1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
|
SUBROUTINE CGETRI( N, A, LDA, IPIV, WORK, LWORK, INFO )
*
* -- LAPACK routine (version 3.2) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LWORK, N
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
COMPLEX A( LDA, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* CGETRI computes the inverse of a matrix using the LU factorization
* computed by CGETRF.
*
* This method inverts U and then computes inv(A) by solving the system
* inv(A)*L = inv(U) for inv(A).
*
* Arguments
* =========
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* A (input/output) COMPLEX array, dimension (LDA,N)
* On entry, the factors L and U from the factorization
* A = P*L*U as computed by CGETRF.
* On exit, if INFO = 0, the inverse of the original matrix A.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* IPIV (input) INTEGER array, dimension (N)
* The pivot indices from CGETRF; for 1<=i<=N, row i of the
* matrix was interchanged with row IPIV(i).
*
* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
* On exit, if INFO=0, then WORK(1) returns the optimal LWORK.
*
* LWORK (input) INTEGER
* The dimension of the array WORK. LWORK >= max(1,N).
* For optimal performance LWORK >= N*NB, where NB is
* the optimal blocksize returned by ILAENV.
*
* If LWORK = -1, then a workspace query is assumed; the routine
* only calculates the optimal size of the WORK array, returns
* this value as the first entry of the WORK array, and no error
* message related to LWORK is issued by XERBLA.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
* > 0: if INFO = i, U(i,i) is exactly zero; the matrix is
* singular and its inverse could not be computed.
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ZERO, ONE
PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ),
$ ONE = ( 1.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
LOGICAL LQUERY
INTEGER I, IWS, J, JB, JJ, JP, LDWORK, LWKOPT, NB,
$ NBMIN, NN
* ..
* .. External Functions ..
INTEGER ILAENV
EXTERNAL ILAENV
* ..
* .. External Subroutines ..
EXTERNAL CGEMM, CGEMV, CSWAP, CTRSM, CTRTRI, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
NB = ILAENV( 1, 'CGETRI', ' ', N, -1, -1, -1 )
LWKOPT = N*NB
WORK( 1 ) = LWKOPT
LQUERY = ( LWORK.EQ.-1 )
IF( N.LT.0 ) THEN
INFO = -1
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -3
ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
INFO = -6
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CGETRI', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Form inv(U). If INFO > 0 from CTRTRI, then U is singular,
* and the inverse is not computed.
*
CALL CTRTRI( 'Upper', 'Non-unit', N, A, LDA, INFO )
IF( INFO.GT.0 )
$ RETURN
*
NBMIN = 2
LDWORK = N
IF( NB.GT.1 .AND. NB.LT.N ) THEN
IWS = MAX( LDWORK*NB, 1 )
IF( LWORK.LT.IWS ) THEN
NB = LWORK / LDWORK
NBMIN = MAX( 2, ILAENV( 2, 'CGETRI', ' ', N, -1, -1, -1 ) )
END IF
ELSE
IWS = N
END IF
*
* Solve the equation inv(A)*L = inv(U) for inv(A).
*
IF( NB.LT.NBMIN .OR. NB.GE.N ) THEN
*
* Use unblocked code.
*
DO 20 J = N, 1, -1
*
* Copy current column of L to WORK and replace with zeros.
*
DO 10 I = J + 1, N
WORK( I ) = A( I, J )
A( I, J ) = ZERO
10 CONTINUE
*
* Compute current column of inv(A).
*
IF( J.LT.N )
$ CALL CGEMV( 'No transpose', N, N-J, -ONE, A( 1, J+1 ),
$ LDA, WORK( J+1 ), 1, ONE, A( 1, J ), 1 )
20 CONTINUE
ELSE
*
* Use blocked code.
*
NN = ( ( N-1 ) / NB )*NB + 1
DO 50 J = NN, 1, -NB
JB = MIN( NB, N-J+1 )
*
* Copy current block column of L to WORK and replace with
* zeros.
*
DO 40 JJ = J, J + JB - 1
DO 30 I = JJ + 1, N
WORK( I+( JJ-J )*LDWORK ) = A( I, JJ )
A( I, JJ ) = ZERO
30 CONTINUE
40 CONTINUE
*
* Compute current block column of inv(A).
*
IF( J+JB.LE.N )
$ CALL CGEMM( 'No transpose', 'No transpose', N, JB,
$ N-J-JB+1, -ONE, A( 1, J+JB ), LDA,
$ WORK( J+JB ), LDWORK, ONE, A( 1, J ), LDA )
CALL CTRSM( 'Right', 'Lower', 'No transpose', 'Unit', N, JB,
$ ONE, WORK( J ), LDWORK, A( 1, J ), LDA )
50 CONTINUE
END IF
*
* Apply column interchanges.
*
DO 60 J = N - 1, 1, -1
JP = IPIV( J )
IF( JP.NE.J )
$ CALL CSWAP( N, A( 1, J ), 1, A( 1, JP ), 1 )
60 CONTINUE
*
WORK( 1 ) = IWS
RETURN
*
* End of CGETRI
*
END
|
