Annotation of rpl/lapack/lapack/dgetf2.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DGETF2
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DGETF2 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgetf2.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgetf2.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgetf2.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DGETF2( M, N, A, LDA, IPIV, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER INFO, LDA, M, N
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * INTEGER IPIV( * )
! 28: * DOUBLE PRECISION A( LDA, * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> DGETF2 computes an LU factorization of a general m-by-n matrix A
! 38: *> using partial pivoting with row interchanges.
! 39: *>
! 40: *> The factorization has the form
! 41: *> A = P * L * U
! 42: *> where P is a permutation matrix, L is lower triangular with unit
! 43: *> diagonal elements (lower trapezoidal if m > n), and U is upper
! 44: *> triangular (upper trapezoidal if m < n).
! 45: *>
! 46: *> This is the right-looking Level 2 BLAS version of the algorithm.
! 47: *> \endverbatim
! 48: *
! 49: * Arguments:
! 50: * ==========
! 51: *
! 52: *> \param[in] M
! 53: *> \verbatim
! 54: *> M is INTEGER
! 55: *> The number of rows of the matrix A. M >= 0.
! 56: *> \endverbatim
! 57: *>
! 58: *> \param[in] N
! 59: *> \verbatim
! 60: *> N is INTEGER
! 61: *> The number of columns of the matrix A. N >= 0.
! 62: *> \endverbatim
! 63: *>
! 64: *> \param[in,out] A
! 65: *> \verbatim
! 66: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 67: *> On entry, the m by n matrix to be factored.
! 68: *> On exit, the factors L and U from the factorization
! 69: *> A = P*L*U; the unit diagonal elements of L are not stored.
! 70: *> \endverbatim
! 71: *>
! 72: *> \param[in] LDA
! 73: *> \verbatim
! 74: *> LDA is INTEGER
! 75: *> The leading dimension of the array A. LDA >= max(1,M).
! 76: *> \endverbatim
! 77: *>
! 78: *> \param[out] IPIV
! 79: *> \verbatim
! 80: *> IPIV is INTEGER array, dimension (min(M,N))
! 81: *> The pivot indices; for 1 <= i <= min(M,N), row i of the
! 82: *> matrix was interchanged with row IPIV(i).
! 83: *> \endverbatim
! 84: *>
! 85: *> \param[out] INFO
! 86: *> \verbatim
! 87: *> INFO is INTEGER
! 88: *> = 0: successful exit
! 89: *> < 0: if INFO = -k, the k-th argument had an illegal value
! 90: *> > 0: if INFO = k, U(k,k) is exactly zero. The factorization
! 91: *> has been completed, but the factor U is exactly
! 92: *> singular, and division by zero will occur if it is used
! 93: *> to solve a system of equations.
! 94: *> \endverbatim
! 95: *
! 96: * Authors:
! 97: * ========
! 98: *
! 99: *> \author Univ. of Tennessee
! 100: *> \author Univ. of California Berkeley
! 101: *> \author Univ. of Colorado Denver
! 102: *> \author NAG Ltd.
! 103: *
! 104: *> \date November 2011
! 105: *
! 106: *> \ingroup doubleGEcomputational
! 107: *
! 108: * =====================================================================
1.1 bertrand 109: SUBROUTINE DGETF2( M, N, A, LDA, IPIV, INFO )
110: *
1.8 ! bertrand 111: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 112: * -- LAPACK is a software package provided by Univ. of Tennessee, --
113: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 114: * November 2011
1.1 bertrand 115: *
116: * .. Scalar Arguments ..
117: INTEGER INFO, LDA, M, N
118: * ..
119: * .. Array Arguments ..
120: INTEGER IPIV( * )
121: DOUBLE PRECISION A( LDA, * )
122: * ..
123: *
124: * =====================================================================
125: *
126: * .. Parameters ..
127: DOUBLE PRECISION ONE, ZERO
128: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
129: * ..
130: * .. Local Scalars ..
131: DOUBLE PRECISION SFMIN
132: INTEGER I, J, JP
133: * ..
134: * .. External Functions ..
135: DOUBLE PRECISION DLAMCH
136: INTEGER IDAMAX
137: EXTERNAL DLAMCH, IDAMAX
138: * ..
139: * .. External Subroutines ..
140: EXTERNAL DGER, DSCAL, DSWAP, XERBLA
141: * ..
142: * .. Intrinsic Functions ..
143: INTRINSIC MAX, MIN
144: * ..
145: * .. Executable Statements ..
146: *
147: * Test the input parameters.
148: *
149: INFO = 0
150: IF( M.LT.0 ) THEN
151: INFO = -1
152: ELSE IF( N.LT.0 ) THEN
153: INFO = -2
154: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
155: INFO = -4
156: END IF
157: IF( INFO.NE.0 ) THEN
158: CALL XERBLA( 'DGETF2', -INFO )
159: RETURN
160: END IF
161: *
162: * Quick return if possible
163: *
164: IF( M.EQ.0 .OR. N.EQ.0 )
165: $ RETURN
166: *
167: * Compute machine safe minimum
168: *
169: SFMIN = DLAMCH('S')
170: *
171: DO 10 J = 1, MIN( M, N )
172: *
173: * Find pivot and test for singularity.
174: *
175: JP = J - 1 + IDAMAX( M-J+1, A( J, J ), 1 )
176: IPIV( J ) = JP
177: IF( A( JP, J ).NE.ZERO ) THEN
178: *
179: * Apply the interchange to columns 1:N.
180: *
181: IF( JP.NE.J )
182: $ CALL DSWAP( N, A( J, 1 ), LDA, A( JP, 1 ), LDA )
183: *
184: * Compute elements J+1:M of J-th column.
185: *
186: IF( J.LT.M ) THEN
187: IF( ABS(A( J, J )) .GE. SFMIN ) THEN
188: CALL DSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 )
189: ELSE
190: DO 20 I = 1, M-J
191: A( J+I, J ) = A( J+I, J ) / A( J, J )
192: 20 CONTINUE
193: END IF
194: END IF
195: *
196: ELSE IF( INFO.EQ.0 ) THEN
197: *
198: INFO = J
199: END IF
200: *
201: IF( J.LT.MIN( M, N ) ) THEN
202: *
203: * Update trailing submatrix.
204: *
205: CALL DGER( M-J, N-J, -ONE, A( J+1, J ), 1, A( J, J+1 ), LDA,
206: $ A( J+1, J+1 ), LDA )
207: END IF
208: 10 CONTINUE
209: RETURN
210: *
211: * End of DGETF2
212: *
213: END
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