Document using matrix-free operators #610
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| A = [-2.0 1 0 0 0 | ||
| 1 -2 1 0 0 | ||
| 0 1 -2 1 0 | ||
| 0 0 1 -2 1 | ||
| 0 0 0 1 -2] |
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| A = [-2.0 1 0 0 0 | |
| 1 -2 1 0 0 | |
| 0 1 -2 1 0 | |
| 0 0 1 -2 1 | |
| 0 0 0 1 -2] | |
| A = [-2.0 1 0 0 0 | |
| 1 -2 1 0 0 | |
| 0 1 -2 1 0 | |
| 0 0 1 -2 1 | |
| 0 0 0 1 -2] |
| non-constant operators, operator algebras, and many more features). This is done by: | ||
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| ```@example linsys1 | ||
| function Afunc!(w,v,u,p,t) |
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| function Afunc!(w,v,u,p,t) | |
| function Afunc!(w, v, u, p, t) |
| function Afunc!(w,v,u,p,t) | ||
| w[1] = -2v[1] + v[2] | ||
| for i in 2:4 | ||
| w[i] = v[i-1] - 2v[i] + v[i+1] |
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| w[i] = v[i-1] - 2v[i] + v[i+1] | |
| w[i] = v[i - 1] - 2v[i] + v[i + 1] |
| nothing | ||
| end | ||
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| function Afunc!(v,u,p,t) |
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| function Afunc!(v,u,p,t) | |
| function Afunc!(v, u, p, t) |
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| function Afunc!(v,u,p,t) | ||
| w = zeros(5) | ||
| Afunc!(w,v,u,p,t) |
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| Afunc!(w,v,u,p,t) | |
| Afunc!(w, v, u, p, t) |
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| ```@example linsys1 | ||
| v = rand(5) | ||
| mfopA*v - A*v |
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| mfopA*v - A*v | |
| mfopA * v - A * v |
| ``` | ||
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| !!! note | ||
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| Note that not all methods can use a matrix-free operator. For example, `LUFactorization()` requires a matrix. If you use an | ||
| invalid method, you will get an error. The methods particularly from KrylovJL are the ones preferred for these cases | ||
| (and are defaulted to). |
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| Note that not all methods can use a matrix-free operator. For example, `LUFactorization()` requires a matrix. If you use an | |
| invalid method, you will get an error. The methods particularly from KrylovJL are the ones preferred for these cases | |
| (and are defaulted to). | |
| Note that not all methods can use a matrix-free operator. For example, `LUFactorization()` requires a matrix. If you use an | |
| invalid method, you will get an error. The methods particularly from KrylovJL are the ones preferred for these cases | |
| (and are defaulted to). |
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