LAPACK  3.10.0 LAPACK: Linear Algebra PACKage
dgetri.f
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1 *> \brief \b DGETRI
2 *
3 * =========== DOCUMENTATION ===========
4 *
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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 *> \ingroup doubleGEcomputational
111 *
112 * =====================================================================
113  SUBROUTINE dgetri( N, A, LDA, IPIV, WORK, LWORK, INFO )
114 *
115 * -- LAPACK computational routine --
116 * -- LAPACK is a software package provided by Univ. of Tennessee, --
117 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118 *
119 * .. Scalar Arguments ..
120  INTEGER INFO, LDA, LWORK, N
121 * ..
122 * .. Array Arguments ..
123  INTEGER IPIV( * )
124  DOUBLE PRECISION A( LDA, * ), WORK( * )
125 * ..
126 *
127 * =====================================================================
128 *
129 * .. Parameters ..
130  DOUBLE PRECISION ZERO, ONE
131  parameter( zero = 0.0d+0, one = 1.0d+0 )
132 * ..
133 * .. Local Scalars ..
134  LOGICAL LQUERY
135  INTEGER I, IWS, J, JB, JJ, JP, LDWORK, LWKOPT, NB,
136  \$ NBMIN, NN
137 * ..
138 * .. External Functions ..
139  INTEGER ILAENV
140  EXTERNAL ilaenv
141 * ..
142 * .. External Subroutines ..
143  EXTERNAL dgemm, dgemv, dswap, dtrsm, dtrtri, xerbla
144 * ..
145 * .. Intrinsic Functions ..
146  INTRINSIC max, min
147 * ..
148 * .. Executable Statements ..
149 *
150 * Test the input parameters.
151 *
152  info = 0
153  nb = ilaenv( 1, 'DGETRI', ' ', n, -1, -1, -1 )
154  lwkopt = n*nb
155  work( 1 ) = lwkopt
156  lquery = ( lwork.EQ.-1 )
157  IF( n.LT.0 ) THEN
158  info = -1
159  ELSE IF( lda.LT.max( 1, n ) ) THEN
160  info = -3
161  ELSE IF( lwork.LT.max( 1, n ) .AND. .NOT.lquery ) THEN
162  info = -6
163  END IF
164  IF( info.NE.0 ) THEN
165  CALL xerbla( 'DGETRI', -info )
166  RETURN
167  ELSE IF( lquery ) THEN
168  RETURN
169  END IF
170 *
171 * Quick return if possible
172 *
173  IF( n.EQ.0 )
174  \$ RETURN
175 *
176 * Form inv(U). If INFO > 0 from DTRTRI, then U is singular,
177 * and the inverse is not computed.
178 *
179  CALL dtrtri( 'Upper', 'Non-unit', n, a, lda, info )
180  IF( info.GT.0 )
181  \$ RETURN
182 *
183  nbmin = 2
184  ldwork = n
185  IF( nb.GT.1 .AND. nb.LT.n ) THEN
186  iws = max( ldwork*nb, 1 )
187  IF( lwork.LT.iws ) THEN
188  nb = lwork / ldwork
189  nbmin = max( 2, ilaenv( 2, 'DGETRI', ' ', n, -1, -1, -1 ) )
190  END IF
191  ELSE
192  iws = n
193  END IF
194 *
195 * Solve the equation inv(A)*L = inv(U) for inv(A).
196 *
197  IF( nb.LT.nbmin .OR. nb.GE.n ) THEN
198 *
199 * Use unblocked code.
200 *
201  DO 20 j = n, 1, -1
202 *
203 * Copy current column of L to WORK and replace with zeros.
204 *
205  DO 10 i = j + 1, n
206  work( i ) = a( i, j )
207  a( i, j ) = zero
208  10 CONTINUE
209 *
210 * Compute current column of inv(A).
211 *
212  IF( j.LT.n )
213  \$ CALL dgemv( 'No transpose', n, n-j, -one, a( 1, j+1 ),
214  \$ lda, work( j+1 ), 1, one, a( 1, j ), 1 )
215  20 CONTINUE
216  ELSE
217 *
218 * Use blocked code.
219 *
220  nn = ( ( n-1 ) / nb )*nb + 1
221  DO 50 j = nn, 1, -nb
222  jb = min( nb, n-j+1 )
223 *
224 * Copy current block column of L to WORK and replace with
225 * zeros.
226 *
227  DO 40 jj = j, j + jb - 1
228  DO 30 i = jj + 1, n
229  work( i+( jj-j )*ldwork ) = a( i, jj )
230  a( i, jj ) = zero
231  30 CONTINUE
232  40 CONTINUE
233 *
234 * Compute current block column of inv(A).
235 *
236  IF( j+jb.LE.n )
237  \$ CALL dgemm( 'No transpose', 'No transpose', n, jb,
238  \$ n-j-jb+1, -one, a( 1, j+jb ), lda,
239  \$ work( j+jb ), ldwork, one, a( 1, j ), lda )
240  CALL dtrsm( 'Right', 'Lower', 'No transpose', 'Unit', n, jb,
241  \$ one, work( j ), ldwork, a( 1, j ), lda )
242  50 CONTINUE
243  END IF
244 *
245 * Apply column interchanges.
246 *
247  DO 60 j = n - 1, 1, -1
248  jp = ipiv( j )
249  IF( jp.NE.j )
250  \$ CALL dswap( n, a( 1, j ), 1, a( 1, jp ), 1 )
251  60 CONTINUE
252 *
253  work( 1 ) = iws
254  RETURN
255 *
256 * End of DGETRI
257 *
258  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dswap(N, DX, INCX, DY, INCY)
DSWAP
Definition: dswap.f:82
subroutine dgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DGEMV
Definition: dgemv.f:156
subroutine dtrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRSM
Definition: dtrsm.f:181
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:187
subroutine dgetri(N, A, LDA, IPIV, WORK, LWORK, INFO)
DGETRI
Definition: dgetri.f:114
subroutine dtrtri(UPLO, DIAG, N, A, LDA, INFO)
DTRTRI
Definition: dtrtri.f:109