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SUBROUTINE ZGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
$ WORK, INFO ) * * -- LAPACK routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2011 -- * * Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH. * * .. Scalar Arguments .. CHARACTER NORM INTEGER INFO, N DOUBLE PRECISION ANORM, RCOND * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * ), WORK( * ) * .. * * Purpose * ======= * * ZGTCON estimates the reciprocal of the condition number of a complex * tridiagonal matrix A using the LU factorization as computed by * ZGTTRF. * * An estimate is obtained for norm(inv(A)), and the reciprocal of the * condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). * * Arguments * ========= * * NORM (input) CHARACTER*1 * Specifies whether the 1-norm condition number or the * infinity-norm condition number is required: * = '1' or 'O': 1-norm; * = 'I': Infinity-norm. * * N (input) INTEGER * The order of the matrix A. N >= 0. * * DL (input) COMPLEX*16 array, dimension (N-1) * The (n-1) multipliers that define the matrix L from the * LU factorization of A as computed by ZGTTRF. * * D (input) COMPLEX*16 array, dimension (N) * The n diagonal elements of the upper triangular matrix U from * the LU factorization of A. * * DU (input) COMPLEX*16 array, dimension (N-1) * The (n-1) elements of the first superdiagonal of U. * * DU2 (input) COMPLEX*16 array, dimension (N-2) * The (n-2) elements of the second superdiagonal of U. * * IPIV (input) INTEGER array, dimension (N) * The pivot indices; for 1 <= i <= n, row i of the matrix was * interchanged with row IPIV(i). IPIV(i) will always be either * i or i+1; IPIV(i) = i indicates a row interchange was not * required. * * ANORM (input) DOUBLE PRECISION * If NORM = '1' or 'O', the 1-norm of the original matrix A. * If NORM = 'I', the infinity-norm of the original matrix A. * * RCOND (output) DOUBLE PRECISION * The reciprocal of the condition number of the matrix A, * computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an * estimate of the 1-norm of inv(A) computed in this routine. * * WORK (workspace) COMPLEX*16 array, dimension (2*N) * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. LOGICAL ONENRM INTEGER I, KASE, KASE1 DOUBLE PRECISION AINVNM * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZGTTRS, ZLACN2 * .. * .. Intrinsic Functions .. INTRINSIC DCMPLX * .. * .. Executable Statements .. * * Test the input arguments. * INFO = 0 ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' ) IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( ANORM.LT.ZERO ) THEN INFO = -8 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGTCON', -INFO ) RETURN END IF * * Quick return if possible * RCOND = ZERO IF( N.EQ.0 ) THEN RCOND = ONE RETURN ELSE IF( ANORM.EQ.ZERO ) THEN RETURN END IF * * Check that D(1:N) is non-zero. * DO 10 I = 1, N IF( D( I ).EQ.DCMPLX( ZERO ) ) $ RETURN 10 CONTINUE * AINVNM = ZERO IF( ONENRM ) THEN KASE1 = 1 ELSE KASE1 = 2 END IF KASE = 0 20 CONTINUE CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) IF( KASE.NE.0 ) THEN IF( KASE.EQ.KASE1 ) THEN * * Multiply by inv(U)*inv(L). * CALL ZGTTRS( 'No transpose', N, 1, DL, D, DU, DU2, IPIV, $ WORK, N, INFO ) ELSE * * Multiply by inv(L**H)*inv(U**H). * CALL ZGTTRS( 'Conjugate transpose', N, 1, DL, D, DU, DU2, $ IPIV, WORK, N, INFO ) END IF GO TO 20 END IF * * Compute the estimate of the reciprocal condition number. * IF( AINVNM.NE.ZERO ) $ RCOND = ( ONE / AINVNM ) / ANORM * RETURN * * End of ZGTCON * END |