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Annotation of rpl/lapack/lapack/dgetc2.f, revision 1.1

1.1     ! bertrand    1:       SUBROUTINE DGETC2( N, A, LDA, IPIV, JPIV, INFO )
        !             2: *
        !             3: *  -- LAPACK auxiliary routine (version 3.2) --
        !             4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
        !             5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
        !             6: *     November 2006
        !             7: *
        !             8: *     .. Scalar Arguments ..
        !             9:       INTEGER            INFO, LDA, N
        !            10: *     ..
        !            11: *     .. Array Arguments ..
        !            12:       INTEGER            IPIV( * ), JPIV( * )
        !            13:       DOUBLE PRECISION   A( LDA, * )
        !            14: *     ..
        !            15: *
        !            16: *  Purpose
        !            17: *  =======
        !            18: *
        !            19: *  DGETC2 computes an LU factorization with complete pivoting of the
        !            20: *  n-by-n matrix A. The factorization has the form A = P * L * U * Q,
        !            21: *  where P and Q are permutation matrices, L is lower triangular with
        !            22: *  unit diagonal elements and U is upper triangular.
        !            23: *
        !            24: *  This is the Level 2 BLAS algorithm.
        !            25: *
        !            26: *  Arguments
        !            27: *  =========
        !            28: *
        !            29: *  N       (input) INTEGER
        !            30: *          The order of the matrix A. N >= 0.
        !            31: *
        !            32: *  A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)
        !            33: *          On entry, the n-by-n matrix A to be factored.
        !            34: *          On exit, the factors L and U from the factorization
        !            35: *          A = P*L*U*Q; the unit diagonal elements of L are not stored.
        !            36: *          If U(k, k) appears to be less than SMIN, U(k, k) is given the
        !            37: *          value of SMIN, i.e., giving a nonsingular perturbed system.
        !            38: *
        !            39: *  LDA     (input) INTEGER
        !            40: *          The leading dimension of the array A.  LDA >= max(1,N).
        !            41: *
        !            42: *  IPIV    (output) INTEGER array, dimension(N).
        !            43: *          The pivot indices; for 1 <= i <= N, row i of the
        !            44: *          matrix has been interchanged with row IPIV(i).
        !            45: *
        !            46: *  JPIV    (output) INTEGER array, dimension(N).
        !            47: *          The pivot indices; for 1 <= j <= N, column j of the
        !            48: *          matrix has been interchanged with column JPIV(j).
        !            49: *
        !            50: *  INFO    (output) INTEGER
        !            51: *           = 0: successful exit
        !            52: *           > 0: if INFO = k, U(k, k) is likely to produce owerflow if
        !            53: *                we try to solve for x in Ax = b. So U is perturbed to
        !            54: *                avoid the overflow.
        !            55: *
        !            56: *  Further Details
        !            57: *  ===============
        !            58: *
        !            59: *  Based on contributions by
        !            60: *     Bo Kagstrom and Peter Poromaa, Department of Computing Science,
        !            61: *     Umea University, S-901 87 Umea, Sweden.
        !            62: *
        !            63: *  =====================================================================
        !            64: *
        !            65: *     .. Parameters ..
        !            66:       DOUBLE PRECISION   ZERO, ONE
        !            67:       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
        !            68: *     ..
        !            69: *     .. Local Scalars ..
        !            70:       INTEGER            I, IP, IPV, J, JP, JPV
        !            71:       DOUBLE PRECISION   BIGNUM, EPS, SMIN, SMLNUM, XMAX
        !            72: *     ..
        !            73: *     .. External Subroutines ..
        !            74:       EXTERNAL           DGER, DSWAP
        !            75: *     ..
        !            76: *     .. External Functions ..
        !            77:       DOUBLE PRECISION   DLAMCH
        !            78:       EXTERNAL           DLAMCH
        !            79: *     ..
        !            80: *     .. Intrinsic Functions ..
        !            81:       INTRINSIC          ABS, MAX
        !            82: *     ..
        !            83: *     .. Executable Statements ..
        !            84: *
        !            85: *     Set constants to control overflow
        !            86: *
        !            87:       INFO = 0
        !            88:       EPS = DLAMCH( 'P' )
        !            89:       SMLNUM = DLAMCH( 'S' ) / EPS
        !            90:       BIGNUM = ONE / SMLNUM
        !            91:       CALL DLABAD( SMLNUM, BIGNUM )
        !            92: *
        !            93: *     Factorize A using complete pivoting.
        !            94: *     Set pivots less than SMIN to SMIN.
        !            95: *
        !            96:       DO 40 I = 1, N - 1
        !            97: *
        !            98: *        Find max element in matrix A
        !            99: *
        !           100:          XMAX = ZERO
        !           101:          DO 20 IP = I, N
        !           102:             DO 10 JP = I, N
        !           103:                IF( ABS( A( IP, JP ) ).GE.XMAX ) THEN
        !           104:                   XMAX = ABS( A( IP, JP ) )
        !           105:                   IPV = IP
        !           106:                   JPV = JP
        !           107:                END IF
        !           108:    10       CONTINUE
        !           109:    20    CONTINUE
        !           110:          IF( I.EQ.1 )
        !           111:      $      SMIN = MAX( EPS*XMAX, SMLNUM )
        !           112: *
        !           113: *        Swap rows
        !           114: *
        !           115:          IF( IPV.NE.I )
        !           116:      $      CALL DSWAP( N, A( IPV, 1 ), LDA, A( I, 1 ), LDA )
        !           117:          IPIV( I ) = IPV
        !           118: *
        !           119: *        Swap columns
        !           120: *
        !           121:          IF( JPV.NE.I )
        !           122:      $      CALL DSWAP( N, A( 1, JPV ), 1, A( 1, I ), 1 )
        !           123:          JPIV( I ) = JPV
        !           124: *
        !           125: *        Check for singularity
        !           126: *
        !           127:          IF( ABS( A( I, I ) ).LT.SMIN ) THEN
        !           128:             INFO = I
        !           129:             A( I, I ) = SMIN
        !           130:          END IF
        !           131:          DO 30 J = I + 1, N
        !           132:             A( J, I ) = A( J, I ) / A( I, I )
        !           133:    30    CONTINUE
        !           134:          CALL DGER( N-I, N-I, -ONE, A( I+1, I ), 1, A( I, I+1 ), LDA,
        !           135:      $              A( I+1, I+1 ), LDA )
        !           136:    40 CONTINUE
        !           137: *
        !           138:       IF( ABS( A( N, N ) ).LT.SMIN ) THEN
        !           139:          INFO = N
        !           140:          A( N, N ) = SMIN
        !           141:       END IF
        !           142: *
        !           143:       RETURN
        !           144: *
        !           145: *     End of DGETC2
        !           146: *
        !           147:       END