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
|
SUBROUTINE STRTRIF( UPLO, DIAG, N, A, LDA, INFO )
*
* -- LAPACK routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* March 31, 1993
*
* .. Scalar Arguments ..
CHARACTER DIAG, UPLO
INTEGER INFO, LDA, N
* ..
* .. Array Arguments ..
REAL A( LDA, * )
* ..
*
* Purpose
* =======
*
* STRTRI computes the inverse of a real upper or lower triangular
* matrix A.
*
* This is the Level 3 BLAS version of the algorithm.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER*1
* = 'U': A is upper triangular;
* = 'L': A is lower triangular.
*
* DIAG (input) CHARACTER*1
* = 'N': A is non-unit triangular;
* = 'U': A is unit triangular.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* A (input/output) REAL array, dimension (LDA,N)
* On entry, the triangular matrix A. If UPLO = 'U', the
* leading N-by-N upper triangular part of the array A contains
* the upper triangular matrix, and the strictly lower
* triangular part of A is not referenced. If UPLO = 'L', the
* leading N-by-N lower triangular part of the array A contains
* the lower triangular matrix, and the strictly upper
* triangular part of A is not referenced. If DIAG = 'U', the
* diagonal elements of A are also not referenced and are
* assumed to be 1.
* On exit, the (triangular) inverse of the original matrix, in
* the same storage format.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
* > 0: if INFO = i, A(i,i) is exactly zero. The triangular
* matrix is singular and its inverse can not be computed.
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL NOUNIT, UPPER
INTEGER J, JB, NB, NN
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL STRMM, STRSM, STRTI2, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
UPPER = LSAME( UPLO, 'U' )
NOUNIT = LSAME( DIAG, 'N' )
IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -5
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'STRTRI', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Check for singularity if non-unit.
*
IF( NOUNIT ) THEN
DO 10 INFO = 1, N
IF( A( INFO, INFO ).EQ.ZERO )
$ RETURN
10 CONTINUE
INFO = 0
END IF
*
* Determine the block size for this environment.
*
NB = 128
IF( NB.LE.1 .OR. NB.GE.N ) THEN
*
* Use unblocked code
*
CALL STRTI2( UPLO, DIAG, N, A, LDA, INFO )
ELSE
*
* Use blocked code
*
IF( UPPER ) THEN
*
* Compute inverse of upper triangular matrix
*
DO 20 J = 1, N, NB
JB = MIN( NB, N-J+1 )
*
* Compute rows 1:j-1 of current block column
*
CALL STRMM( 'Left', 'Upper', 'No transpose', DIAG, J-1,
$ JB, ONE, A, LDA, A( 1, J ), LDA )
CALL STRSM( 'Right', 'Upper', 'No transpose', DIAG, J-1,
$ JB, -ONE, A( J, J ), LDA, A( 1, J ), LDA )
*
* Compute inverse of current diagonal block
*
CALL STRTI2( 'Upper', DIAG, JB, A( J, J ), LDA, INFO )
20 CONTINUE
ELSE
*
* Compute inverse of lower triangular matrix
*
NN = ( ( N-1 ) / NB )*NB + 1
DO 30 J = NN, 1, -NB
JB = MIN( NB, N-J+1 )
IF( J+JB.LE.N ) THEN
*
* Compute rows j+jb:n of current block column
*
CALL STRMM( 'Left', 'Lower', 'No transpose', DIAG,
$ N-J-JB+1, JB, ONE, A( J+JB, J+JB ), LDA,
$ A( J+JB, J ), LDA )
CALL STRSM( 'Right', 'Lower', 'No transpose', DIAG,
$ N-J-JB+1, JB, -ONE, A( J, J ), LDA,
$ A( J+JB, J ), LDA )
END IF
*
* Compute inverse of current diagonal block
*
CALL STRTI2( 'Lower', DIAG, JB, A( J, J ), LDA, INFO )
30 CONTINUE
END IF
END IF
*
RETURN
*
* End of STRTRI
*
END
|