|
7 | 7 | Compute an orthonormal basis `V` for the image of the matrix `A`, as well as a matrix `C` |
8 | 8 | (the corestriction) such that `A` factors as `A = V * C`. |
9 | 9 |
|
10 | | -This is a high-level wrapper where te keyword arguments can be used to specify and control |
| 10 | +This is a high-level wrapper where the keyword arguments can be used to specify and control |
11 | 11 | the specific orthogonal decomposition that should be used to factor `A`, whereas `trunc` |
12 | 12 | can optionally be used to control the precision in determining the rank of `A`, typically |
13 | 13 | via its singular values. |
14 | 14 |
|
| 15 | +## Truncation |
| 16 | +The optional truncation strategy can be controlled via the `trunc` keyword argument, and |
| 17 | +any non-trivial strategy typically requires an SVD-based decompositions. This keyword can |
| 18 | +be either a `NamedTuple` or a [`TruncationStrategy`](@ref). |
| 19 | +
|
| 20 | +### `trunc::NamedTuple` |
| 21 | +The supported truncation keyword arguments are: |
| 22 | +
|
| 23 | +$(docs_truncation_kwargs) |
| 24 | +
|
| 25 | +### `trunc::TruncationStrategy` |
| 26 | +For more control, a truncation strategy can be supplied directly. |
| 27 | +By default, MatrixAlgebraKit supplies the following: |
| 28 | +
|
| 29 | +$(docs_truncation_strategies) |
| 30 | +
|
15 | 31 | ## Keyword arguments |
16 | 32 | There are 3 major modes of operation, based on the `alg` keyword, with slightly different |
17 | 33 | application purposes. |
@@ -51,22 +67,6 @@ In this expert mode the algorithm is supplied directly, and the kind of decompos |
51 | 67 | deduced from that. This hinges on the implementation of the algorithm trait |
52 | 68 | [`MatrixAlgebraKit.left_orth_kind(alg)`](@ref). |
53 | 69 |
|
54 | | -## Truncation |
55 | | -The optional truncation strategy can be controlled via the `trunc` keyword argument, and |
56 | | -any non-trivial strategy typically requires an SVD-based decompositions. This keyword can |
57 | | -be either a `NamedTuple` or a [`TruncationStrategy`](@ref). |
58 | | -
|
59 | | -### `trunc::NamedTuple` |
60 | | -The supported truncation keyword arguments are: |
61 | | -
|
62 | | -$(docs_truncation_kwargs) |
63 | | -
|
64 | | -### `trunc::TruncationStrategy` |
65 | | -For more control, a truncation strategy can be supplied directly. |
66 | | -By default, MatrixAlgebraKit supplies the following: |
67 | | -
|
68 | | -$(docs_truncation_strategies) |
69 | | -
|
70 | 70 | --- |
71 | 71 |
|
72 | 72 | !!! note |
@@ -96,6 +96,22 @@ the specific orthogonal decomposition that should be used to factor `A`, whereas |
96 | 96 | optionally be used to control the precision in determining the rank of `A`, typically via |
97 | 97 | its singular values. |
98 | 98 |
|
| 99 | +## Truncation |
| 100 | +The optional truncation strategy can be controlled via the `trunc` keyword argument, and |
| 101 | +any non-trivial strategy typically requires an SVD-based decompositions. This keyword can |
| 102 | +be either a `NamedTuple` or a [`TruncationStrategy`](@ref). |
| 103 | +
|
| 104 | +### `trunc::NamedTuple` |
| 105 | +The supported truncation keyword arguments are: |
| 106 | +
|
| 107 | +$(docs_truncation_kwargs) |
| 108 | +
|
| 109 | +### `trunc::TruncationStrategy` |
| 110 | +For more control, a truncation strategy can be supplied directly. |
| 111 | +By default, MatrixAlgebraKit supplies the following: |
| 112 | +
|
| 113 | +$(docs_truncation_strategies) |
| 114 | +
|
99 | 115 | ## Keyword arguments |
100 | 116 | There are 3 major modes of operation, based on the `alg` keyword, with slightly different |
101 | 117 | application purposes. |
@@ -135,22 +151,6 @@ In this expert mode the algorithm is supplied directly, and the kind of decompos |
135 | 151 | deduced from that. This hinges on the implementation of the algorithm trait |
136 | 152 | [`MatrixAlgebraKit.right_orth_kind(alg)`](@ref). |
137 | 153 |
|
138 | | -## Truncation |
139 | | -The optional truncation strategy can be controlled via the `trunc` keyword argument, and |
140 | | -any non-trivial strategy typically requires an SVD-based decompositions. This keyword can |
141 | | -be either a `NamedTuple` or a [`TruncationStrategy`](@ref). |
142 | | -
|
143 | | -### `trunc::NamedTuple` |
144 | | -The supported truncation keyword arguments are: |
145 | | -
|
146 | | -$(docs_truncation_kwargs) |
147 | | -
|
148 | | -### `trunc::TruncationStrategy` |
149 | | -For more control, a truncation strategy can be supplied directly. |
150 | | -By default, MatrixAlgebraKit supplies the following: |
151 | | -
|
152 | | -$(docs_truncation_strategies) |
153 | | -
|
154 | 154 | --- |
155 | 155 |
|
156 | 156 | !!! note |
@@ -182,6 +182,26 @@ the underlying orthogonal decomposition that should be used to find the null spa |
182 | 182 | whereas `trunc` can optionally be used to control the precision in determining the rank of |
183 | 183 | `A`, typically via its singular values. |
184 | 184 |
|
| 185 | +## Truncation |
| 186 | +The optional truncation strategy can be controlled via the `trunc` keyword argument, and any |
| 187 | +non-trivial strategy typically requires an SVD-based decomposition. This keyword can be |
| 188 | +either a `NamedTuple` or a [`TruncationStrategy`](@ref). |
| 189 | +
|
| 190 | +### `trunc::NamedTuple` |
| 191 | +The supported truncation keyword arguments are: |
| 192 | +
|
| 193 | +$(docs_null_truncation_kwargs) |
| 194 | +
|
| 195 | +### `trunc::TruncationStrategy` |
| 196 | +For more control, a truncation strategy can be supplied directly. By default, |
| 197 | +MatrixAlgebraKit supplies the following: |
| 198 | +
|
| 199 | +$(docs_truncation_strategies) |
| 200 | +
|
| 201 | +!!! note |
| 202 | + Here [`notrunc`](@ref) has special meaning, and signifies keeping the values that |
| 203 | + correspond to the exact zeros determined from the additional columns of `A`. |
| 204 | +
|
185 | 205 | ## Keyword arguments |
186 | 206 | There are 3 major modes of operation, based on the `alg` keyword, with slightly different |
187 | 207 | application purposes. |
@@ -215,26 +235,6 @@ In this expert mode the algorithm is supplied directly, and the kind of decompos |
215 | 235 | deduced from that. This hinges on the implementation of the algorithm trait |
216 | 236 | [`MatrixAlgebraKit.left_null_kind(alg)`](@ref). |
217 | 237 |
|
218 | | -## Truncation |
219 | | -The optional truncation strategy can be controlled via the `trunc` keyword argument, and any |
220 | | -non-trivial strategy typically requires an SVD-based decomposition. This keyword can be |
221 | | -either a `NamedTuple` or a [`TruncationStrategy`](@ref). |
222 | | -
|
223 | | -### `trunc::NamedTuple` |
224 | | -The supported truncation keyword arguments are: |
225 | | -
|
226 | | -$(docs_null_truncation_kwargs) |
227 | | -
|
228 | | -### `trunc::TruncationStrategy` |
229 | | -For more control, a truncation strategy can be supplied directly. By default, |
230 | | -MatrixAlgebraKit supplies the following: |
231 | | -
|
232 | | -$(docs_truncation_strategies) |
233 | | -
|
234 | | -!!! note |
235 | | - Here [`notrunc`](@ref) has special meaning, and signifies keeping the values that |
236 | | - correspond to the exact zeros determined from the additional columns of `A`. |
237 | | -
|
238 | 238 | --- |
239 | 239 |
|
240 | 240 | !!! note |
@@ -263,6 +263,26 @@ the underlying orthogonal decomposition that should be used to find the null spa |
263 | 263 | whereas `trunc` can optionally be used to control the precision in determining the rank of |
264 | 264 | `A`, typically via its singular values. |
265 | 265 |
|
| 266 | +## Truncation |
| 267 | +The optional truncation strategy can be controlled via the `trunc` keyword argument, and any |
| 268 | +non-trivial strategy typically requires an SVD-based decomposition. This keyword can be |
| 269 | +either a `NamedTuple` or a [`TruncationStrategy`](@ref). |
| 270 | +
|
| 271 | +### `trunc::NamedTuple` |
| 272 | +The supported truncation keyword arguments are: |
| 273 | +
|
| 274 | +$(docs_null_truncation_kwargs) |
| 275 | +
|
| 276 | +### `trunc::TruncationStrategy` |
| 277 | +For more control, a truncation strategy can be supplied directly. By default, |
| 278 | +MatrixAlgebraKit supplies the following: |
| 279 | +
|
| 280 | +$(docs_truncation_strategies) |
| 281 | +
|
| 282 | +!!! note |
| 283 | + Here [`notrunc`](@ref) has special meaning, and signifies keeping the values that |
| 284 | + correspond to the exact zeros determined from the additional rows of `A`. |
| 285 | +
|
266 | 286 | ## Keyword arguments |
267 | 287 | There are 3 major modes of operation, based on the `alg` keyword, with slightly different |
268 | 288 | application purposes. |
@@ -296,26 +316,6 @@ In this expert mode the algorithm is supplied directly, and the kind of decompos |
296 | 316 | deduced from that. This hinges on the implementation of the algorithm trait |
297 | 317 | [`MatrixAlgebraKit.right_null_kind(alg)`](@ref). |
298 | 318 |
|
299 | | -## Truncation |
300 | | -The optional truncation strategy can be controlled via the `trunc` keyword argument, and any |
301 | | -non-trivial strategy typically requires an SVD-based decomposition. This keyword can be |
302 | | -either a `NamedTuple` or a [`TruncationStrategy`](@ref). |
303 | | -
|
304 | | -### `trunc::NamedTuple` |
305 | | -The supported truncation keyword arguments are: |
306 | | -
|
307 | | -$(docs_null_truncation_kwargs) |
308 | | -
|
309 | | -### `trunc::TruncationStrategy` |
310 | | -For more control, a truncation strategy can be supplied directly. By default, |
311 | | -MatrixAlgebraKit supplies the following: |
312 | | -
|
313 | | -$(docs_truncation_strategies) |
314 | | -
|
315 | | -!!! note |
316 | | - Here [`notrunc`](@ref) has special meaning, and signifies keeping the values that |
317 | | - correspond to the exact zeros determined from the additional rows of `A`. |
318 | | -
|
319 | 319 | --- |
320 | 320 |
|
321 | 321 | !!! note |
|
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