Annotation of rpl/lapack/lapack/dgetrf.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DGETRF
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DGETRF + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgetrf.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgetrf.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgetrf.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DGETRF( 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: *> DGETRF 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 3 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 = -i, the i-th argument had an illegal value
! 90: *> > 0: if INFO = i, U(i,i) 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 DGETRF( 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
128: PARAMETER ( ONE = 1.0D+0 )
129: * ..
130: * .. Local Scalars ..
131: INTEGER I, IINFO, J, JB, NB
132: * ..
133: * .. External Subroutines ..
134: EXTERNAL DGEMM, DGETF2, DLASWP, DTRSM, XERBLA
135: * ..
136: * .. External Functions ..
137: INTEGER ILAENV
138: EXTERNAL ILAENV
139: * ..
140: * .. Intrinsic Functions ..
141: INTRINSIC MAX, MIN
142: * ..
143: * .. Executable Statements ..
144: *
145: * Test the input parameters.
146: *
147: INFO = 0
148: IF( M.LT.0 ) THEN
149: INFO = -1
150: ELSE IF( N.LT.0 ) THEN
151: INFO = -2
152: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
153: INFO = -4
154: END IF
155: IF( INFO.NE.0 ) THEN
156: CALL XERBLA( 'DGETRF', -INFO )
157: RETURN
158: END IF
159: *
160: * Quick return if possible
161: *
162: IF( M.EQ.0 .OR. N.EQ.0 )
163: $ RETURN
164: *
165: * Determine the block size for this environment.
166: *
167: NB = ILAENV( 1, 'DGETRF', ' ', M, N, -1, -1 )
168: IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN
169: *
170: * Use unblocked code.
171: *
172: CALL DGETF2( M, N, A, LDA, IPIV, INFO )
173: ELSE
174: *
175: * Use blocked code.
176: *
177: DO 20 J = 1, MIN( M, N ), NB
178: JB = MIN( MIN( M, N )-J+1, NB )
179: *
180: * Factor diagonal and subdiagonal blocks and test for exact
181: * singularity.
182: *
183: CALL DGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO )
184: *
185: * Adjust INFO and the pivot indices.
186: *
187: IF( INFO.EQ.0 .AND. IINFO.GT.0 )
188: $ INFO = IINFO + J - 1
189: DO 10 I = J, MIN( M, J+JB-1 )
190: IPIV( I ) = J - 1 + IPIV( I )
191: 10 CONTINUE
192: *
193: * Apply interchanges to columns 1:J-1.
194: *
195: CALL DLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 )
196: *
197: IF( J+JB.LE.N ) THEN
198: *
199: * Apply interchanges to columns J+JB:N.
200: *
201: CALL DLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1,
202: $ IPIV, 1 )
203: *
204: * Compute block row of U.
205: *
206: CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB,
207: $ N-J-JB+1, ONE, A( J, J ), LDA, A( J, J+JB ),
208: $ LDA )
209: IF( J+JB.LE.M ) THEN
210: *
211: * Update trailing submatrix.
212: *
213: CALL DGEMM( 'No transpose', 'No transpose', M-J-JB+1,
214: $ N-J-JB+1, JB, -ONE, A( J+JB, J ), LDA,
215: $ A( J, J+JB ), LDA, ONE, A( J+JB, J+JB ),
216: $ LDA )
217: END IF
218: END IF
219: 20 CONTINUE
220: END IF
221: RETURN
222: *
223: * End of DGETRF
224: *
225: END
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