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
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
|
/* ztrtri.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static doublecomplex c_b1 = {1.,0.};
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__2 = 2;
/* Subroutine */ int ztrtri_(char *uplo, char *diag, integer *n,
doublecomplex *a, integer *lda, integer *info)
{
/* System generated locals */
address a__1[2];
integer a_dim1, a_offset, i__1, i__2, i__3[2], i__4, i__5;
doublecomplex z__1;
char ch__1[2];
/* Builtin functions */
/* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
/* Local variables */
integer j, jb, nb, nn;
extern logical lsame_(char *, char *);
logical upper;
extern /* Subroutine */ int ztrmm_(char *, char *, char *, char *,
integer *, integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *),
ztrsm_(char *, char *, char *, char *, integer *, integer *,
doublecomplex *, doublecomplex *, integer *, doublecomplex *,
integer *), ztrti2_(char *, char *
, integer *, doublecomplex *, integer *, integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
logical nounit;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZTRTRI computes the inverse of a complex 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) COMPLEX*16 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 .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
/* Function Body */
*info = 0;
upper = lsame_(uplo, "U");
nounit = lsame_(diag, "N");
if (! upper && ! lsame_(uplo, "L")) {
*info = -1;
} else if (! nounit && ! lsame_(diag, "U")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*lda < max(1,*n)) {
*info = -5;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZTRTRI", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Check for singularity if non-unit. */
if (nounit) {
i__1 = *n;
for (*info = 1; *info <= i__1; ++(*info)) {
i__2 = *info + *info * a_dim1;
if (a[i__2].r == 0. && a[i__2].i == 0.) {
return 0;
}
/* L10: */
}
*info = 0;
}
/* Determine the block size for this environment. */
/* Writing concatenation */
i__3[0] = 1, a__1[0] = uplo;
i__3[1] = 1, a__1[1] = diag;
s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
nb = ilaenv_(&c__1, "ZTRTRI", ch__1, n, &c_n1, &c_n1, &c_n1);
if (nb <= 1 || nb >= *n) {
/* Use unblocked code */
ztrti2_(uplo, diag, n, &a[a_offset], lda, info);
} else {
/* Use blocked code */
if (upper) {
/* Compute inverse of upper triangular matrix */
i__1 = *n;
i__2 = nb;
for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/* Computing MIN */
i__4 = nb, i__5 = *n - j + 1;
jb = min(i__4,i__5);
/* Compute rows 1:j-1 of current block column */
i__4 = j - 1;
ztrmm_("Left", "Upper", "No transpose", diag, &i__4, &jb, &
c_b1, &a[a_offset], lda, &a[j * a_dim1 + 1], lda);
i__4 = j - 1;
z__1.r = -1., z__1.i = -0.;
ztrsm_("Right", "Upper", "No transpose", diag, &i__4, &jb, &
z__1, &a[j + j * a_dim1], lda, &a[j * a_dim1 + 1],
lda);
/* Compute inverse of current diagonal block */
ztrti2_("Upper", diag, &jb, &a[j + j * a_dim1], lda, info);
/* L20: */
}
} else {
/* Compute inverse of lower triangular matrix */
nn = (*n - 1) / nb * nb + 1;
i__2 = -nb;
for (j = nn; i__2 < 0 ? j >= 1 : j <= 1; j += i__2) {
/* Computing MIN */
i__1 = nb, i__4 = *n - j + 1;
jb = min(i__1,i__4);
if (j + jb <= *n) {
/* Compute rows j+jb:n of current block column */
i__1 = *n - j - jb + 1;
ztrmm_("Left", "Lower", "No transpose", diag, &i__1, &jb,
&c_b1, &a[j + jb + (j + jb) * a_dim1], lda, &a[j
+ jb + j * a_dim1], lda);
i__1 = *n - j - jb + 1;
z__1.r = -1., z__1.i = -0.;
ztrsm_("Right", "Lower", "No transpose", diag, &i__1, &jb,
&z__1, &a[j + j * a_dim1], lda, &a[j + jb + j *
a_dim1], lda);
}
/* Compute inverse of current diagonal block */
ztrti2_("Lower", diag, &jb, &a[j + j * a_dim1], lda, info);
/* L30: */
}
}
}
return 0;
/* End of ZTRTRI */
} /* ztrtri_ */
|
