Annotation of rpl/lapack/lapack/dgetri.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DGETRI
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DGETRI + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgetri.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgetri.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgetri.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER INFO, LDA, LWORK, N
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * INTEGER IPIV( * )
! 28: * DOUBLE PRECISION A( LDA, * ), WORK( * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> DGETRI computes the inverse of a matrix using the LU factorization
! 38: *> computed by DGETRF.
! 39: *>
! 40: *> This method inverts U and then computes inv(A) by solving the system
! 41: *> inv(A)*L = inv(U) for inv(A).
! 42: *> \endverbatim
! 43: *
! 44: * Arguments:
! 45: * ==========
! 46: *
! 47: *> \param[in] N
! 48: *> \verbatim
! 49: *> N is INTEGER
! 50: *> The order of the matrix A. N >= 0.
! 51: *> \endverbatim
! 52: *>
! 53: *> \param[in,out] A
! 54: *> \verbatim
! 55: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 56: *> On entry, the factors L and U from the factorization
! 57: *> A = P*L*U as computed by DGETRF.
! 58: *> On exit, if INFO = 0, the inverse of the original matrix A.
! 59: *> \endverbatim
! 60: *>
! 61: *> \param[in] LDA
! 62: *> \verbatim
! 63: *> LDA is INTEGER
! 64: *> The leading dimension of the array A. LDA >= max(1,N).
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[in] IPIV
! 68: *> \verbatim
! 69: *> IPIV is INTEGER array, dimension (N)
! 70: *> The pivot indices from DGETRF; for 1<=i<=N, row i of the
! 71: *> matrix was interchanged with row IPIV(i).
! 72: *> \endverbatim
! 73: *>
! 74: *> \param[out] WORK
! 75: *> \verbatim
! 76: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 77: *> On exit, if INFO=0, then WORK(1) returns the optimal LWORK.
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[in] LWORK
! 81: *> \verbatim
! 82: *> LWORK is INTEGER
! 83: *> The dimension of the array WORK. LWORK >= max(1,N).
! 84: *> For optimal performance LWORK >= N*NB, where NB is
! 85: *> the optimal blocksize returned by ILAENV.
! 86: *>
! 87: *> If LWORK = -1, then a workspace query is assumed; the routine
! 88: *> only calculates the optimal size of the WORK array, returns
! 89: *> this value as the first entry of the WORK array, and no error
! 90: *> message related to LWORK is issued by XERBLA.
! 91: *> \endverbatim
! 92: *>
! 93: *> \param[out] INFO
! 94: *> \verbatim
! 95: *> INFO is INTEGER
! 96: *> = 0: successful exit
! 97: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 98: *> > 0: if INFO = i, U(i,i) is exactly zero; the matrix is
! 99: *> singular and its inverse could not be computed.
! 100: *> \endverbatim
! 101: *
! 102: * Authors:
! 103: * ========
! 104: *
! 105: *> \author Univ. of Tennessee
! 106: *> \author Univ. of California Berkeley
! 107: *> \author Univ. of Colorado Denver
! 108: *> \author NAG Ltd.
! 109: *
! 110: *> \date November 2011
! 111: *
! 112: *> \ingroup doubleGEcomputational
! 113: *
! 114: * =====================================================================
1.1 bertrand 115: SUBROUTINE DGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
116: *
1.8 ! bertrand 117: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 118: * -- LAPACK is a software package provided by Univ. of Tennessee, --
119: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 120: * November 2011
1.1 bertrand 121: *
122: * .. Scalar Arguments ..
123: INTEGER INFO, LDA, LWORK, N
124: * ..
125: * .. Array Arguments ..
126: INTEGER IPIV( * )
127: DOUBLE PRECISION A( LDA, * ), WORK( * )
128: * ..
129: *
130: * =====================================================================
131: *
132: * .. Parameters ..
133: DOUBLE PRECISION ZERO, ONE
134: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
135: * ..
136: * .. Local Scalars ..
137: LOGICAL LQUERY
138: INTEGER I, IWS, J, JB, JJ, JP, LDWORK, LWKOPT, NB,
139: $ NBMIN, NN
140: * ..
141: * .. External Functions ..
142: INTEGER ILAENV
143: EXTERNAL ILAENV
144: * ..
145: * .. External Subroutines ..
146: EXTERNAL DGEMM, DGEMV, DSWAP, DTRSM, DTRTRI, XERBLA
147: * ..
148: * .. Intrinsic Functions ..
149: INTRINSIC MAX, MIN
150: * ..
151: * .. Executable Statements ..
152: *
153: * Test the input parameters.
154: *
155: INFO = 0
156: NB = ILAENV( 1, 'DGETRI', ' ', N, -1, -1, -1 )
157: LWKOPT = N*NB
158: WORK( 1 ) = LWKOPT
159: LQUERY = ( LWORK.EQ.-1 )
160: IF( N.LT.0 ) THEN
161: INFO = -1
162: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
163: INFO = -3
164: ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
165: INFO = -6
166: END IF
167: IF( INFO.NE.0 ) THEN
168: CALL XERBLA( 'DGETRI', -INFO )
169: RETURN
170: ELSE IF( LQUERY ) THEN
171: RETURN
172: END IF
173: *
174: * Quick return if possible
175: *
176: IF( N.EQ.0 )
177: $ RETURN
178: *
179: * Form inv(U). If INFO > 0 from DTRTRI, then U is singular,
180: * and the inverse is not computed.
181: *
182: CALL DTRTRI( 'Upper', 'Non-unit', N, A, LDA, INFO )
183: IF( INFO.GT.0 )
184: $ RETURN
185: *
186: NBMIN = 2
187: LDWORK = N
188: IF( NB.GT.1 .AND. NB.LT.N ) THEN
189: IWS = MAX( LDWORK*NB, 1 )
190: IF( LWORK.LT.IWS ) THEN
191: NB = LWORK / LDWORK
192: NBMIN = MAX( 2, ILAENV( 2, 'DGETRI', ' ', N, -1, -1, -1 ) )
193: END IF
194: ELSE
195: IWS = N
196: END IF
197: *
198: * Solve the equation inv(A)*L = inv(U) for inv(A).
199: *
200: IF( NB.LT.NBMIN .OR. NB.GE.N ) THEN
201: *
202: * Use unblocked code.
203: *
204: DO 20 J = N, 1, -1
205: *
206: * Copy current column of L to WORK and replace with zeros.
207: *
208: DO 10 I = J + 1, N
209: WORK( I ) = A( I, J )
210: A( I, J ) = ZERO
211: 10 CONTINUE
212: *
213: * Compute current column of inv(A).
214: *
215: IF( J.LT.N )
216: $ CALL DGEMV( 'No transpose', N, N-J, -ONE, A( 1, J+1 ),
217: $ LDA, WORK( J+1 ), 1, ONE, A( 1, J ), 1 )
218: 20 CONTINUE
219: ELSE
220: *
221: * Use blocked code.
222: *
223: NN = ( ( N-1 ) / NB )*NB + 1
224: DO 50 J = NN, 1, -NB
225: JB = MIN( NB, N-J+1 )
226: *
227: * Copy current block column of L to WORK and replace with
228: * zeros.
229: *
230: DO 40 JJ = J, J + JB - 1
231: DO 30 I = JJ + 1, N
232: WORK( I+( JJ-J )*LDWORK ) = A( I, JJ )
233: A( I, JJ ) = ZERO
234: 30 CONTINUE
235: 40 CONTINUE
236: *
237: * Compute current block column of inv(A).
238: *
239: IF( J+JB.LE.N )
240: $ CALL DGEMM( 'No transpose', 'No transpose', N, JB,
241: $ N-J-JB+1, -ONE, A( 1, J+JB ), LDA,
242: $ WORK( J+JB ), LDWORK, ONE, A( 1, J ), LDA )
243: CALL DTRSM( 'Right', 'Lower', 'No transpose', 'Unit', N, JB,
244: $ ONE, WORK( J ), LDWORK, A( 1, J ), LDA )
245: 50 CONTINUE
246: END IF
247: *
248: * Apply column interchanges.
249: *
250: DO 60 J = N - 1, 1, -1
251: JP = IPIV( J )
252: IF( JP.NE.J )
253: $ CALL DSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 )
254: 60 CONTINUE
255: *
256: WORK( 1 ) = IWS
257: RETURN
258: *
259: * End of DGETRI
260: *
261: END
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