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--- saxpy [May 05, 2026 at 14:57] – yanevskiv
+++ saxpy [June 13, 2026 at 03:13] (current) – external edit 127.0.0.1
@@ Line 1: / Line 1: @@
+# SAXPY
+**SAXPY** is an algorithm in high-performance computing (HPC).
+## Math
+### Vectors
+Let $\mathbf{y}^{(t)}, \mathbf{x}^{(t)}\in\mathbb{R}^n$ be vectors over real numbers at some discrete time $t\in\mathbb{N}$ and let $a\in\mathbb{R}$ be a real parameter.
+SAXPY is defined as a vector update of $\mathbf{y}$ at time $t+1$ according to the formula:
+$$\mathbf{y}^{(t+1)} = a\mathbf{x}^{(t)} + \mathbf{y}^{(t)}$$
+### Elements
+We can write $\mathbf{y}^{(t)} = (y_0^{(t)}, y_1^{(t)}, \dots, y_n^{(t)})$ and $\mathbf{x}^{(t)} = (x_0^{(t)}, x_1^{(t)}, \dots, x_n^{(t)})$
+Thus if we look at individual vector elements, where $k\in\{0, 1, \dots, n\}$, we have the following formula:
+$$y_k^{(t + 1)} = a\cdot x_k^{(t)} + y_k^{(t)}$$
+## C
+```c
+// y - Y vector
+// x - X vector
+// a - parameter
+// N - size of both vectors
+void saxpy(float* y, float* x, float a, size_t N)
+{
+    size_t i;
+    for (i = 0; i < N; i++) {
+        y[i] = a * x[i] + y[i];
+    }
+}
+```