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

1.1     ! bertrand    1:       SUBROUTINE DSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK,
        !             2:      $                   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          UPLO
        !            13:       INTEGER            INFO, LDA, N
        !            14:       DOUBLE PRECISION   ANORM, RCOND
        !            15: *     ..
        !            16: *     .. Array Arguments ..
        !            17:       INTEGER            IPIV( * ), IWORK( * )
        !            18:       DOUBLE PRECISION   A( LDA, * ), WORK( * )
        !            19: *     ..
        !            20: *
        !            21: *  Purpose
        !            22: *  =======
        !            23: *
        !            24: *  DSYCON estimates the reciprocal of the condition number (in the
        !            25: *  1-norm) of a real symmetric matrix A using the factorization
        !            26: *  A = U*D*U**T or A = L*D*L**T computed by DSYTRF.
        !            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**T;
        !            38: *          = 'L':  Lower triangular, form is A = L*D*L**T.
        !            39: *
        !            40: *  N       (input) INTEGER
        !            41: *          The order of the matrix A.  N >= 0.
        !            42: *
        !            43: *  A       (input) DOUBLE PRECISION 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 DSYTRF.
        !            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 DSYTRF.
        !            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) DOUBLE PRECISION array, dimension (2*N)
        !            63: *
        !            64: *  IWORK    (workspace) INTEGER array, dimension (N)
        !            65: *
        !            66: *  INFO    (output) INTEGER
        !            67: *          = 0:  successful exit
        !            68: *          < 0:  if INFO = -i, the i-th argument had an illegal value
        !            69: *
        !            70: *  =====================================================================
        !            71: *
        !            72: *     .. Parameters ..
        !            73:       DOUBLE PRECISION   ONE, ZERO
        !            74:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
        !            75: *     ..
        !            76: *     .. Local Scalars ..
        !            77:       LOGICAL            UPPER
        !            78:       INTEGER            I, KASE
        !            79:       DOUBLE PRECISION   AINVNM
        !            80: *     ..
        !            81: *     .. Local Arrays ..
        !            82:       INTEGER            ISAVE( 3 )
        !            83: *     ..
        !            84: *     .. External Functions ..
        !            85:       LOGICAL            LSAME
        !            86:       EXTERNAL           LSAME
        !            87: *     ..
        !            88: *     .. External Subroutines ..
        !            89:       EXTERNAL           DLACN2, DSYTRS, XERBLA
        !            90: *     ..
        !            91: *     .. Intrinsic Functions ..
        !            92:       INTRINSIC          MAX
        !            93: *     ..
        !            94: *     .. Executable Statements ..
        !            95: *
        !            96: *     Test the input parameters.
        !            97: *
        !            98:       INFO = 0
        !            99:       UPPER = LSAME( UPLO, 'U' )
        !           100:       IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
        !           101:          INFO = -1
        !           102:       ELSE IF( N.LT.0 ) THEN
        !           103:          INFO = -2
        !           104:       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
        !           105:          INFO = -4
        !           106:       ELSE IF( ANORM.LT.ZERO ) THEN
        !           107:          INFO = -6
        !           108:       END IF
        !           109:       IF( INFO.NE.0 ) THEN
        !           110:          CALL XERBLA( 'DSYCON', -INFO )
        !           111:          RETURN
        !           112:       END IF
        !           113: *
        !           114: *     Quick return if possible
        !           115: *
        !           116:       RCOND = ZERO
        !           117:       IF( N.EQ.0 ) THEN
        !           118:          RCOND = ONE
        !           119:          RETURN
        !           120:       ELSE IF( ANORM.LE.ZERO ) THEN
        !           121:          RETURN
        !           122:       END IF
        !           123: *
        !           124: *     Check that the diagonal matrix D is nonsingular.
        !           125: *
        !           126:       IF( UPPER ) THEN
        !           127: *
        !           128: *        Upper triangular storage: examine D from bottom to top
        !           129: *
        !           130:          DO 10 I = N, 1, -1
        !           131:             IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
        !           132:      $         RETURN
        !           133:    10    CONTINUE
        !           134:       ELSE
        !           135: *
        !           136: *        Lower triangular storage: examine D from top to bottom.
        !           137: *
        !           138:          DO 20 I = 1, N
        !           139:             IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.ZERO )
        !           140:      $         RETURN
        !           141:    20    CONTINUE
        !           142:       END IF
        !           143: *
        !           144: *     Estimate the 1-norm of the inverse.
        !           145: *
        !           146:       KASE = 0
        !           147:    30 CONTINUE
        !           148:       CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
        !           149:       IF( KASE.NE.0 ) THEN
        !           150: *
        !           151: *        Multiply by inv(L*D*L') or inv(U*D*U').
        !           152: *
        !           153:          CALL DSYTRS( UPLO, N, 1, A, LDA, IPIV, WORK, N, INFO )
        !           154:          GO TO 30
        !           155:       END IF
        !           156: *
        !           157: *     Compute the estimate of the reciprocal condition number.
        !           158: *
        !           159:       IF( AINVNM.NE.ZERO )
        !           160:      $   RCOND = ( ONE / AINVNM ) / ANORM
        !           161: *
        !           162:       RETURN
        !           163: *
        !           164: *     End of DSYCON
        !           165: *
        !           166:       END