135 lines
3.7 KiB
Fortran
135 lines
3.7 KiB
Fortran
SUBROUTINE SGETF2F( M, N, A, LDA, IPIV, INFO )
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*
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* -- LAPACK routine (version 3.0) --
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* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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* Courant Institute, Argonne National Lab, and Rice University
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* June 30, 1992
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*
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* .. Scalar Arguments ..
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INTEGER INFO, LDA, M, N
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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REAL A( LDA, * )
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* ..
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*
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* Purpose
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* =======
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*
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* SGETF2 computes an LU factorization of a general m-by-n matrix A
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* using partial pivoting with row interchanges.
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*
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* The factorization has the form
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* A = P * L * U
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* where P is a permutation matrix, L is lower triangular with unit
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* diagonal elements (lower trapezoidal if m > n), and U is upper
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* triangular (upper trapezoidal if m < n).
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*
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* This is the right-looking Level 2 BLAS version of the algorithm.
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*
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* Arguments
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* =========
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*
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* M (input) INTEGER
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* The number of rows of the matrix A. M >= 0.
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*
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* N (input) INTEGER
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* The number of columns of the matrix A. N >= 0.
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*
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* A (input/output) REAL array, dimension (LDA,N)
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* On entry, the m by n matrix to be factored.
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* On exit, the factors L and U from the factorization
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* A = P*L*U; the unit diagonal elements of L are not stored.
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A. LDA >= max(1,M).
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*
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* IPIV (output) INTEGER array, dimension (min(M,N))
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* The pivot indices; for 1 <= i <= min(M,N), row i of the
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* matrix was interchanged with row IPIV(i).
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -k, the k-th argument had an illegal value
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* > 0: if INFO = k, U(k,k) is exactly zero. The factorization
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* has been completed, but the factor U is exactly
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* singular, and division by zero will occur if it is used
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* to solve a system of equations.
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ONE, ZERO
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PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER J, JP
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* ..
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* .. External Functions ..
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INTEGER ISAMAX
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EXTERNAL ISAMAX
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* ..
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* .. External Subroutines ..
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EXTERNAL SGER, SSCAL, SSWAP, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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IF( M.LT.0 ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -4
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SGETF2', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( M.EQ.0 .OR. N.EQ.0 )
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$ RETURN
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*
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DO 10 J = 1, MIN( M, N )
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*
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* Find pivot and test for singularity.
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*
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JP = J - 1 + ISAMAX( M-J+1, A( J, J ), 1 )
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IPIV( J ) = JP
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IF( A( JP, J ).NE.ZERO ) THEN
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*
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* Apply the interchange to columns 1:N.
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*
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IF( JP.NE.J )
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$ CALL SSWAP( N, A( J, 1 ), LDA, A( JP, 1 ), LDA )
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*
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* Compute elements J+1:M of J-th column.
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*
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IF( J.LT.M )
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$ CALL SSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 )
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*
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ELSE IF( INFO.EQ.0 ) THEN
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*
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INFO = J
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END IF
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*
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IF( J.LT.MIN( M, N ) ) THEN
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*
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* Update trailing submatrix.
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*
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CALL SGER( M-J, N-J, -ONE, A( J+1, J ), 1, A( J, J+1 ), LDA,
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$ A( J+1, J+1 ), LDA )
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END IF
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10 CONTINUE
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RETURN
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*
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* End of SGETF2
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*
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END
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