LAPACK 3.3.0

cgetf2.f

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00001       SUBROUTINE CGETF2( 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       COMPLEX            A( LDA, * )
00014 *     ..
00015 *
00016 *  Purpose
00017 *  =======
00018 *
00019 *  CGETF2 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) COMPLEX 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       COMPLEX            ONE, ZERO
00063       PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ),
00064      $                   ZERO = ( 0.0E+0, 0.0E+0 ) )
00065 *     ..
00066 *     .. Local Scalars ..
00067       REAL               SFMIN
00068       INTEGER            I, J, JP
00069 *     ..
00070 *     .. External Functions ..
00071       REAL               SLAMCH
00072       INTEGER            ICAMAX
00073       EXTERNAL           SLAMCH, ICAMAX
00074 *     ..
00075 *     .. External Subroutines ..
00076       EXTERNAL           CGERU, CSCAL, CSWAP, XERBLA
00077 *     ..
00078 *     .. Intrinsic Functions ..
00079       INTRINSIC          MAX, MIN
00080 *     ..
00081 *     .. Executable Statements ..
00082 *
00083 *     Test the input parameters.
00084 *
00085       INFO = 0
00086       IF( M.LT.0 ) THEN
00087          INFO = -1
00088       ELSE IF( N.LT.0 ) THEN
00089          INFO = -2
00090       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
00091          INFO = -4
00092       END IF
00093       IF( INFO.NE.0 ) THEN
00094          CALL XERBLA( 'CGETF2', -INFO )
00095          RETURN
00096       END IF
00097 *
00098 *     Quick return if possible
00099 *
00100       IF( M.EQ.0 .OR. N.EQ.0 )
00101      $   RETURN
00102 *
00103 *     Compute machine safe minimum
00104 *
00105       SFMIN = SLAMCH('S') 
00106 *
00107       DO 10 J = 1, MIN( M, N )
00108 *
00109 *        Find pivot and test for singularity.
00110 *
00111          JP = J - 1 + ICAMAX( M-J+1, A( J, J ), 1 )
00112          IPIV( J ) = JP
00113          IF( A( JP, J ).NE.ZERO ) THEN
00114 *
00115 *           Apply the interchange to columns 1:N.
00116 *
00117             IF( JP.NE.J )
00118      $         CALL CSWAP( N, A( J, 1 ), LDA, A( JP, 1 ), LDA )
00119 *
00120 *           Compute elements J+1:M of J-th column.
00121 *
00122             IF( J.LT.M ) THEN
00123                IF( ABS(A( J, J )) .GE. SFMIN ) THEN
00124                   CALL CSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 )
00125                ELSE
00126                   DO 20 I = 1, M-J
00127                      A( J+I, J ) = A( J+I, J ) / A( J, J )
00128    20             CONTINUE
00129                END IF
00130             END IF
00131 *
00132          ELSE IF( INFO.EQ.0 ) THEN
00133 *
00134             INFO = J
00135          END IF
00136 *
00137          IF( J.LT.MIN( M, N ) ) THEN
00138 *
00139 *           Update trailing submatrix.
00140 *
00141             CALL CGERU( M-J, N-J, -ONE, A( J+1, J ), 1, A( J, J+1 ),
00142      $                  LDA, A( J+1, J+1 ), LDA )
00143          END IF
00144    10 CONTINUE
00145       RETURN
00146 *
00147 *     End of CGETF2
00148 *
00149       END
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