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
|
/* zlansy.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 integer c__1 = 1;
doublereal zlansy_(char *norm, char *uplo, integer *n, doublecomplex *a,
integer *lda, doublereal *work)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
doublereal ret_val, d__1, d__2;
/* Builtin functions */
double z_abs(doublecomplex *), sqrt(doublereal);
/* Local variables */
integer i__, j;
doublereal sum, absa, scale;
extern logical lsame_(char *, char *);
doublereal value;
extern /* Subroutine */ int zlassq_(integer *, doublecomplex *, integer *,
doublereal *, doublereal *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLANSY returns the value of the one norm, or the Frobenius norm, or */
/* the infinity norm, or the element of largest absolute value of a */
/* complex symmetric matrix A. */
/* Description */
/* =========== */
/* ZLANSY returns the value */
/* ZLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm' */
/* ( */
/* ( norm1(A), NORM = '1', 'O' or 'o' */
/* ( */
/* ( normI(A), NORM = 'I' or 'i' */
/* ( */
/* ( normF(A), NORM = 'F', 'f', 'E' or 'e' */
/* where norm1 denotes the one norm of a matrix (maximum column sum), */
/* normI denotes the infinity norm of a matrix (maximum row sum) and */
/* normF denotes the Frobenius norm of a matrix (square root of sum of */
/* squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. */
/* Arguments */
/* ========= */
/* NORM (input) CHARACTER*1 */
/* Specifies the value to be returned in ZLANSY as described */
/* above. */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the upper or lower triangular part of the */
/* symmetric matrix A is to be referenced. */
/* = 'U': Upper triangular part of A is referenced */
/* = 'L': Lower triangular part of A is referenced */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. When N = 0, ZLANSY is */
/* set to zero. */
/* A (input) COMPLEX*16 array, dimension (LDA,N) */
/* The symmetric matrix A. If UPLO = 'U', the leading n by n */
/* upper triangular part of A contains the upper triangular part */
/* of the matrix A, and the strictly lower triangular part of A */
/* is not referenced. If UPLO = 'L', the leading n by n lower */
/* triangular part of A contains the lower triangular part of */
/* the matrix A, and the strictly upper triangular part of A is */
/* not referenced. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(N,1). */
/* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), */
/* where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, */
/* WORK is not referenced. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--work;
/* Function Body */
if (*n == 0) {
value = 0.;
} else if (lsame_(norm, "M")) {
/* Find max(abs(A(i,j))). */
value = 0.;
if (lsame_(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = z_abs(&a[i__ + j * a_dim1]);
value = max(d__1,d__2);
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = z_abs(&a[i__ + j * a_dim1]);
value = max(d__1,d__2);
/* L30: */
}
/* L40: */
}
}
} else if (lsame_(norm, "I") || lsame_(norm, "O") || *(unsigned char *)norm == '1') {
/* Find normI(A) ( = norm1(A), since A is symmetric). */
value = 0.;
if (lsame_(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = 0.;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
absa = z_abs(&a[i__ + j * a_dim1]);
sum += absa;
work[i__] += absa;
/* L50: */
}
work[j] = sum + z_abs(&a[j + j * a_dim1]);
/* L60: */
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = work[i__];
value = max(d__1,d__2);
/* L70: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 0.;
/* L80: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = work[j] + z_abs(&a[j + j * a_dim1]);
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
absa = z_abs(&a[i__ + j * a_dim1]);
sum += absa;
work[i__] += absa;
/* L90: */
}
value = max(value,sum);
/* L100: */
}
}
} else if (lsame_(norm, "F") || lsame_(norm, "E")) {
/* Find normF(A). */
scale = 0.;
sum = 1.;
if (lsame_(uplo, "U")) {
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
i__2 = j - 1;
zlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum);
/* L110: */
}
} else {
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = *n - j;
zlassq_(&i__2, &a[j + 1 + j * a_dim1], &c__1, &scale, &sum);
/* L120: */
}
}
sum *= 2;
i__1 = *lda + 1;
zlassq_(n, &a[a_offset], &i__1, &scale, &sum);
value = scale * sqrt(sum);
}
ret_val = value;
return ret_val;
/* End of ZLANSY */
} /* zlansy_ */
|
