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Annotation of rpl/lapack/lapack/zgetf2.f, revision 1.1.1.1

1.1       bertrand    1:       SUBROUTINE ZGETF2( M, N, A, LDA, IPIV, INFO )
                      2: *
                      3: *  -- LAPACK 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, M, N
                     10: *     ..
                     11: *     .. Array Arguments ..
                     12:       INTEGER            IPIV( * )
                     13:       COMPLEX*16         A( LDA, * )
                     14: *     ..
                     15: *
                     16: *  Purpose
                     17: *  =======
                     18: *
                     19: *  ZGETF2 computes an LU factorization of a general m-by-n matrix A
                     20: *  using partial pivoting with row interchanges.
                     21: *
                     22: *  The factorization has the form
                     23: *     A = P * L * U
                     24: *  where P is a permutation matrix, L is lower triangular with unit
                     25: *  diagonal elements (lower trapezoidal if m > n), and U is upper
                     26: *  triangular (upper trapezoidal if m < n).
                     27: *
                     28: *  This is the right-looking Level 2 BLAS version of the algorithm.
                     29: *
                     30: *  Arguments
                     31: *  =========
                     32: *
                     33: *  M       (input) INTEGER
                     34: *          The number of rows of the matrix A.  M >= 0.
                     35: *
                     36: *  N       (input) INTEGER
                     37: *          The number of columns of the matrix A.  N >= 0.
                     38: *
                     39: *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
                     40: *          On entry, the m by n matrix to be factored.
                     41: *          On exit, the factors L and U from the factorization
                     42: *          A = P*L*U; the unit diagonal elements of L are not stored.
                     43: *
                     44: *  LDA     (input) INTEGER
                     45: *          The leading dimension of the array A.  LDA >= max(1,M).
                     46: *
                     47: *  IPIV    (output) INTEGER array, dimension (min(M,N))
                     48: *          The pivot indices; for 1 <= i <= min(M,N), row i of the
                     49: *          matrix was interchanged with row IPIV(i).
                     50: *
                     51: *  INFO    (output) INTEGER
                     52: *          = 0: successful exit
                     53: *          < 0: if INFO = -k, the k-th argument had an illegal value
                     54: *          > 0: if INFO = k, U(k,k) is exactly zero. The factorization
                     55: *               has been completed, but the factor U is exactly
                     56: *               singular, and division by zero will occur if it is used
                     57: *               to solve a system of equations.
                     58: *
                     59: *  =====================================================================
                     60: *
                     61: *     .. Parameters ..
                     62:       COMPLEX*16         ONE, ZERO
                     63:       PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ),
                     64:      $                   ZERO = ( 0.0D+0, 0.0D+0 ) )
                     65: *     ..
                     66: *     .. Local Scalars ..
                     67:       DOUBLE PRECISION   SFMIN
                     68:       INTEGER            I, J, JP
                     69: *     ..
                     70: *     .. External Functions ..
                     71:       DOUBLE PRECISION   DLAMCH
                     72:       INTEGER            IZAMAX
                     73:       EXTERNAL           DLAMCH, IZAMAX
                     74: *     ..
                     75: *     .. External Subroutines ..
                     76:       EXTERNAL           XERBLA, ZGERU, ZSCAL, ZSWAP
                     77: *     ..
                     78: *     .. Intrinsic Functions ..
                     79:       INTRINSIC          MAX, MIN
                     80: *     ..
                     81: *     .. Executable Statements ..
                     82: *
                     83: *     Test the input parameters.
                     84: *
                     85:       INFO = 0
                     86:       IF( M.LT.0 ) THEN
                     87:          INFO = -1
                     88:       ELSE IF( N.LT.0 ) THEN
                     89:          INFO = -2
                     90:       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
                     91:          INFO = -4
                     92:       END IF
                     93:       IF( INFO.NE.0 ) THEN
                     94:          CALL XERBLA( 'ZGETF2', -INFO )
                     95:          RETURN
                     96:       END IF
                     97: *
                     98: *     Quick return if possible
                     99: *
                    100:       IF( M.EQ.0 .OR. N.EQ.0 )
                    101:      $   RETURN
                    102: *
                    103: *     Compute machine safe minimum
                    104: *
                    105:       SFMIN = DLAMCH('S') 
                    106: *
                    107:       DO 10 J = 1, MIN( M, N )
                    108: *
                    109: *        Find pivot and test for singularity.
                    110: *
                    111:          JP = J - 1 + IZAMAX( M-J+1, A( J, J ), 1 )
                    112:          IPIV( J ) = JP
                    113:          IF( A( JP, J ).NE.ZERO ) THEN
                    114: *
                    115: *           Apply the interchange to columns 1:N.
                    116: *
                    117:             IF( JP.NE.J )
                    118:      $         CALL ZSWAP( N, A( J, 1 ), LDA, A( JP, 1 ), LDA )
                    119: *
                    120: *           Compute elements J+1:M of J-th column.
                    121: *
                    122:             IF( J.LT.M ) THEN
                    123:                IF( ABS(A( J, J )) .GE. SFMIN ) THEN
                    124:                   CALL ZSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 )
                    125:                ELSE
                    126:                   DO 20 I = 1, M-J
                    127:                      A( J+I, J ) = A( J+I, J ) / A( J, J )
                    128:    20             CONTINUE
                    129:                END IF
                    130:             END IF
                    131: *
                    132:          ELSE IF( INFO.EQ.0 ) THEN
                    133: *
                    134:             INFO = J
                    135:          END IF
                    136: *
                    137:          IF( J.LT.MIN( M, N ) ) THEN
                    138: *
                    139: *           Update trailing submatrix.
                    140: *
                    141:             CALL ZGERU( M-J, N-J, -ONE, A( J+1, J ), 1, A( J, J+1 ),
                    142:      $                  LDA, A( J+1, J+1 ), LDA )
                    143:          END IF
                    144:    10 CONTINUE
                    145:       RETURN
                    146: *
                    147: *     End of ZGETF2
                    148: *
                    149:       END