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
|
/* ../../../dependencies/lapack/src/dlanhs.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"
/* Table of constant values */
static integer c__1 = 1;
doublereal dlanhs_(char *norm, integer *n, doublereal *a, integer *lda,
doublereal *work, ftnlen norm_len)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
doublereal ret_val, d__1, d__2, d__3;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static integer i__, j;
static doublereal sum, scale;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
static doublereal value;
extern /* Subroutine */ int dlassq_(integer *, doublereal *, integer *,
doublereal *, doublereal *);
/* -- LAPACK auxiliary routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* October 31, 1992 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLANHS returns the value of the one norm, or the Frobenius norm, or */
/* the infinity norm, or the element of largest absolute value of a */
/* Hessenberg matrix A. */
/* Description */
/* =========== */
/* DLANHS returns the value */
/* DLANHS = ( 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 matrix norm. */
/* Arguments */
/* ========= */
/* NORM (input) CHARACTER*1 */
/* Specifies the value to be returned in DLANHS as described */
/* above. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. When N = 0, DLANHS is */
/* set to zero. */
/* A (input) DOUBLE PRECISION array, dimension (LDA,N) */
/* The n by n upper Hessenberg matrix A; the part of A below the */
/* first sub-diagonal is not referenced. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(N,1). */
/* WORK (workspace) DOUBLE PRECISION array, dimension (LWORK), */
/* where LWORK >= N when NORM = 'I'; otherwise, WORK is not */
/* referenced. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. 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", (ftnlen)1, (ftnlen)1)) {
/* Find max(abs(A(i,j))). */
value = 0.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__3 = *n, i__4 = j + 1;
i__2 = min(i__3,i__4);
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = value, d__3 = (d__1 = a[i__ + j * a_dim1], abs(d__1));
value = max(d__2,d__3);
/* L10: */
}
/* L20: */
}
} else if (lsame_(norm, "O", (ftnlen)1, (ftnlen)1) || *(unsigned char *)
norm == '1') {
/* Find norm1(A). */
value = 0.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = 0.;
/* Computing MIN */
i__3 = *n, i__4 = j + 1;
i__2 = min(i__3,i__4);
for (i__ = 1; i__ <= i__2; ++i__) {
sum += (d__1 = a[i__ + j * a_dim1], abs(d__1));
/* L30: */
}
value = max(value,sum);
/* L40: */
}
} else if (lsame_(norm, "I", (ftnlen)1, (ftnlen)1)) {
/* Find normI(A). */
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 0.;
/* L50: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__3 = *n, i__4 = j + 1;
i__2 = min(i__3,i__4);
for (i__ = 1; i__ <= i__2; ++i__) {
work[i__] += (d__1 = a[i__ + j * a_dim1], abs(d__1));
/* L60: */
}
/* L70: */
}
value = 0.;
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);
/* L80: */
}
} else if (lsame_(norm, "F", (ftnlen)1, (ftnlen)1) || lsame_(norm, "E", (
ftnlen)1, (ftnlen)1)) {
/* Find normF(A). */
scale = 0.;
sum = 1.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__3 = *n, i__4 = j + 1;
i__2 = min(i__3,i__4);
dlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum);
/* L90: */
}
value = scale * sqrt(sum);
}
ret_val = value;
return ret_val;
/* End of DLANHS */
} /* dlanhs_ */
|
