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The above coverage report was generated for the changes in this PR. |
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/stdlib update-copyright-years |
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Signed-off-by: Athan <[email protected]>
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# dlarf1f | ||
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> Apply a real elementary reflector `H = I - tau * v * v ^ T` to a real M by N matrix `C`. |
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> Apply a real elementary reflector `H = I - tau * v * v ^ T` to a real M by N matrix `C`. | |
> Apply a real elementary reflector `H = I - tau * v * v^T` to a real M by N matrix `C`. |
Applies here and throughout this PR. This follows conventions used elsewhere in stdlib regarding the transpose of a matrix/vector.
The function has the following parameters: | ||
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- **order**: storage layout. | ||
- **side**: specifies the side of multiplication with `C`. Use `left` to form `H * C` and `right` to from `C * H`. |
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- **side**: specifies the side of multiplication with `C`. Use `left` to form `H * C` and `right` to from `C * H`. | |
- **side**: specifies the side of multiplication with `C`. Use `'left'` to form `H * C` and `'right'` to form `C * H`. |
Based on the `side` of multiplication, the expected storage of the array changes: | ||
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- `work` should have `N` indexed elements if `side` = `left` and `M` indexed elements if `side` = `right`. | ||
- `V` should have `1 + (M-1) * abs(incv)` indexed elements if `side` = `left` and `1 + (N-1) * abs(incv)` indexed elements if `side` = `right`. |
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Based on the `side` of multiplication, the expected storage of the array changes: | |
- `work` should have `N` indexed elements if `side` = `left` and `M` indexed elements if `side` = `right`. | |
- `V` should have `1 + (M-1) * abs(incv)` indexed elements if `side` = `left` and `1 + (N-1) * abs(incv)` indexed elements if `side` = `right`. | |
When `side` is `'left'`, | |
- `work` should have `N` indexed elements. | |
- `V` should have `1 + (M-1) * abs(incv)` indexed elements. | |
When `side` is `'right'`, | |
- `work` should have `M` indexed elements. | |
- `V` should have `1 + (N-1) * abs(incv)` indexed elements. |
- **side**: specifies the side of multiplication with `C`. Use `left` to form `H * C` and `right` to from `C * H`. | ||
- **M**: number of rows in `C`. | ||
- **N**: number of columns in `C`. | ||
- **V**: the vector `v` in the representation of `H` as a [`Float64Array`][mdn-float64array]. |
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- **V**: the vector `v` in the representation of `H` as a [`Float64Array`][mdn-float64array]. | |
- **V**: the vector `v` as a [`Float64Array`][mdn-float64array]. |
- **N**: number of columns in `C`. | ||
- **V**: the vector `v` in the representation of `H` as a [`Float64Array`][mdn-float64array]. | ||
- **incv**: stride length for `V`. If `incv` is negative, the elements of `V` are accessed in reverse order. | ||
- **tau**: the value of `tau` in representation of `H`. |
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- **tau**: the value of `tau` in representation of `H`. | |
- **tau**: scalar constant. |
var Float64Array = require( '@stdlib/array/float64' ); | ||
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var C = new Float64Array( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] ); | ||
var V = new Float64Array( [ 0.5, 0.5, 0.5, 0.5 ] ); | ||
var work = new Float64Array( 3 ); | ||
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var out = dlarf1f( 'row-major', 'left', 4, 3, V, -1, 1.0, C, 3, work ); | ||
// returns <Float64Array>[ -4.5, -10.5, -16.5, -0.75, -1.75, -2.75, 0.25, -0.75, -1.75, 1.25, 0.25, -0.75 ] |
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This example is not super informative, as V
is symmetric. Whether you go forward or reverse, you get the same values. I suggest updating this example to make it more meaningful.
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The function has the following additional parameters: | ||
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- **side**: specifies the side of multiplication with `C`. Use `left` to form `H * C` and `right` to from `C * H`. |
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Same edits here as done above.
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Based on the `side` of multiplication, the expected storage of the array changes: | ||
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- `work` should have `N` indexed elements if `side` = `left` and `M` indexed elements if `side` = `right`. |
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Same comments as above.
Number of columns in `C`. | ||
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V: Float64Array | ||
The vector `v` in the representation of `H`. |
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Same comments as elsewhere, and likely applicable throughout this PR.
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lapack/base/dlarf1f
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