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[project @ 2006-03-07 15:57:52 by jwe]
author jwe
date Tue, 07 Mar 2006 15:57:52 +0000
parents 09a3064a3a17
children fd42779a8428
comparison
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5646:2b20d1707f29 5647:9e3a2d1e5e72
1 @node Matrix Factorizations, Ranges, Matrix and Vector Operations, Top 1 @node Matrix Factorizations, Ranges, Matrix and Vector Operations, Top
2 @chapter Matrix Factorizations 2 @chapter Matrix Factorizations
3 @cindex matrix factorizations 3 @cindex matrix factorizations
4 @cindex factorizations 4 @cindex factorizations
5 5
6 @deftypefn {} {}AEPBALANCE (void) 6 @deftypefn {} {} AEPBALANCE (void)
7 @deftypefnx {} {}AEPBALANCE (const Matrix &@var{a}, const char *@var{balance_job}) 7 @deftypefnx {} {} AEPBALANCE (const Matrix &@var{a}, const char *@var{balance_job})
8 @deftypefnx {} {}AEPBALANCE (const AEPBALANCE &@var{a}) 8 @deftypefnx {} {} AEPBALANCE (const AEPBALANCE &@var{a})
9 @end deftypefn 9 @end deftypefn
10 10
11 @deftypefn {} AEPBALANCE& {operator =} (const AEPBALANCE &@var{a}) 11 @deftypefn {} AEPBALANCE& {operator =} (const AEPBALANCE &@var{a})
12 @end deftypefn 12 @end deftypefn
13 13
16 @end deftypefn 16 @end deftypefn
17 17
18 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const AEPBALANCE &@var{a}) 18 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const AEPBALANCE &@var{a})
19 @end deftypefn 19 @end deftypefn
20 20
21 @deftypefn {} ComplexAEPBALANCE (void) 21 @deftypefn {} {} ComplexAEPBALANCE (void)
22 @deftypefnx {} ComplexAEPBALANCE (const ComplexMatrix &@var{a}, const char *@var{balance_job}) 22 @deftypefnx {} {} ComplexAEPBALANCE (const ComplexMatrix &@var{a}, const char *@var{balance_job})
23 @deftypefnx {} ComplexAEPBALANCE (const ComplexAEPBALANCE &@var{a}) 23 @deftypefnx {} {} ComplexAEPBALANCE (const ComplexAEPBALANCE &@var{a})
24 @end deftypefn 24 @end deftypefn
25 25
26 @deftypefn {} ComplexAEPBALANCE& {operator =} (const ComplexAEPBALANCE &@var{a}) 26 @deftypefn {} ComplexAEPBALANCE& {operator =} (const ComplexAEPBALANCE &@var{a})
27 @end deftypefn 27 @end deftypefn
28 28
31 @end deftypefn 31 @end deftypefn
32 32
33 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexAEPBALANCE &@var{a}) 33 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexAEPBALANCE &@var{a})
34 @end deftypefn 34 @end deftypefn
35 35
36 @deftypefn {} {}DET (void) 36 @deftypefn {} {} DET (void)
37 @deftypefnx {} {}DET (const DET &@var{a}) 37 @deftypefnx {} {} DET (const DET &@var{a})
38 @end deftypefn 38 @end deftypefn
39 39
40 @deftypefn {} DET& {operator =} (const DET &@var{a}) 40 @deftypefn {} DET& {operator =} (const DET &@var{a})
41 @end deftypefn 41 @end deftypefn
42 42
50 @end deftypefn 50 @end deftypefn
51 51
52 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const DET &@var{a}) 52 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const DET &@var{a})
53 @end deftypefn 53 @end deftypefn
54 54
55 @deftypefn {} {}ComplexDET (void) 55 @deftypefn {} {} ComplexDET (void)
56 @deftypefnx {} {}ComplexDET (const ComplexDET &@var{a}) 56 @deftypefnx {} {} ComplexDET (const ComplexDET &@var{a})
57 @end deftypefn 57 @end deftypefn
58 58
59 @deftypefn {} ComplexDET& {operator =} (const ComplexDET &@var{a}) 59 @deftypefn {} ComplexDET& {operator =} (const ComplexDET &@var{a})
60 @end deftypefn 60 @end deftypefn
61 61
69 @end deftypefn 69 @end deftypefn
70 70
71 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexDET &@var{a}) 71 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexDET &@var{a})
72 @end deftypefn 72 @end deftypefn
73 73
74 @deftypefn {} {}GEPBALANCE (void) 74 @deftypefn {} {} GEPBALANCE (void)
75 @deftypefnx {} {}GEPBALANCE (const Matrix &@var{a}, const Matrix &, const char *@var{balance_job}) 75 @deftypefnx {} {} GEPBALANCE (const Matrix &@var{a}, const Matrix &, const char *@var{balance_job})
76 @deftypefnx {} {}GEPBALANCE (const GEPBALANCE &@var{a}) 76 @deftypefnx {} {} GEPBALANCE (const GEPBALANCE &@var{a})
77 @end deftypefn 77 @end deftypefn
78 78
79 @deftypefn {} GEPBALANCE& {operator =} (const GEPBALANCE &@var{a}) 79 @deftypefn {} GEPBALANCE& {operator =} (const GEPBALANCE &@var{a})
80 @end deftypefn 80 @end deftypefn
81 81
86 @end deftypefn 86 @end deftypefn
87 87
88 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const GEPBALANCE &@var{a}) 88 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const GEPBALANCE &@var{a})
89 @end deftypefn 89 @end deftypefn
90 90
91 @deftypefn {} {}CHOL (void) 91 @deftypefn {} {} CHOL (void)
92 @deftypefnx {} {}CHOL (const Matrix &@var{a}) 92 @deftypefnx {} {} CHOL (const Matrix &@var{a})
93 @deftypefnx {} {}CHOL (const Matrix &@var{a}, int &@var{info}) 93 @deftypefnx {} {} CHOL (const Matrix &@var{a}, int &@var{info})
94 @deftypefnx {} {}CHOL (const CHOL &@var{a}) 94 @deftypefnx {} {} CHOL (const CHOL &@var{a})
95 @end deftypefn 95 @end deftypefn
96 96
97 @deftypefn {} CHOL& {operator =} (const CHOL &@var{a}) 97 @deftypefn {} CHOL& {operator =} (const CHOL &@var{a})
98 @end deftypefn 98 @end deftypefn
99 99
101 @end deftypefn 101 @end deftypefn
102 102
103 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const CHOL &@var{a}) 103 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const CHOL &@var{a})
104 @end deftypefn 104 @end deftypefn
105 105
106 @deftypefn {} {}ComplexCHOL (void) 106 @deftypefn {} {} ComplexCHOL (void)
107 @deftypefnx {} {}ComplexCHOL (const ComplexMatrix &@var{a}) 107 @deftypefnx {} {} ComplexCHOL (const ComplexMatrix &@var{a})
108 @deftypefnx {} {}ComplexCHOL (const ComplexMatrix &@var{a}, int &@var{info}) 108 @deftypefnx {} {} ComplexCHOL (const ComplexMatrix &@var{a}, int &@var{info})
109 @deftypefnx {} {}ComplexCHOL (const ComplexCHOL &@var{a}) 109 @deftypefnx {} {} ComplexCHOL (const ComplexCHOL &@var{a})
110 @end deftypefn 110 @end deftypefn
111 111
112 @deftypefn {} ComplexCHOL& {operator =} (const ComplexCHOL &@var{a}) 112 @deftypefn {} ComplexCHOL& {operator =} (const ComplexCHOL &@var{a})
113 @end deftypefn 113 @end deftypefn
114 114
116 @end deftypefn 116 @end deftypefn
117 117
118 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexCHOL &@var{a}) 118 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexCHOL &@var{a})
119 @end deftypefn 119 @end deftypefn
120 120
121 @deftypefn {} {}HESS (void) 121 @deftypefn {} {} HESS (void)
122 @deftypefnx {} {}HESS (const Matrix &@var{a}) 122 @deftypefnx {} {} HESS (const Matrix &@var{a})
123 @deftypefnx {} {}HESS (const Matrix&a, int &@var{info}) 123 @deftypefnx {} {} HESS (const Matrix&a, int &@var{info})
124 @deftypefnx {} {}HESS (const HESS &@var{a}) 124 @deftypefnx {} {} HESS (const HESS &@var{a})
125 @end deftypefn 125 @end deftypefn
126 126
127 @deftypefn {} HESS& {operator =} (const HESS &@var{a}) 127 @deftypefn {} HESS& {operator =} (const HESS &@var{a})
128 @end deftypefn 128 @end deftypefn
129 129
132 @end deftypefn 132 @end deftypefn
133 133
134 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const HESS &@var{a}) 134 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const HESS &@var{a})
135 @end deftypefn 135 @end deftypefn
136 136
137 @deftypefn {} {}ComplexHESS (void) 137 @deftypefn {} {} ComplexHESS (void)
138 @deftypefnx {} {}ComplexHESS (const ComplexMatrix &@var{a}) 138 @deftypefnx {} {} ComplexHESS (const ComplexMatrix &@var{a})
139 @deftypefnx {} {}ComplexHESS (const ComplexMatrix &@var{a}, int &@var{info}) 139 @deftypefnx {} {} ComplexHESS (const ComplexMatrix &@var{a}, int &@var{info})
140 @deftypefnx {} {}ComplexHESS (const ComplexHESS &@var{a}) 140 @deftypefnx {} {} ComplexHESS (const ComplexHESS &@var{a})
141 @end deftypefn 141 @end deftypefn
142 142
143 @deftypefn {} ComplexHESS& {operator =} (const ComplexHESS &@var{a}) 143 @deftypefn {} ComplexHESS& {operator =} (const ComplexHESS &@var{a})
144 @end deftypefn 144 @end deftypefn
145 145
148 @end deftypefn 148 @end deftypefn
149 149
150 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexHESS &@var{a}) 150 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexHESS &@var{a})
151 @end deftypefn 151 @end deftypefn
152 152
153 @deftypefn {} {}SCHUR (void) 153 @deftypefn {} {} SCHUR (void)
154 @deftypefnx {} {}SCHUR (const Matrix &@var{a}, const char *@var{ord}) 154 @deftypefnx {} {} SCHUR (const Matrix &@var{a}, const char *@var{ord})
155 @deftypefnx {} {}SCHUR (const Matrix &@var{a}, const char *@var{ord}, int &@var{info}) 155 @deftypefnx {} {} SCHUR (const Matrix &@var{a}, const char *@var{ord}, int &@var{info})
156 @deftypefnx {} {}SCHUR (const SCHUR &@var{a}, const char *@var{ord}) 156 @deftypefnx {} {} SCHUR (const SCHUR &@var{a}, const char *@var{ord})
157 @end deftypefn 157 @end deftypefn
158 158
159 @deftypefn {} SCHUR& {operator =} (const SCHUR &@var{a}) 159 @deftypefn {} SCHUR& {operator =} (const SCHUR &@var{a})
160 @end deftypefn 160 @end deftypefn
161 161
164 @end deftypefn 164 @end deftypefn
165 165
166 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const SCHUR &@var{a}) 166 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const SCHUR &@var{a})
167 @end deftypefn 167 @end deftypefn
168 168
169 @deftypefn {} {}ComplexSCHUR (void) 169 @deftypefn {} {} ComplexSCHUR (void)
170 @deftypefnx {} {}ComplexSCHUR (const ComplexMatrix &@var{a}, const char *@var{ord}) 170 @deftypefnx {} {} ComplexSCHUR (const ComplexMatrix &@var{a}, const char *@var{ord})
171 @deftypefnx {} {}ComplexSCHUR (const ComplexMatrix &@var{a}, const char *@var{ord}, int &@var{info}) 171 @deftypefnx {} {} ComplexSCHUR (const ComplexMatrix &@var{a}, const char *@var{ord}, int &@var{info})
172 @deftypefnx {} {}ComplexSCHUR (const ComplexSCHUR &@var{a}, const char *@var{ord}) 172 @deftypefnx {} {} ComplexSCHUR (const ComplexSCHUR &@var{a}, const char *@var{ord})
173 @end deftypefn 173 @end deftypefn
174 174
175 @deftypefn {} ComplexSCHUR& {operator =} (const ComplexSCHUR &@var{a}) 175 @deftypefn {} ComplexSCHUR& {operator =} (const ComplexSCHUR &@var{a})
176 @end deftypefn 176 @end deftypefn
177 177
180 @end deftypefn 180 @end deftypefn
181 181
182 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexSCHUR &@var{a}) 182 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexSCHUR &@var{a})
183 @end deftypefn 183 @end deftypefn
184 184
185 @deftypefn {} {}SVD (void) 185 @deftypefn {} {} SVD (void)
186 @deftypefnx {} {}SVD (const Matrix &@var{a}) 186 @deftypefnx {} {} SVD (const Matrix &@var{a})
187 @deftypefnx {} {}SVD (const Matrix &@var{a}, int &@var{info}) 187 @deftypefnx {} {} SVD (const Matrix &@var{a}, int &@var{info})
188 @deftypefnx {} {}SVD (const SVD &@var{a}) 188 @deftypefnx {} {} SVD (const SVD &@var{a})
189 @end deftypefn 189 @end deftypefn
190 190
191 @deftypefn {} SVD& {operator =} (const SVD &@var{a}) 191 @deftypefn {} SVD& {operator =} (const SVD &@var{a})
192 @end deftypefn 192 @end deftypefn
193 193
197 @end deftypefn 197 @end deftypefn
198 198
199 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const SVD &@var{a}) 199 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const SVD &@var{a})
200 @end deftypefn 200 @end deftypefn
201 201
202 @deftypefn {} {}ComplexSVD (void) 202 @deftypefn {} {} ComplexSVD (void)
203 @deftypefnx {} {}ComplexSVD (const ComplexMatrix &@var{a}) 203 @deftypefnx {} {} ComplexSVD (const ComplexMatrix &@var{a})
204 @deftypefnx {} {}ComplexSVD (const ComplexMatrix &@var{a}, int &@var{info}) 204 @deftypefnx {} {} ComplexSVD (const ComplexMatrix &@var{a}, int &@var{info})
205 @deftypefnx {} {}ComplexSVD (const ComplexSVD &@var{a}) 205 @deftypefnx {} {} ComplexSVD (const ComplexSVD &@var{a})
206 @end deftypefn 206 @end deftypefn
207 207
208 @deftypefn {} ComplexSVD& {operator =} (const ComplexSVD &@var{a}) 208 @deftypefn {} ComplexSVD& {operator =} (const ComplexSVD &@var{a})
209 @end deftypefn 209 @end deftypefn
210 210
214 @end deftypefn 214 @end deftypefn
215 215
216 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexSVD &@var{a}) 216 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexSVD &@var{a})
217 @end deftypefn 217 @end deftypefn
218 218
219 @deftypefn {} {}EIG (void) 219 @deftypefn {} {} EIG (void)
220 @deftypefnx {} {}EIG (const Matrix &@var{a}) 220 @deftypefnx {} {} EIG (const Matrix &@var{a})
221 @deftypefnx {} {}EIG (const Matrix &@var{a}, int &@var{info}) 221 @deftypefnx {} {} EIG (const Matrix &@var{a}, int &@var{info})
222 @deftypefnx {} {}EIG (const ComplexMatrix &@var{a}) 222 @deftypefnx {} {} EIG (const ComplexMatrix &@var{a})
223 @deftypefnx {} {}EIG (const ComplexMatrix &@var{a}, int &@var{info}) 223 @deftypefnx {} {} EIG (const ComplexMatrix &@var{a}, int &@var{info})
224 @deftypefnx {} {}EIG (const EIG &@var{a}) 224 @deftypefnx {} {} EIG (const EIG &@var{a})
225 @end deftypefn 225 @end deftypefn
226 226
227 @deftypefn {} EIG& {operator =} (const EIG &@var{a}) 227 @deftypefn {} EIG& {operator =} (const EIG &@var{a})
228 @end deftypefn 228 @end deftypefn
229 229
234 @end deftypefn 234 @end deftypefn
235 235
236 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const EIG &@var{a}) 236 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const EIG &@var{a})
237 @end deftypefn 237 @end deftypefn
238 238
239 @deftypefn {} {}LU (void) 239 @deftypefn {} {} LU (void)
240 @deftypefnx {} {}LU (const Matrix &@var{a}) 240 @deftypefnx {} {} LU (const Matrix &@var{a})
241 @deftypefnx {} {}LU (const LU &@var{a}) 241 @deftypefnx {} {} LU (const LU &@var{a})
242 @end deftypefn 242 @end deftypefn
243 243
244 @deftypefn {} LU& {operator =} (const LU &@var{a}) 244 @deftypefn {} LU& {operator =} (const LU &@var{a})
245 @end deftypefn 245 @end deftypefn
246 246
250 @end deftypefn 250 @end deftypefn
251 251
252 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const LU &@var{a}) 252 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const LU &@var{a})
253 @end deftypefn 253 @end deftypefn
254 254
255 @deftypefn {} {}ComplexLU (void) 255 @deftypefn {} {} ComplexLU (void)
256 @deftypefnx {} {}ComplexLU (const ComplexMatrix &@var{a}) 256 @deftypefnx {} {} ComplexLU (const ComplexMatrix &@var{a})
257 @deftypefnx {} {}ComplexLU (const ComplexLU &@var{a}) 257 @deftypefnx {} {} ComplexLU (const ComplexLU &@var{a})
258 @end deftypefn 258 @end deftypefn
259 259
260 @deftypefn {} ComplexLU& {operator =} (const ComplexLU &@var{a}) 260 @deftypefn {} ComplexLU& {operator =} (const ComplexLU &@var{a})
261 @end deftypefn 261 @end deftypefn
262 262
266 @end deftypefn 266 @end deftypefn
267 267
268 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexLU &@var{a}) 268 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const ComplexLU &@var{a})
269 @end deftypefn 269 @end deftypefn
270 270
271 @deftypefn {} {}QR (void) 271 @deftypefn {} {} QR (void)
272 @deftypefnx {} {}QR (const Matrix &@var{A}) 272 @deftypefnx {} {} QR (const Matrix &@var{A})
273 @deftypefnx {} {}QR (const QR &@var{a}) 273 @deftypefnx {} {} QR (const QR &@var{a})
274 @end deftypefn 274 @end deftypefn
275 275
276 @deftypefn {} QR& {operator =} (const QR &@var{a}) 276 @deftypefn {} QR& {operator =} (const QR &@var{a})
277 @end deftypefn 277 @end deftypefn
278 278
281 @end deftypefn 281 @end deftypefn
282 282
283 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const QR &@var{a}) 283 @deftypefn {} {ostream&} {operator <<} (ostream &@var{os}, const QR &@var{a})
284 @end deftypefn 284 @end deftypefn
285 285
286 @deftypefn {} {}ComplexQR (void) 286 @deftypefn {} {} ComplexQR (void)
287 @deftypefnx {} {}ComplexQR (const ComplexMatrix &@var{A}) 287 @deftypefnx {} {} ComplexQR (const ComplexMatrix &@var{A})
288 @deftypefnx {} {}ComplexQR (const ComplexQR &@var{a}) 288 @deftypefnx {} {} ComplexQR (const ComplexQR &@var{a})
289 @end deftypefn 289 @end deftypefn
290 290
291 @deftypefn {} ComplexQR& {operator =} (const ComplexQR &@var{a}) 291 @deftypefn {} ComplexQR& {operator =} (const ComplexQR &@var{a})
292 @end deftypefn 292 @end deftypefn
293 293