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 CTPTRI( UPLO, DIAG, N, AP, INFO )
*
* -- LAPACK routine (version 3.2) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
CHARACTER DIAG, UPLO
INTEGER INFO, N
* ..
* .. Array Arguments ..
COMPLEX AP( * )
* ..
*
* Purpose
* =======
*
* CTPTRI computes the inverse of a complex upper or lower triangular
* matrix A stored in packed format.
*
* 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.
*
* AP (input/output) COMPLEX array, dimension (N*(N+1)/2)
* On entry, the upper or lower triangular matrix A, stored
* columnwise in a linear array. The j-th column of A is stored
* in the array AP as follows:
* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
* if UPLO = 'L', AP(i + (j-1)*((2*n-j)/2) = A(i,j) for j<=i<=n.
* See below for further details.
* On exit, the (triangular) inverse of the original matrix, in
* the same packed storage format.
*
* 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.
*
* Further Details
* ===============
*
* A triangular matrix A can be transferred to packed storage using one
* of the following program segments:
*
* UPLO = 'U': UPLO = 'L':
*
* JC = 1 JC = 1
* DO 2 J = 1, N DO 2 J = 1, N
* DO 1 I = 1, J DO 1 I = J, N
* AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J)
* 1 CONTINUE 1 CONTINUE
* JC = JC + J JC = JC + N - J + 1
* 2 CONTINUE 2 CONTINUE
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ONE, ZERO
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ),
$ ZERO = ( 0.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
LOGICAL NOUNIT, UPPER
INTEGER J, JC, JCLAST, JJ
COMPLEX AJJ
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL CSCAL, CTPMV, XERBLA
* ..
* .. 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
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CTPTRI', -INFO )
RETURN
END IF
*
* Check for singularity if non-unit.
*
IF( NOUNIT ) THEN
IF( UPPER ) THEN
JJ = 0
DO 10 INFO = 1, N
JJ = JJ + INFO
IF( AP( JJ ).EQ.ZERO )
$ RETURN
10 CONTINUE
ELSE
JJ = 1
DO 20 INFO = 1, N
IF( AP( JJ ).EQ.ZERO )
$ RETURN
JJ = JJ + N - INFO + 1
20 CONTINUE
END IF
INFO = 0
END IF
*
IF( UPPER ) THEN
*
* Compute inverse of upper triangular matrix.
*
JC = 1
DO 30 J = 1, N
IF( NOUNIT ) THEN
AP( JC+J-1 ) = ONE / AP( JC+J-1 )
AJJ = -AP( JC+J-1 )
ELSE
AJJ = -ONE
END IF
*
* Compute elements 1:j-1 of j-th column.
*
CALL CTPMV( 'Upper', 'No transpose', DIAG, J-1, AP,
$ AP( JC ), 1 )
CALL CSCAL( J-1, AJJ, AP( JC ), 1 )
JC = JC + J
30 CONTINUE
*
ELSE
*
* Compute inverse of lower triangular matrix.
*
JC = N*( N+1 ) / 2
DO 40 J = N, 1, -1
IF( NOUNIT ) THEN
AP( JC ) = ONE / AP( JC )
AJJ = -AP( JC )
ELSE
AJJ = -ONE
END IF
IF( J.LT.N ) THEN
*
* Compute elements j+1:n of j-th column.
*
CALL CTPMV( 'Lower', 'No transpose', DIAG, N-J,
$ AP( JCLAST ), AP( JC+1 ), 1 )
CALL CSCAL( N-J, AJJ, AP( JC+1 ), 1 )
END IF
JCLAST = JC
JC = JC - N + J - 2
40 CONTINUE
END IF
*
RETURN
*
* End of CTPTRI
*
END
|
