LAPACK 3.3.1 Linear Algebra PACKage

# zgtcon.f

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```00001       SUBROUTINE ZGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
00002      \$                   WORK, INFO )
00003 *
00004 *  -- LAPACK routine (version 3.3.1) --
00005 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00006 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00007 *  -- April 2011                                                      --
00008 *
00009 *     Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH.
00010 *
00011 *     .. Scalar Arguments ..
00012       CHARACTER          NORM
00013       INTEGER            INFO, N
00014       DOUBLE PRECISION   ANORM, RCOND
00015 *     ..
00016 *     .. Array Arguments ..
00017       INTEGER            IPIV( * )
00018       COMPLEX*16         D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
00019 *     ..
00020 *
00021 *  Purpose
00022 *  =======
00023 *
00024 *  ZGTCON estimates the reciprocal of the condition number of a complex
00025 *  tridiagonal matrix A using the LU factorization as computed by
00026 *  ZGTTRF.
00027 *
00028 *  An estimate is obtained for norm(inv(A)), and the reciprocal of the
00029 *  condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
00030 *
00031 *  Arguments
00032 *  =========
00033 *
00034 *  NORM    (input) CHARACTER*1
00035 *          Specifies whether the 1-norm condition number or the
00036 *          infinity-norm condition number is required:
00037 *          = '1' or 'O':  1-norm;
00038 *          = 'I':         Infinity-norm.
00039 *
00040 *  N       (input) INTEGER
00041 *          The order of the matrix A.  N >= 0.
00042 *
00043 *  DL      (input) COMPLEX*16 array, dimension (N-1)
00044 *          The (n-1) multipliers that define the matrix L from the
00045 *          LU factorization of A as computed by ZGTTRF.
00046 *
00047 *  D       (input) COMPLEX*16 array, dimension (N)
00048 *          The n diagonal elements of the upper triangular matrix U from
00049 *          the LU factorization of A.
00050 *
00051 *  DU      (input) COMPLEX*16 array, dimension (N-1)
00052 *          The (n-1) elements of the first superdiagonal of U.
00053 *
00054 *  DU2     (input) COMPLEX*16 array, dimension (N-2)
00055 *          The (n-2) elements of the second superdiagonal of U.
00056 *
00057 *  IPIV    (input) INTEGER array, dimension (N)
00058 *          The pivot indices; for 1 <= i <= n, row i of the matrix was
00059 *          interchanged with row IPIV(i).  IPIV(i) will always be either
00060 *          i or i+1; IPIV(i) = i indicates a row interchange was not
00061 *          required.
00062 *
00063 *  ANORM   (input) DOUBLE PRECISION
00064 *          If NORM = '1' or 'O', the 1-norm of the original matrix A.
00065 *          If NORM = 'I', the infinity-norm of the original matrix A.
00066 *
00067 *  RCOND   (output) DOUBLE PRECISION
00068 *          The reciprocal of the condition number of the matrix A,
00069 *          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
00070 *          estimate of the 1-norm of inv(A) computed in this routine.
00071 *
00072 *  WORK    (workspace) COMPLEX*16 array, dimension (2*N)
00073 *
00074 *  INFO    (output) INTEGER
00075 *          = 0:  successful exit
00076 *          < 0:  if INFO = -i, the i-th argument had an illegal value
00077 *
00078 *  =====================================================================
00079 *
00080 *     .. Parameters ..
00081       DOUBLE PRECISION   ONE, ZERO
00082       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00083 *     ..
00084 *     .. Local Scalars ..
00085       LOGICAL            ONENRM
00086       INTEGER            I, KASE, KASE1
00087       DOUBLE PRECISION   AINVNM
00088 *     ..
00089 *     .. Local Arrays ..
00090       INTEGER            ISAVE( 3 )
00091 *     ..
00092 *     .. External Functions ..
00093       LOGICAL            LSAME
00094       EXTERNAL           LSAME
00095 *     ..
00096 *     .. External Subroutines ..
00097       EXTERNAL           XERBLA, ZGTTRS, ZLACN2
00098 *     ..
00099 *     .. Intrinsic Functions ..
00100       INTRINSIC          DCMPLX
00101 *     ..
00102 *     .. Executable Statements ..
00103 *
00104 *     Test the input arguments.
00105 *
00106       INFO = 0
00107       ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
00108       IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
00109          INFO = -1
00110       ELSE IF( N.LT.0 ) THEN
00111          INFO = -2
00112       ELSE IF( ANORM.LT.ZERO ) THEN
00113          INFO = -8
00114       END IF
00115       IF( INFO.NE.0 ) THEN
00116          CALL XERBLA( 'ZGTCON', -INFO )
00117          RETURN
00118       END IF
00119 *
00120 *     Quick return if possible
00121 *
00122       RCOND = ZERO
00123       IF( N.EQ.0 ) THEN
00124          RCOND = ONE
00125          RETURN
00126       ELSE IF( ANORM.EQ.ZERO ) THEN
00127          RETURN
00128       END IF
00129 *
00130 *     Check that D(1:N) is non-zero.
00131 *
00132       DO 10 I = 1, N
00133          IF( D( I ).EQ.DCMPLX( ZERO ) )
00134      \$      RETURN
00135    10 CONTINUE
00136 *
00137       AINVNM = ZERO
00138       IF( ONENRM ) THEN
00139          KASE1 = 1
00140       ELSE
00141          KASE1 = 2
00142       END IF
00143       KASE = 0
00144    20 CONTINUE
00145       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
00146       IF( KASE.NE.0 ) THEN
00147          IF( KASE.EQ.KASE1 ) THEN
00148 *
00149 *           Multiply by inv(U)*inv(L).
00150 *
00151             CALL ZGTTRS( 'No transpose', N, 1, DL, D, DU, DU2, IPIV,
00152      \$                   WORK, N, INFO )
00153          ELSE
00154 *
00155 *           Multiply by inv(L**H)*inv(U**H).
00156 *
00157             CALL ZGTTRS( 'Conjugate transpose', N, 1, DL, D, DU, DU2,
00158      \$                   IPIV, WORK, N, INFO )
00159          END IF
00160          GO TO 20
00161       END IF
00162 *
00163 *     Compute the estimate of the reciprocal condition number.
00164 *
00165       IF( AINVNM.NE.ZERO )
00166      \$   RCOND = ( ONE / AINVNM ) / ANORM
00167 *
00168       RETURN
00169 *
00170 *     End of ZGTCON
00171 *
00172       END
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