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cppdraft/linalg/scaled/intro.md

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+[linalg.scaled.intro]
+
+# 29 Numerics library [[numerics]](./#numerics)
+
+## 29.9 Basic linear algebra algorithms [[linalg]](linalg#scaled.intro)
+
+### 29.9.8 Scaled in-place transformation [[linalg.scaled]](linalg.scaled#intro)
+
+#### 29.9.8.1 Introduction [linalg.scaled.intro]
+
+[1](#1)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12572)
+
+The scaled function
+takes a value alpha and an mdspan x, and
+returns a new read-only mdspan that represents
+the elementwise product of alpha with each element of x[.](#1.sentence-1)
+
+[*Example [1](#example-1)*: using Vec = mdspan<double, dextents<size_t, 1>>;
+
+// z = alpha * x + yvoid z_equals_alpha_times_x_plus_y(double alpha, Vec x, Vec y, Vec z) { add(scaled(alpha, x), y, z);}// z = alpha * x + beta * yvoid z_equals_alpha_times_x_plus_beta_times_y(double alpha, Vec x, double beta, Vec y, Vec z) { add(scaled(alpha, x), scaled(beta, y), z);} — *end example*]

cppdraft/linalg/scaled/scaled.md

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+[linalg.scaled.scaled]
+
+# 29 Numerics library [[numerics]](./#numerics)
+
+## 29.9 Basic linear algebra algorithms [[linalg]](linalg#scaled.scaled)
+
+### 29.9.8 Scaled in-place transformation [[linalg.scaled]](linalg.scaled#scaled)
+
+#### 29.9.8.3 Function template scaled [linalg.scaled.scaled]
+
+[1](#1)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12712)
+
+The scaled function template takes
+a scaling factor alpha and
+an mdspan x, and
+returns a new read-only mdspan with the same domain as x,
+that represents the elementwise product of alpha with each element of x[.](#1.sentence-1)
+
+[🔗](#lib:scaled)
+
+`  template<class ScalingFactor,
+           class ElementType, class Extents, class Layout, class Accessor>
+    constexpr auto scaled(ScalingFactor alpha, mdspan<ElementType, Extents, Layout, Accessor> x);
+`
+
+[2](#2)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12728)
+
+Let SA be scaled_accessor<ScalingFactor, Accessor>[.](#2.sentence-1)
+
+[3](#3)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12731)
+
+*Returns*: mdspan<typename SA::element_type, Extents, Layout, SA>(x.data_handle(), x.mapping(),
+ SA(alpha, x.accessor()))
+
+[4](#4)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12739)
+
+[*Example [1](#example-1)*: void test_scaled(mdspan<double, extents<int, 10>> x){auto x_scaled = scaled(5.0, x); for (int i = 0; i < x.extent(0); ++i) { assert(x_scaled[i] == 5.0 * x[i]); }} — *end example*]

cppdraft/linalg/scaled/scaledaccessor.md

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+[linalg.scaled.scaledaccessor]
+
+# 29 Numerics library [[numerics]](./#numerics)
+
+## 29.9 Basic linear algebra algorithms [[linalg]](linalg#scaled.scaledaccessor)
+
+### 29.9.8 Scaled in-place transformation [[linalg.scaled]](linalg.scaled#scaledaccessor)
+
+#### 29.9.8.2 Class template scaled_accessor [linalg.scaled.scaledaccessor]
+
+[1](#1)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12596)
+
+The class template scaled_accessor is an mdspan accessor policy
+which upon access produces scaled elements[.](#1.sentence-1)
+
+It is part of the implementation of scaled ([[linalg.scaled.scaled]](linalg.scaled.scaled "29.9.8.3 Function template scaled"))[.](#1.sentence-2)
+
+namespace std::linalg {template<class ScalingFactor, class NestedAccessor>class [scaled_accessor](#lib:scaled_accessor "29.9.8.2 Class template scaled_­accessor [linalg.scaled.scaledaccessor]") {public:using element_type = add_const_t<decltype(declval<ScalingFactor>() * declval<NestedAccessor::element_type>())>; using reference = remove_const_t<element_type>; using data_handle_type = NestedAccessor::data_handle_type; using offset_policy = scaled_accessor<ScalingFactor, NestedAccessor::offset_policy>; constexpr scaled_accessor() = default; template<class OtherNestedAccessor>explicit(!is_convertible_v<OtherNestedAccessor, NestedAccessor>)constexpr scaled_accessor(const scaled_accessor<ScalingFactor,
+ OtherNestedAccessor>& other); constexpr scaled_accessor(const ScalingFactor& s, const NestedAccessor& a); constexpr reference access(data_handle_type p, size_t i) const; constexpr offset_policy::data_handle_type offset(data_handle_type p, size_t i) const; constexpr const ScalingFactor& scaling_factor() const noexcept { return *scaling-factor*; }constexpr const NestedAccessor& nested_accessor() const noexcept { return *nested-accessor*; }private: ScalingFactor *scaling-factor*{}; // *exposition only* NestedAccessor *nested-accessor*{}; // *exposition only*};}
+
+[2](#2)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12631)
+
+*Mandates*: 
+
+- [(2.1)](#2.1)
+
+element_type is valid and denotes a type,
+
+- [(2.2)](#2.2)
+
+is_copy_constructible_v<reference> is true,
+
+- [(2.3)](#2.3)
+
+is_reference_v<element_type> is false,
+
+- [(2.4)](#2.4)
+
+ScalingFactor models [semiregular](concepts.object#concept:semiregular "18.6 Object concepts [concepts.object]"), and
+
+- [(2.5)](#2.5)
+
+NestedAccessor meets the accessor policy requirements ([[mdspan.accessor.reqmts]](mdspan.accessor.reqmts "23.7.3.5.2 Requirements"))[.](#2.sentence-1)
+
+[🔗](#lib:scaled_accessor,constructor)
+
+`template<class OtherNestedAccessor>
+  explicit(!is_convertible_v<OtherNestedAccessor, NestedAccessor>)
+    constexpr scaled_accessor(const scaled_accessor<ScalingFactor, OtherNestedAccessor>& other);
+`
+
+[3](#3)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12654)
+
+*Constraints*: is_constructible_v<NestedAccessor, const OtherNestedAccessor&> is true[.](#3.sentence-1)
+
+[4](#4)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12658)
+
+*Effects*: 
+
+- [(4.1)](#4.1)
+
+Direct-non-list-initializes *scaling-factor* with other.scaling_factor(), and
+
+- [(4.2)](#4.2)
+
+direct-non-list-initializes *nested-accessor* with other.nested_accessor()[.](#4.sentence-1)
+
+[🔗](#lib:scaled_accessor,constructor_)
+
+`constexpr scaled_accessor(const ScalingFactor& s, const NestedAccessor& a);
+`
+
+[5](#5)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12676)
+
+*Effects*: 
+
+- [(5.1)](#5.1)
+
+Direct-non-list-initializes *scaling-factor* with s, and
+
+- [(5.2)](#5.2)
+
+direct-non-list-initializes *nested-accessor* with a[.](#5.sentence-1)
+
+[🔗](#lib:scaled_accessor,access)
+
+`constexpr reference access(data_handle_type p, size_t i) const;
+`
+
+[6](#6)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12692)
+
+*Returns*: scaling_factor() * NestedAccessor::element_type(*nested-accessor*.access(p, i))
+
+[🔗](#lib:scaled_accessor,offset)
+
+`constexpr offset_policy::data_handle_type offset(data_handle_type p, size_t i) const;
+`
+
+[7](#7)
+
+[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L12705)
+
+*Returns*: *nested-accessor*.offset(p, i)