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
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
|
/**************************************************************************
**
** Copyright (C) 1993 David E. Steward & Zbigniew Leyk, all rights reserved.
**
** Meschach Library
**
** This Meschach Library is provided "as is" without any express
** or implied warranty of any kind with respect to this software.
** In particular the authors shall not be liable for any direct,
** indirect, special, incidental or consequential damages arising
** in any way from use of the software.
**
** Everyone is granted permission to copy, modify and redistribute this
** Meschach Library, provided:
** 1. All copies contain this copyright notice.
** 2. All modified copies shall carry a notice stating who
** made the last modification and the date of such modification.
** 3. No charge is made for this software or works derived from it.
** This clause shall not be construed as constraining other software
** distributed on the same medium as this software, nor is a
** distribution fee considered a charge.
**
***************************************************************************/
/* Main include file for zmeschach library -- complex vectors and matrices */
#ifndef ZMATRIXH
#define ZMATRIXH
#include "matrix.h"
/* Type definitions for complex vectors and matrices */
/*Real r;*/
/* complex definition */
typedef struct {
Real re, im;
} complex;
/* complex vector definition */
typedef struct {
u_int dim, max_dim;
complex *ve;
} ZVEC;
/* complex matrix definition */
typedef struct {
u_int m, n;
u_int max_m, max_n, max_size;
complex *base; /* base is base of alloc'd mem */
complex **me;
} ZMAT;
#define ZVNULL ((ZVEC *)NULL)
#define ZMNULL ((ZMAT *)NULL)
#define Z_CONJ 1
#define Z_NOCONJ 0
/* memory functions */
#ifdef ANSI_C
int zv_get_vars(int dim,...);
int zm_get_vars(int m,int n,...);
int zv_resize_vars(int new_dim,...);
int zm_resize_vars(int m,int n,...);
int zv_free_vars(ZVEC **,...);
int zm_free_vars(ZMAT **,...);
#elif VARARGS
int zv_get_vars();
int zm_get_vars();
int zv_resize_vars();
int zm_resize_vars();
int zv_free_vars();
int zm_free_vars();
#endif
#ifdef ANSI_C
extern ZMAT *_zm_copy(ZMAT *in,ZMAT *out,u_int i0,u_int j0);
extern ZMAT * zm_move(ZMAT *, int, int, int, int, ZMAT *, int, int);
extern ZMAT *zvm_move(ZVEC *, int, ZMAT *, int, int, int, int);
extern ZVEC *_zv_copy(ZVEC *in,ZVEC *out,u_int i0);
extern ZVEC * zv_move(ZVEC *, int, int, ZVEC *, int);
extern ZVEC *zmv_move(ZMAT *, int, int, int, int, ZVEC *, int);
extern complex z_finput(FILE *fp);
extern ZMAT *zm_finput(FILE *fp,ZMAT *a);
extern ZVEC *zv_finput(FILE *fp,ZVEC *x);
extern ZMAT *zm_add(ZMAT *mat1,ZMAT *mat2,ZMAT *out);
extern ZMAT *zm_sub(ZMAT *mat1,ZMAT *mat2,ZMAT *out);
extern ZMAT *zm_mlt(ZMAT *A,ZMAT *B,ZMAT *OUT);
extern ZMAT *zmma_mlt(ZMAT *A,ZMAT *B,ZMAT *OUT);
extern ZMAT *zmam_mlt(ZMAT *A,ZMAT *B,ZMAT *OUT);
extern ZVEC *zmv_mlt(ZMAT *A,ZVEC *b,ZVEC *out);
extern ZMAT *zsm_mlt(complex scalar,ZMAT *matrix,ZMAT *out);
extern ZVEC *zvm_mlt(ZMAT *A,ZVEC *b,ZVEC *out);
extern ZMAT *zm_adjoint(ZMAT *in,ZMAT *out);
extern ZMAT *zswap_rows(ZMAT *A,int i,int j,int lo,int hi);
extern ZMAT *zswap_cols(ZMAT *A,int i,int j,int lo,int hi);
extern ZMAT *mz_mltadd(ZMAT *A1,ZMAT *A2,complex s,ZMAT *out);
extern ZVEC *zmv_mltadd(ZVEC *v1,ZVEC *v2,ZMAT *A,complex alpha,ZVEC *out);
extern ZVEC *zvm_mltadd(ZVEC *v1,ZVEC *v2,ZMAT *A,complex alpha,ZVEC *out);
extern ZVEC *zv_zero(ZVEC *x);
extern ZMAT *zm_zero(ZMAT *A);
extern ZMAT *zm_get(int m,int n);
extern ZVEC *zv_get(int dim);
extern ZMAT *zm_resize(ZMAT *A,int new_m,int new_n);
extern complex _zin_prod(ZVEC *x,ZVEC *y,u_int i0,u_int flag);
extern ZVEC *zv_resize(ZVEC *x,int new_dim);
extern ZVEC *zv_mlt(complex scalar,ZVEC *vector,ZVEC *out);
extern ZVEC *zv_add(ZVEC *vec1,ZVEC *vec2,ZVEC *out);
extern ZVEC *zv_mltadd(ZVEC *v1,ZVEC *v2,complex scale,ZVEC *out);
extern ZVEC *zv_sub(ZVEC *vec1,ZVEC *vec2,ZVEC *out);
#ifdef PROTOTYPES_IN_STRUCT
extern ZVEC *zv_map(complex (*f)(),ZVEC *x,ZVEC *out);
extern ZVEC *_zv_map(complex (*f)(),void *params,ZVEC *x,ZVEC *out);
#else
extern ZVEC *zv_map(complex (*f)(complex),ZVEC *x,ZVEC *out);
extern ZVEC *_zv_map(complex (*f)(void *,complex),void *params,ZVEC *x,ZVEC *out);
#endif
extern ZVEC *zv_lincomb(int n,ZVEC *v[],complex a[],ZVEC *out);
extern ZVEC *zv_linlist(ZVEC *out,ZVEC *v1,complex a1,...);
extern ZVEC *zv_star(ZVEC *x1, ZVEC *x2, ZVEC *out);
extern ZVEC *zv_slash(ZVEC *x1, ZVEC *x2, ZVEC *out);
extern int zm_free(ZMAT *mat);
extern int zv_free(ZVEC *vec);
extern ZVEC *zv_rand(ZVEC *x);
extern ZMAT *zm_rand(ZMAT *A);
extern ZVEC *zget_row(ZMAT *A, int i, ZVEC *out);
extern ZVEC *zget_col(ZMAT *A, int j, ZVEC *out);
extern ZMAT *zset_row(ZMAT *A, int i, ZVEC *in);
extern ZMAT *zset_col(ZMAT *A, int j, ZVEC *in);
extern ZVEC *px_zvec(PERM *pi, ZVEC *in, ZVEC *out);
extern ZVEC *pxinv_zvec(PERM *pi, ZVEC *in, ZVEC *out);
extern void __zconj__(complex zp[], int len);
extern complex __zip__(complex zp1[],complex zp2[],int len,int flag);
extern void __zmltadd__(complex zp1[],complex zp2[],
complex s,int len,int flag);
extern void __zmlt__(complex zp[],complex s,complex out[],int len);
extern void __zadd__(complex zp1[],complex zp2[],complex out[],int len);
extern void __zsub__(complex zp1[],complex zp2[],complex out[],int len);
extern void __zzero__(complex zp[],int len);
extern void z_foutput(FILE *fp,complex z);
extern void zm_foutput(FILE *fp,ZMAT *a);
extern void zv_foutput(FILE *fp,ZVEC *x);
extern void zm_dump(FILE *fp,ZMAT *a);
extern void zv_dump(FILE *fp,ZVEC *x);
extern double _zv_norm1(ZVEC *x, VEC *scale);
extern double _zv_norm2(ZVEC *x, VEC *scale);
extern double _zv_norm_inf(ZVEC *x, VEC *scale);
extern double zm_norm1(ZMAT *A);
extern double zm_norm_inf(ZMAT *A);
extern double zm_norm_frob(ZMAT *A);
complex zmake(double real, double imag);
double zabs(complex z);
complex zadd(complex z1,complex z2);
complex zsub(complex z1,complex z2);
complex zmlt(complex z1,complex z2);
complex zinv(complex z);
complex zdiv(complex z1,complex z2);
complex zsqrt(complex z);
complex zexp(complex z);
complex zlog(complex z);
complex zconj(complex z);
complex zneg(complex z);
#else
extern ZMAT *_zm_copy();
extern ZVEC *_zv_copy();
extern ZMAT *zm_finput();
extern ZVEC *zv_finput();
extern ZMAT *zm_add();
extern ZMAT *zm_sub();
extern ZMAT *zm_mlt();
extern ZMAT *zmma_mlt();
extern ZMAT *zmam_mlt();
extern ZVEC *zmv_mlt();
extern ZMAT *zsm_mlt();
extern ZVEC *zvm_mlt();
extern ZMAT *zm_adjoint();
extern ZMAT *zswap_rows();
extern ZMAT *zswap_cols();
extern ZMAT *mz_mltadd();
extern ZVEC *zmv_mltadd();
extern ZVEC *zvm_mltadd();
extern ZVEC *zv_zero();
extern ZMAT *zm_zero();
extern ZMAT *zm_get();
extern ZVEC *zv_get();
extern ZMAT *zm_resize();
extern ZVEC *zv_resize();
extern complex _zin_prod();
extern ZVEC *zv_mlt();
extern ZVEC *zv_add();
extern ZVEC *zv_mltadd();
extern ZVEC *zv_sub();
extern ZVEC *zv_map();
extern ZVEC *_zv_map();
extern ZVEC *zv_lincomb();
extern ZVEC *zv_linlist();
extern ZVEC *zv_star();
extern ZVEC *zv_slash();
extern ZVEC *px_zvec();
extern ZVEC *pxinv_zvec();
extern ZVEC *zv_rand();
extern ZMAT *zm_rand();
extern ZVEC *zget_row();
extern ZVEC *zget_col();
extern ZMAT *zset_row();
extern ZMAT *zset_col();
extern int zm_free();
extern int zv_free();
extern void __zconj__();
extern complex __zip__();
extern void __zmltadd__();
extern void __zmlt__();
extern void __zadd__();
extern void __zsub__();
extern void __zzero__();
extern void zm_foutput();
extern void zv_foutput();
extern void zm_dump();
extern void zv_dump();
extern double _zv_norm1();
extern double _zv_norm2();
extern double _zv_norm_inf();
extern double zm_norm1();
extern double zm_norm_inf();
extern double zm_norm_frob();
complex zmake();
double zabs();
complex zadd();
complex zsub();
complex zmlt();
complex zinv();
complex zdiv();
complex zsqrt();
complex zexp();
complex zlog();
complex zconj();
complex zneg();
#endif
#define zv_copy(x,y) _zv_copy(x,y,0)
#define zm_copy(A,B) _zm_copy(A,B,0,0)
#define z_input() z_finput(stdin)
#define zv_input(x) zv_finput(stdin,x)
#define zm_input(A) zm_finput(stdin,A)
#define z_output(z) z_foutput(stdout,z)
#define zv_output(x) zv_foutput(stdout,x)
#define zm_output(A) zm_foutput(stdout,A)
#define ZV_FREE(x) ( zv_free(x), (x) = ZVNULL )
#define ZM_FREE(A) ( zm_free(A), (A) = ZMNULL )
#define zin_prod(x,y) _zin_prod(x,y,0,Z_CONJ)
#define zv_norm1(x) _zv_norm1(x,VNULL)
#define zv_norm2(x) _zv_norm2(x,VNULL)
#define zv_norm_inf(x) _zv_norm_inf(x,VNULL)
#endif
|
