Annotation of rpl/lapack/lapack/zgetri.f, revision 1.16
1.8 bertrand 1: *> \brief \b ZGETRI
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.14 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.14 bertrand 9: *> Download ZGETRI + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgetri.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgetri.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgetri.f">
1.8 bertrand 15: *> [TXT]</a>
1.14 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
1.14 bertrand 22: *
1.8 bertrand 23: * .. Scalar Arguments ..
24: * INTEGER INFO, LDA, LWORK, N
25: * ..
26: * .. Array Arguments ..
27: * INTEGER IPIV( * )
28: * COMPLEX*16 A( LDA, * ), WORK( * )
29: * ..
1.14 bertrand 30: *
1.8 bertrand 31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZGETRI computes the inverse of a matrix using the LU factorization
38: *> computed by ZGETRF.
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 COMPLEX*16 array, dimension (LDA,N)
56: *> On entry, the factors L and U from the factorization
57: *> A = P*L*U as computed by ZGETRF.
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 ZGETRF; 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 COMPLEX*16 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: *
1.14 bertrand 105: *> \author Univ. of Tennessee
106: *> \author Univ. of California Berkeley
107: *> \author Univ. of Colorado Denver
108: *> \author NAG Ltd.
1.8 bertrand 109: *
1.14 bertrand 110: *> \date December 2016
1.8 bertrand 111: *
112: *> \ingroup complex16GEcomputational
113: *
114: * =====================================================================
1.1 bertrand 115: SUBROUTINE ZGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
116: *
1.14 bertrand 117: * -- LAPACK computational routine (version 3.7.0) --
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..--
1.14 bertrand 120: * December 2016
1.1 bertrand 121: *
122: * .. Scalar Arguments ..
123: INTEGER INFO, LDA, LWORK, N
124: * ..
125: * .. Array Arguments ..
126: INTEGER IPIV( * )
127: COMPLEX*16 A( LDA, * ), WORK( * )
128: * ..
129: *
130: * =====================================================================
131: *
132: * .. Parameters ..
133: COMPLEX*16 ZERO, ONE
134: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ),
135: $ ONE = ( 1.0D+0, 0.0D+0 ) )
136: * ..
137: * .. Local Scalars ..
138: LOGICAL LQUERY
139: INTEGER I, IWS, J, JB, JJ, JP, LDWORK, LWKOPT, NB,
140: $ NBMIN, NN
141: * ..
142: * .. External Functions ..
143: INTEGER ILAENV
144: EXTERNAL ILAENV
145: * ..
146: * .. External Subroutines ..
147: EXTERNAL XERBLA, ZGEMM, ZGEMV, ZSWAP, ZTRSM, ZTRTRI
148: * ..
149: * .. Intrinsic Functions ..
150: INTRINSIC MAX, MIN
151: * ..
152: * .. Executable Statements ..
153: *
154: * Test the input parameters.
155: *
156: INFO = 0
157: NB = ILAENV( 1, 'ZGETRI', ' ', N, -1, -1, -1 )
158: LWKOPT = N*NB
159: WORK( 1 ) = LWKOPT
160: LQUERY = ( LWORK.EQ.-1 )
161: IF( N.LT.0 ) THEN
162: INFO = -1
163: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
164: INFO = -3
165: ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
166: INFO = -6
167: END IF
168: IF( INFO.NE.0 ) THEN
169: CALL XERBLA( 'ZGETRI', -INFO )
170: RETURN
171: ELSE IF( LQUERY ) THEN
172: RETURN
173: END IF
174: *
175: * Quick return if possible
176: *
177: IF( N.EQ.0 )
178: $ RETURN
179: *
180: * Form inv(U). If INFO > 0 from ZTRTRI, then U is singular,
181: * and the inverse is not computed.
182: *
183: CALL ZTRTRI( 'Upper', 'Non-unit', N, A, LDA, INFO )
184: IF( INFO.GT.0 )
185: $ RETURN
186: *
187: NBMIN = 2
188: LDWORK = N
189: IF( NB.GT.1 .AND. NB.LT.N ) THEN
190: IWS = MAX( LDWORK*NB, 1 )
191: IF( LWORK.LT.IWS ) THEN
192: NB = LWORK / LDWORK
193: NBMIN = MAX( 2, ILAENV( 2, 'ZGETRI', ' ', N, -1, -1, -1 ) )
194: END IF
195: ELSE
196: IWS = N
197: END IF
198: *
199: * Solve the equation inv(A)*L = inv(U) for inv(A).
200: *
201: IF( NB.LT.NBMIN .OR. NB.GE.N ) THEN
202: *
203: * Use unblocked code.
204: *
205: DO 20 J = N, 1, -1
206: *
207: * Copy current column of L to WORK and replace with zeros.
208: *
209: DO 10 I = J + 1, N
210: WORK( I ) = A( I, J )
211: A( I, J ) = ZERO
212: 10 CONTINUE
213: *
214: * Compute current column of inv(A).
215: *
216: IF( J.LT.N )
217: $ CALL ZGEMV( 'No transpose', N, N-J, -ONE, A( 1, J+1 ),
218: $ LDA, WORK( J+1 ), 1, ONE, A( 1, J ), 1 )
219: 20 CONTINUE
220: ELSE
221: *
222: * Use blocked code.
223: *
224: NN = ( ( N-1 ) / NB )*NB + 1
225: DO 50 J = NN, 1, -NB
226: JB = MIN( NB, N-J+1 )
227: *
228: * Copy current block column of L to WORK and replace with
229: * zeros.
230: *
231: DO 40 JJ = J, J + JB - 1
232: DO 30 I = JJ + 1, N
233: WORK( I+( JJ-J )*LDWORK ) = A( I, JJ )
234: A( I, JJ ) = ZERO
235: 30 CONTINUE
236: 40 CONTINUE
237: *
238: * Compute current block column of inv(A).
239: *
240: IF( J+JB.LE.N )
241: $ CALL ZGEMM( 'No transpose', 'No transpose', N, JB,
242: $ N-J-JB+1, -ONE, A( 1, J+JB ), LDA,
243: $ WORK( J+JB ), LDWORK, ONE, A( 1, J ), LDA )
244: CALL ZTRSM( 'Right', 'Lower', 'No transpose', 'Unit', N, JB,
245: $ ONE, WORK( J ), LDWORK, A( 1, J ), LDA )
246: 50 CONTINUE
247: END IF
248: *
249: * Apply column interchanges.
250: *
251: DO 60 J = N - 1, 1, -1
252: JP = IPIV( J )
253: IF( JP.NE.J )
254: $ CALL ZSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 )
255: 60 CONTINUE
256: *
257: WORK( 1 ) = IWS
258: RETURN
259: *
260: * End of ZGETRI
261: *
262: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zgetri.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack