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Annotation of rpl/lapack/lapack/zhecon.f, revision 1.1

1.1     ! bertrand    1:       SUBROUTINE ZHECON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
        !             2:      $                   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 ZLACN2 in place of ZLACON, 10 Feb 03, SJH.
        !            10: *
        !            11: *     .. Scalar Arguments ..
        !            12:       CHARACTER          UPLO
        !            13:       INTEGER            INFO, LDA, N
        !            14:       DOUBLE PRECISION   ANORM, RCOND
        !            15: *     ..
        !            16: *     .. Array Arguments ..
        !            17:       INTEGER            IPIV( * )
        !            18:       COMPLEX*16         A( LDA, * ), WORK( * )
        !            19: *     ..
        !            20: *
        !            21: *  Purpose
        !            22: *  =======
        !            23: *
        !            24: *  ZHECON estimates the reciprocal of the condition number of a complex
        !            25: *  Hermitian matrix A using the factorization A = U*D*U**H or
        !            26: *  A = L*D*L**H computed by ZHETRF.
        !            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: *  UPLO    (input) CHARACTER*1
        !            35: *          Specifies whether the details of the factorization are stored
        !            36: *          as an upper or lower triangular matrix.
        !            37: *          = 'U':  Upper triangular, form is A = U*D*U**H;
        !            38: *          = 'L':  Lower triangular, form is A = L*D*L**H.
        !            39: *
        !            40: *  N       (input) INTEGER
        !            41: *          The order of the matrix A.  N >= 0.
        !            42: *
        !            43: *  A       (input) COMPLEX*16 array, dimension (LDA,N)
        !            44: *          The block diagonal matrix D and the multipliers used to
        !            45: *          obtain the factor U or L as computed by ZHETRF.
        !            46: *
        !            47: *  LDA     (input) INTEGER
        !            48: *          The leading dimension of the array A.  LDA >= max(1,N).
        !            49: *
        !            50: *  IPIV    (input) INTEGER array, dimension (N)
        !            51: *          Details of the interchanges and the block structure of D
        !            52: *          as determined by ZHETRF.
        !            53: *
        !            54: *  ANORM   (input) DOUBLE PRECISION
        !            55: *          The 1-norm of the original matrix A.
        !            56: *
        !            57: *  RCOND   (output) DOUBLE PRECISION
        !            58: *          The reciprocal of the condition number of the matrix A,
        !            59: *          computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
        !            60: *          estimate of the 1-norm of inv(A) computed in this routine.
        !            61: *
        !            62: *  WORK    (workspace) COMPLEX*16 array, dimension (2*N)
        !            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   ONE, ZERO
        !            72:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
        !            73: *     ..
        !            74: *     .. Local Scalars ..
        !            75:       LOGICAL            UPPER
        !            76:       INTEGER            I, KASE
        !            77:       DOUBLE PRECISION   AINVNM
        !            78: *     ..
        !            79: *     .. Local Arrays ..
        !            80:       INTEGER            ISAVE( 3 )
        !            81: *     ..
        !            82: *     .. External Functions ..
        !            83:       LOGICAL            LSAME
        !            84:       EXTERNAL           LSAME
        !            85: *     ..
        !            86: *     .. External Subroutines ..
        !            87:       EXTERNAL           XERBLA, ZHETRS, ZLACN2
        !            88: *     ..
        !            89: *     .. Intrinsic Functions ..
        !            90:       INTRINSIC          MAX
        !            91: *     ..
        !            92: *     .. Executable Statements ..
        !            93: *
        !            94: *     Test the input parameters.
        !            95: *
        !            96:       INFO = 0
        !            97:       UPPER = LSAME( UPLO, 'U' )
        !            98:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
        !            99:          INFO = -1
        !           100:       ELSE IF( N.LT.0 ) THEN
        !           101:          INFO = -2
        !           102:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
        !           103:          INFO = -4
        !           104:       ELSE IF( ANORM.LT.ZERO ) THEN
        !           105:          INFO = -6
        !           106:       END IF
        !           107:       IF( INFO.NE.0 ) THEN
        !           108:          CALL XERBLA( 'ZHECON', -INFO )
        !           109:          RETURN
        !           110:       END IF
        !           111: *
        !           112: *     Quick return if possible
        !           113: *
        !           114:       RCOND = ZERO
        !           115:       IF( N.EQ.0 ) THEN
        !           116:          RCOND = ONE
        !           117:          RETURN
        !           118:       ELSE IF( ANORM.LE.ZERO ) THEN
        !           119:          RETURN
        !           120:       END IF
        !           121: *
        !           122: *     Check that the diagonal matrix D is nonsingular.
        !           123: *
        !           124:       IF( UPPER ) THEN
        !           125: *
        !           126: *        Upper triangular storage: examine D from bottom to top
        !           127: *
        !           128:          DO 10 I = N, 1, -1
        !           129:             IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
        !           130:      $         RETURN
        !           131:    10    CONTINUE
        !           132:       ELSE
        !           133: *
        !           134: *        Lower triangular storage: examine D from top to bottom.
        !           135: *
        !           136:          DO 20 I = 1, N
        !           137:             IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
        !           138:      $         RETURN
        !           139:    20    CONTINUE
        !           140:       END IF
        !           141: *
        !           142: *     Estimate the 1-norm of the inverse.
        !           143: *
        !           144:       KASE = 0
        !           145:    30 CONTINUE
        !           146:       CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
        !           147:       IF( KASE.NE.0 ) THEN
        !           148: *
        !           149: *        Multiply by inv(L*D*L') or inv(U*D*U').
        !           150: *
        !           151:          CALL ZHETRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
        !           152:          GO TO 30
        !           153:       END IF
        !           154: *
        !           155: *     Compute the estimate of the reciprocal condition number.
        !           156: *
        !           157:       IF( AINVNM.NE.ZERO )
        !           158:      $   RCOND = ( ONE / AINVNM ) / ANORM
        !           159: *
        !           160:       RETURN
        !           161: *
        !           162: *     End of ZHECON
        !           163: *
        !           164:       END