND = ( ONE / AINVNM ) / ANORM
! 166: *
! 167: RETURN
! 168: *
! 169: * End of DGTCON
! 170: *
! 171: END
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