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Annotation of rpl/lapack/lapack/dgetf2.f, revision 1.7

1.1       bertrand    1:       SUBROUTINE DGETF2( 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:       DOUBLE PRECISION   A( LDA, * )
                     14: *     ..
                     15: *
                     16: *  Purpose
                     17: *  =======
                     18: *
                     19: *  DGETF2 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) DOUBLE PRECISION 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:       DOUBLE PRECISION   ONE, ZERO
                     63:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
                     64: *     ..
                     65: *     .. Local Scalars ..
                     66:       DOUBLE PRECISION   SFMIN 
                     67:       INTEGER            I, J, JP
                     68: *     ..
                     69: *     .. External Functions ..
                     70:       DOUBLE PRECISION   DLAMCH      
                     71:       INTEGER            IDAMAX
                     72:       EXTERNAL           DLAMCH, IDAMAX
                     73: *     ..
                     74: *     .. External Subroutines ..
                     75:       EXTERNAL           DGER, DSCAL, DSWAP, XERBLA
                     76: *     ..
                     77: *     .. Intrinsic Functions ..
                     78:       INTRINSIC          MAX, MIN
                     79: *     ..
                     80: *     .. Executable Statements ..
                     81: *
                     82: *     Test the input parameters.
                     83: *
                     84:       INFO = 0
                     85:       IF( M.LT.0 ) THEN
                     86:          INFO = -1
                     87:       ELSE IF( N.LT.0 ) THEN
                     88:          INFO = -2
                     89:       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
                     90:          INFO = -4
                     91:       END IF
                     92:       IF( INFO.NE.0 ) THEN
                     93:          CALL XERBLA( 'DGETF2', -INFO )
                     94:          RETURN
                     95:       END IF
                     96: *
                     97: *     Quick return if possible
                     98: *
                     99:       IF( M.EQ.0 .OR. N.EQ.0 )
                    100:      $   RETURN
                    101: *
                    102: *     Compute machine safe minimum 
                    103: * 
                    104:       SFMIN = DLAMCH('S')  
                    105: *
                    106:       DO 10 J = 1, MIN( M, N )
                    107: *
                    108: *        Find pivot and test for singularity.
                    109: *
                    110:          JP = J - 1 + IDAMAX( M-J+1, A( J, J ), 1 )
                    111:          IPIV( J ) = JP
                    112:          IF( A( JP, J ).NE.ZERO ) THEN
                    113: *
                    114: *           Apply the interchange to columns 1:N.
                    115: *
                    116:             IF( JP.NE.J )
                    117:      $         CALL DSWAP( N, A( J, 1 ), LDA, A( JP, 1 ), LDA )
                    118: *
                    119: *           Compute elements J+1:M of J-th column.
                    120: *
                    121:             IF( J.LT.M ) THEN 
                    122:                IF( ABS(A( J, J )) .GE. SFMIN ) THEN 
                    123:                   CALL DSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 ) 
                    124:                ELSE 
                    125:                  DO 20 I = 1, M-J 
                    126:                     A( J+I, J ) = A( J+I, J ) / A( J, J ) 
                    127:    20            CONTINUE 
                    128:                END IF 
                    129:             END IF 
                    130: *
                    131:          ELSE IF( INFO.EQ.0 ) THEN
                    132: *
                    133:             INFO = J
                    134:          END IF
                    135: *
                    136:          IF( J.LT.MIN( M, N ) ) THEN
                    137: *
                    138: *           Update trailing submatrix.
                    139: *
                    140:             CALL DGER( M-J, N-J, -ONE, A( J+1, J ), 1, A( J, J+1 ), LDA,
                    141:      $                 A( J+1, J+1 ), LDA )
                    142:          END IF
                    143:    10 CONTINUE
                    144:       RETURN
                    145: *
                    146: *     End of DGETF2
                    147: *
                    148:       END