tmp/tmp_ygvnfiy/{from.md → to.md}
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#### Frobenius norm of a matrix <a id="linalg.algs.blas1.matfrobnorm">[[linalg.algs.blas1.matfrobnorm]]</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_frob_norm(InMat A, Scalar init);
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template<class ExecutionPolicy, in-matrix InMat, class Scalar>
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Scalar matrix_frob_norm(ExecutionPolicy&& exec, InMat A, Scalar init);
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```
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*Mandates:* Let `a` be
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*`abs-if-needed`*`(declval<typename InMat::value_type>())`. Then,
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`decltype(init + a * a)` is convertible to `Scalar`.
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*Returns:* The square root of the sum of squares of `init` and the
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absolute values of the elements of `A`.
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[*Note 1*: For `init` equal to zero, this is the Frobenius norm of the
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matrix `A`. — *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_frob_norm(InMat A);
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template<class ExecutionPolicy, in-matrix InMat>
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auto matrix_frob_norm(ExecutionPolicy&& exec, InMat A);
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```
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*Effects:* Let `a` be
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*`abs-if-needed`*`(declval<typename InMat::value_type>())`. Let `T` be
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`decltype(a * a)`. Then,
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- the one-parameter overload is equivalent to:
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``` cpp
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return matrix_frob_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_frob_norm(std::forward<ExecutionPolicy>(exec), A, T{});
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```
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