Add update function for vector algebra

Author: wigging

Sources/Numerix/LinearAlgebra/Algebra.swift

@@ -26,11 +26,17 @@ public protocol Algebra {
     static func scale(_ a: inout Matrix<Self>, by k: Self)
     static func transpose(_ a: Matrix<Self>) -> Matrix<Self>
     static func swapValues(a: inout Matrix<Self>, b: inout Matrix<Self>)
+
+    static func update(a: inout Vector<Self>, k: Self, b: Vector<Self>)
 }
 
 @_documentation(visibility: private)
 extension Int: Algebra {
 
+    public static func update(a: inout Vector<Int>, k: Int, b: Vector<Int>) {
+        fatalError("Not supported for integer values")
+    }
+
     // Vector
 
     public static func swapValues(a: inout Vector<Int>, b: inout Vector<Int>) {
@@ -127,6 +133,10 @@ extension Int: Algebra {
 @_documentation(visibility: private)
 extension Float: Algebra {
 
+    public static func update(a: inout Vector<Float>, k: Float, b: Vector<Float>) {
+        cblas_saxpy(b.size, k, b.buffer.baseAddress, 1, a.buffer.baseAddress, 1)
+    }
+
     // Vector
 
     public static func swapValues(a: inout Vector<Float>, b: inout Vector<Float>) {
@@ -225,6 +235,10 @@ extension Float: Algebra {
 @_documentation(visibility: private)
 extension Double: Algebra {
 
+    public static func update(a: inout Vector<Double>, k: Double, b: Vector<Double>) {
+        cblas_daxpy(b.size, k, b.buffer.baseAddress, 1, a.buffer.baseAddress, 1)
+    }
+
     // Vector
 
     public static func swapValues(a: inout Vector<Double>, b: inout Vector<Double>) {
@@ -322,6 +336,17 @@ extension Double: Algebra {
 
 extension Vector where Scalar: Algebra {
 
+    /// Update the vector with element-wise addition of another vector multiplied by a scalar value.
+    ///
+    /// This performs the Level 1 BLAS operation axpy which is represented by equation `y = y + αx` where `y` and `x`
+    /// are vectors and `α` is a scalar value.
+    /// - Parameters:
+    ///   - b: The vector `b` in `a = a + b * k`.
+    ///   - k: The scalar value `k` in `a = a + b * k`.
+    public mutating func update(with b: Vector, times k: Scalar = 1) where Scalar: Numeric {
+        Scalar.update(a: &self, k: k, b: b)
+    }
+
     /// Calculate the dot product of two vectors.
     ///
     /// This calculates the dot product as `c = aᵀb` where `a` and `b` are vectors

Tests/VectorTests.swift

@@ -252,6 +252,14 @@ struct VectorTests {
         swapValues(&d, &e)
         #expect(d == [1, 2, 3, 4])
         #expect(e == [8, 9, 10, 11])
+
+        var y = Vector<Float>([2, 3, 4, 5, 6, 7])
+        let x = Vector<Float>([1, 2, 3, 4, 5, 6])
+        y.update(with: x)
+        #expect(y == [3, 5, 7, 9, 11, 13])
+
+        y.update(with: x, times: 2)
+        #expect(y == [5, 9, 13, 17, 21, 25])
     }
 
     @Test func doubleAlgebra() {