tmp/tmpan6pjwwt/{from.md → to.md}
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| 1 |
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#### Infinity norm of a matrix <a id="linalg.algs.blas1.matinfnorm">[[linalg.algs.blas1.matinfnorm]]</a>
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[*Note 1*: These functions exist in the BLAS standard but are not part
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of the reference implementation. — *end note*]
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``` cpp
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template<in-matrix InMat, class Scalar>
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Scalar matrix_inf_norm(InMat A, Scalar init);
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template<class ExecutionPolicy, in-matrix InMat, class Scalar>
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Scalar matrix_inf_norm(ExecutionPolicy&& exec, InMat A, Scalar init);
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```
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*Mandates:*
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`decltype(`*`abs-if-needed`*`(declval<typename InMat::value_type>()))`
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is convertible to `Scalar`.
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*Returns:*
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- `init` if `A.extent(0)` is zero;
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- otherwise, the sum of `init` and the infinity norm of the matrix `A`.
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[*Note 1*: The infinity norm of the matrix `A` is the maximum over all
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rows of `A`, of the sum of the absolute values of the elements of the
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row. — *end note*]
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*Remarks:* If `InMat::value_type` and `Scalar` are all floating-point
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types or specializations of `complex`, and if `Scalar` has higher
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precision than `InMat::value_type`, then intermediate terms in the sum
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use `Scalar`’s precision or greater.
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``` cpp
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template<in-matrix InMat>
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auto matrix_inf_norm(InMat A);
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template<class ExecutionPolicy, in-matrix InMat>
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auto matrix_inf_norm(ExecutionPolicy&& exec, InMat A);
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```
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*Effects:* Let `T` be
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`decltype(`*`abs-if-needed`*`(declval<typename InMat::value_type>())`.
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Then,
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- the one-parameter overload is equivalent to:
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``` cpp
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return matrix_inf_norm(A, T{});
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```
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and
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- the two-parameter overload is equivalent to:
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``` cpp
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return matrix_inf_norm(std::forward<ExecutionPolicy>(exec), A, T{});
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```
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