-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathmat_lzz_p.cpp.html
181 lines (121 loc) · 9.47 KB
/
mat_lzz_p.cpp.html
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
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd">
<html>
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
<title>/Volumes/Unix/unix-files.noindex/ntl-new/ntl-9.6.0/doc/mat_lzz_p.cpp.html</title>
<meta name="Generator" content="Vim/7.3">
<meta name="plugin-version" content="vim7.3_v6">
<meta name="syntax" content="cpp">
<meta name="settings" content="use_css">
<style type="text/css">
<!--
pre { font-family: monospace; color: #000000; background-color: #ffffff; }
body { font-family: monospace; color: #000000; background-color: #ffffff; }
.Statement { color: #b03060; font-weight: bold; }
.Type { color: #008b00; font-weight: bold; }
.String { color: #4a708b; }
.PreProc { color: #1874cd; }
.Comment { color: #0000ee; font-style: italic; }
-->
</style>
</head>
<body>
<pre>
<span class="Comment">/*</span><span class="Comment">*************************************************************************\</span>
<span class="Comment">MODULE: mat_zz_p</span>
<span class="Comment">SUMMARY:</span>
<span class="Comment">Defines the class mat_zz_p.</span>
<span class="Comment">\*************************************************************************</span><span class="Comment">*/</span>
<span class="PreProc">#include </span><span class="String"><NTL/matrix.h></span>
<span class="PreProc">#include </span><span class="String">"vec_vec_zz_p.h"</span>
<span class="Type">typedef</span> Mat<zz_p> mat_zz_p; <span class="Comment">// backward compatibility</span>
<span class="Type">void</span> add(mat_zz_p& X, <span class="Type">const</span> mat_zz_p& A, <span class="Type">const</span> mat_zz_p& B);
<span class="Comment">// X = A + B</span>
<span class="Type">void</span> sub(mat_zz_p& X, <span class="Type">const</span> mat_zz_p& A, <span class="Type">const</span> mat_zz_p& B);
<span class="Comment">// X = A - B</span>
<span class="Type">void</span> mul(mat_zz_p& X, <span class="Type">const</span> mat_zz_p& A, <span class="Type">const</span> mat_zz_p& B);
<span class="Comment">// X = A * B</span>
<span class="Type">void</span> mul(vec_zz_p& x, <span class="Type">const</span> mat_zz_p& A, <span class="Type">const</span> vec_zz_p& b);
<span class="Comment">// x = A * b</span>
<span class="Type">void</span> mul(vec_zz_p& x, <span class="Type">const</span> vec_zz_p& a, <span class="Type">const</span> mat_zz_p& B);
<span class="Comment">// x = a * B</span>
<span class="Type">void</span> mul(mat_zz_p& X, <span class="Type">const</span> mat_zz_p& A, zz_p b);
<span class="Type">void</span> mul(mat_zz_p& X, <span class="Type">const</span> mat_zz_p& A, <span class="Type">long</span> b);
<span class="Comment">// X = A * b</span>
<span class="Type">void</span> mul(mat_zz_p& X, zz_p a, <span class="Type">const</span> mat_zz_p& B);
<span class="Type">void</span> mul(mat_zz_p& X, <span class="Type">long</span> a, <span class="Type">const</span> mat_zz_p& B);
<span class="Comment">// X = a * B</span>
<span class="Type">void</span> determinant(zz_p& d, <span class="Type">const</span> mat_zz_p& A);
zz_p determinant(<span class="Type">const</span> mat_zz_p& a);
<span class="Comment">// d = determinant(A)</span>
<span class="Type">void</span> transpose(mat_zz_p& X, <span class="Type">const</span> mat_zz_p& A);
mat_zz_p transpose(<span class="Type">const</span> mat_zz_p& A);
<span class="Comment">// X = transpose of A</span>
<span class="Type">void</span> solve(zz_p& d, vec_zz_p& X,
<span class="Type">const</span> mat_zz_p& A, <span class="Type">const</span> vec_zz_p& b);
<span class="Comment">// A is an n x n matrix, b is a length n vector. Computes d =</span>
<span class="Comment">// determinant(A). If d != 0, solves x*A = b.</span>
<span class="Type">void</span> inv(zz_p& d, mat_zz_p& X, <span class="Type">const</span> mat_zz_p& A);
<span class="Comment">// A is an n x n matrix. Computes d = determinant(A). If d != 0,</span>
<span class="Comment">// computes X = A^{-1}.</span>
<span class="Type">void</span> sqr(mat_zz_p& X, <span class="Type">const</span> mat_zz_p& A);
mat_zz_p sqr(<span class="Type">const</span> mat_zz_p& A);
<span class="Comment">// X = A*A </span>
<span class="Type">void</span> inv(mat_zz_p& X, <span class="Type">const</span> mat_zz_p& A);
mat_zz_p inv(<span class="Type">const</span> mat_zz_p& A);
<span class="Comment">// X = A^{-1}; error is raised if A is singular</span>
<span class="Type">void</span> power(mat_zz_p& X, <span class="Type">const</span> mat_zz_p& A, <span class="Type">const</span> ZZ& e);
mat_zz_p power(<span class="Type">const</span> mat_zz_p& A, <span class="Type">const</span> ZZ& e);
<span class="Type">void</span> power(mat_zz_p& X, <span class="Type">const</span> mat_zz_p& A, <span class="Type">long</span> e);
mat_zz_p power(<span class="Type">const</span> mat_zz_p& A, <span class="Type">long</span> e);
<span class="Comment">// X = A^e; e may be negative (in which case A must be nonsingular).</span>
<span class="Type">void</span> ident(mat_zz_p& X, <span class="Type">long</span> n);
mat_zz_p ident_mat_zz_p(<span class="Type">long</span> n);
<span class="Comment">// X = n x n identity matrix</span>
<span class="Type">long</span> IsIdent(<span class="Type">const</span> mat_zz_p& A, <span class="Type">long</span> n);
<span class="Comment">// test if A is the n x n identity matrix</span>
<span class="Type">void</span> diag(mat_zz_p& X, <span class="Type">long</span> n, zz_p d);
mat_zz_p diag(<span class="Type">long</span> n, zz_p d);
<span class="Comment">// X = n x n diagonal matrix with d on diagonal</span>
<span class="Type">long</span> IsDiag(<span class="Type">const</span> mat_zz_p& A, <span class="Type">long</span> n, zz_p d);
<span class="Comment">// test if X is an n x n diagonal matrix with d on diagonal</span>
<span class="Type">long</span> gauss(mat_zz_p& M);
<span class="Type">long</span> gauss(mat_zz_p& M, <span class="Type">long</span> w);
<span class="Comment">// Performs unitary row operations so as to bring M into row echelon</span>
<span class="Comment">// form. If the optional argument w is supplied, stops when first w</span>
<span class="Comment">// columns are in echelon form. The return value is the rank (or the</span>
<span class="Comment">// rank of the first w columns).</span>
<span class="Type">void</span> image(mat_zz_p& X, <span class="Type">const</span> mat_zz_p& A);
<span class="Comment">// The rows of X are computed as basis of A's row space. X is is row</span>
<span class="Comment">// echelon form</span>
<span class="Type">void</span> kernel(mat_zz_p& X, <span class="Type">const</span> mat_zz_p& A);
<span class="Comment">// Computes a basis for the kernel of the map x -> x*A. where x is a</span>
<span class="Comment">// row vector.</span>
<span class="Comment">// miscellaneous:</span>
<span class="Type">void</span> clear(mat_zz_p& a);
<span class="Comment">// x = 0 (dimension unchanged)</span>
<span class="Type">long</span> IsZero(<span class="Type">const</span> mat_zz_p& a);
<span class="Comment">// test if a is the zero matrix (any dimension)</span>
<span class="Comment">// operator notation:</span>
mat_zz_p <span class="Statement">operator</span>+(<span class="Type">const</span> mat_zz_p& a, <span class="Type">const</span> mat_zz_p& b);
mat_zz_p <span class="Statement">operator</span>-(<span class="Type">const</span> mat_zz_p& a, <span class="Type">const</span> mat_zz_p& b);
mat_zz_p <span class="Statement">operator</span>*(<span class="Type">const</span> mat_zz_p& a, <span class="Type">const</span> mat_zz_p& b);
mat_zz_p <span class="Statement">operator</span>-(<span class="Type">const</span> mat_zz_p& a);
<span class="Comment">// matrix/scalar multiplication:</span>
mat_zz_p <span class="Statement">operator</span>*(<span class="Type">const</span> mat_zz_p& a, zz_p b);
mat_zz_p <span class="Statement">operator</span>*(<span class="Type">const</span> mat_zz_p& a, <span class="Type">long</span> b);
mat_zz_p <span class="Statement">operator</span>*(zz_p a, <span class="Type">const</span> mat_zz_p& b);
mat_zz_p <span class="Statement">operator</span>*(<span class="Type">long</span> a, <span class="Type">const</span> mat_zz_p& b);
<span class="Comment">// matrix/vector multiplication:</span>
vec_zz_p <span class="Statement">operator</span>*(<span class="Type">const</span> mat_zz_p& a, <span class="Type">const</span> vec_zz_p& b);
vec_zz_p <span class="Statement">operator</span>*(<span class="Type">const</span> vec_zz_p& a, <span class="Type">const</span> mat_zz_p& b);
<span class="Comment">// assignment operator notation:</span>
mat_zz_p& <span class="Statement">operator</span>+=(mat_zz_p& x, <span class="Type">const</span> mat_zz_p& a);
mat_zz_p& <span class="Statement">operator</span>-=(mat_zz_p& x, <span class="Type">const</span> mat_zz_p& a);
mat_zz_p& <span class="Statement">operator</span>*=(mat_zz_p& x, <span class="Type">const</span> mat_zz_p& a);
mat_zz_p& <span class="Statement">operator</span>*=(mat_zz_p& x, zz_p a);
mat_zz_p& <span class="Statement">operator</span>*=(mat_zz_p& x, <span class="Type">long</span> a);
vec_zz_p& <span class="Statement">operator</span>*=(vec_zz_p& x, <span class="Type">const</span> mat_zz_p& a);
</pre>
</body>
</html>