LAPACK 3.3.1 Linear Algebra PACKage

dgetf2.f

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```00001       SUBROUTINE DGETF2( M, N, A, LDA, IPIV, INFO )
00002 *
00003 *  -- LAPACK routine (version 3.2) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       INTEGER            INFO, LDA, M, N
00010 *     ..
00011 *     .. Array Arguments ..
00012       INTEGER            IPIV( * )
00013       DOUBLE PRECISION   A( LDA, * )
00014 *     ..
00015 *
00016 *  Purpose
00017 *  =======
00018 *
00019 *  DGETF2 computes an LU factorization of a general m-by-n matrix A
00020 *  using partial pivoting with row interchanges.
00021 *
00022 *  The factorization has the form
00023 *     A = P * L * U
00024 *  where P is a permutation matrix, L is lower triangular with unit
00025 *  diagonal elements (lower trapezoidal if m > n), and U is upper
00026 *  triangular (upper trapezoidal if m < n).
00027 *
00028 *  This is the right-looking Level 2 BLAS version of the algorithm.
00029 *
00030 *  Arguments
00031 *  =========
00032 *
00033 *  M       (input) INTEGER
00034 *          The number of rows of the matrix A.  M >= 0.
00035 *
00036 *  N       (input) INTEGER
00037 *          The number of columns of the matrix A.  N >= 0.
00038 *
00039 *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
00040 *          On entry, the m by n matrix to be factored.
00041 *          On exit, the factors L and U from the factorization
00042 *          A = P*L*U; the unit diagonal elements of L are not stored.
00043 *
00044 *  LDA     (input) INTEGER
00045 *          The leading dimension of the array A.  LDA >= max(1,M).
00046 *
00047 *  IPIV    (output) INTEGER array, dimension (min(M,N))
00048 *          The pivot indices; for 1 <= i <= min(M,N), row i of the
00049 *          matrix was interchanged with row IPIV(i).
00050 *
00051 *  INFO    (output) INTEGER
00052 *          = 0: successful exit
00053 *          < 0: if INFO = -k, the k-th argument had an illegal value
00054 *          > 0: if INFO = k, U(k,k) is exactly zero. The factorization
00055 *               has been completed, but the factor U is exactly
00056 *               singular, and division by zero will occur if it is used
00057 *               to solve a system of equations.
00058 *
00059 *  =====================================================================
00060 *
00061 *     .. Parameters ..
00062       DOUBLE PRECISION   ONE, ZERO
00063       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
00064 *     ..
00065 *     .. Local Scalars ..
00066       DOUBLE PRECISION   SFMIN
00067       INTEGER            I, J, JP
00068 *     ..
00069 *     .. External Functions ..
00070       DOUBLE PRECISION   DLAMCH
00071       INTEGER            IDAMAX
00072       EXTERNAL           DLAMCH, IDAMAX
00073 *     ..
00074 *     .. External Subroutines ..
00075       EXTERNAL           DGER, DSCAL, DSWAP, XERBLA
00076 *     ..
00077 *     .. Intrinsic Functions ..
00078       INTRINSIC          MAX, MIN
00079 *     ..
00080 *     .. Executable Statements ..
00081 *
00082 *     Test the input parameters.
00083 *
00084       INFO = 0
00085       IF( M.LT.0 ) THEN
00086          INFO = -1
00087       ELSE IF( N.LT.0 ) THEN
00088          INFO = -2
00089       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
00090          INFO = -4
00091       END IF
00092       IF( INFO.NE.0 ) THEN
00093          CALL XERBLA( 'DGETF2', -INFO )
00094          RETURN
00095       END IF
00096 *
00097 *     Quick return if possible
00098 *
00099       IF( M.EQ.0 .OR. N.EQ.0 )
00100      \$   RETURN
00101 *
00102 *     Compute machine safe minimum
00103 *
00104       SFMIN = DLAMCH('S')
00105 *
00106       DO 10 J = 1, MIN( M, N )
00107 *
00108 *        Find pivot and test for singularity.
00109 *
00110          JP = J - 1 + IDAMAX( M-J+1, A( J, J ), 1 )
00111          IPIV( J ) = JP
00112          IF( A( JP, J ).NE.ZERO ) THEN
00113 *
00114 *           Apply the interchange to columns 1:N.
00115 *
00116             IF( JP.NE.J )
00117      \$         CALL DSWAP( N, A( J, 1 ), LDA, A( JP, 1 ), LDA )
00118 *
00119 *           Compute elements J+1:M of J-th column.
00120 *
00121             IF( J.LT.M ) THEN
00122                IF( ABS(A( J, J )) .GE. SFMIN ) THEN
00123                   CALL DSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 )
00124                ELSE
00125                  DO 20 I = 1, M-J
00126                     A( J+I, J ) = A( J+I, J ) / A( J, J )
00127    20            CONTINUE
00128                END IF
00129             END IF
00130 *
00131          ELSE IF( INFO.EQ.0 ) THEN
00132 *
00133             INFO = J
00134          END IF
00135 *
00136          IF( J.LT.MIN( M, N ) ) THEN
00137 *
00138 *           Update trailing submatrix.
00139 *
00140             CALL DGER( M-J, N-J, -ONE, A( J+1, J ), 1, A( J, J+1 ), LDA,
00141      \$                 A( J+1, J+1 ), LDA )
00142          END IF
00143    10 CONTINUE
00144       RETURN
00145 *
00146 *     End of DGETF2
00147 *
00148       END
```