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Annotation of rpl/lapack/lapack/zgetc2.f, revision 1.4

1.1       bertrand    1:       SUBROUTINE ZGETC2( 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:       COMPLEX*16         A( LDA, * )
                     14: *     ..
                     15: *
                     16: *  Purpose
                     17: *  =======
                     18: *
                     19: *  ZGETC2 computes an LU factorization, using 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 a level 1 BLAS version of the algorithm.
                     25: *
                     26: *  Arguments
                     27: *  =========
                     28: *
                     29: *  N       (input) INTEGER
                     30: *          The order of the matrix A. N >= 0.
                     31: *
                     32: *  A       (input/output) COMPLEX*16 array, dimension (LDA, N)
                     33: *          On entry, the n-by-n matrix 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, 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 overflow if
                     53: *                one tries to solve for x in Ax = b. So U is perturbed
                     54: *                to 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           ZGERU, ZSWAP
                     75: *     ..
                     76: *     .. External Functions ..
                     77:       DOUBLE PRECISION   DLAMCH
                     78:       EXTERNAL           DLAMCH
                     79: *     ..
                     80: *     .. Intrinsic Functions ..
                     81:       INTRINSIC          ABS, DCMPLX, 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 ZSWAP( 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 ZSWAP( 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 ) = DCMPLX( SMIN, ZERO )
                    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 ZGERU( N-I, N-I, -DCMPLX( ONE ), A( I+1, I ), 1,
                    135:      $               A( I, I+1 ), LDA, 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 ) = DCMPLX( SMIN, ZERO )
                    141:       END IF
                    142:       RETURN
                    143: *
                    144: *     End of ZGETC2
                    145: *
                    146:       END