feat: initial release

Assisted-by: GLM 5.3 Flash

examples/pde/main.go

@@ -0,0 +1,103 @@
+// Copyright (c) 2026 Petr Balvín <opensource@petrbalvin.org> (https://petrbalvin.org)
+// SPDX-License-Identifier: MIT
+
+// Command pde solves the two canonical one-dimensional partial
+// differential equations: the heat equation by Crank-Nicolson and the
+// wave equation by velocity Verlet. Both start from the same Gaussian
+// pulse on a rod, and the diagnostics show diffusion flattening the
+// pulse while the wave keeps its shape and travels.
+//
+// Usage: go run ./examples/pde
+package main
+
+import (
+	"fmt"
+	"log"
+	"math"
+
+	"sourcedock.dev/petrbalvin/tensor"
+)
+
+func main() {
+	const (
+		n  = 201
+		dx = 0.01 // metres, a 2 m rod
+		k  = 1e-3 // thermal diffusivity, m^2/s
+		c  = 0.5  // wave speed, m/s
+	)
+	pulse := make([]float64, n)
+	for i := range n {
+		x := float64(i)*dx - 1.0
+		pulse[i] = math.Exp(-(x * x) / 0.01)
+	}
+	u0, err := tensor.FromFloats(pulse, n)
+	if err != nil {
+		log.Fatal(err)
+	}
+
+	fmt.Println("heat equation (Crank-Nicolson, ends held at zero):")
+	fmt.Println("  time     peak      mean (interior)")
+	for _, tf := range []float64{0, 0.5, 2, 5} {
+		var row *tensor.Array
+		if tf == 0 {
+			row = u0 // the initial pulse itself
+		} else {
+			u, err := tensor.IntegrateHeat1D(u0, k, dx, tf, tf/400, 5, 0, 0)
+			if err != nil {
+				log.Fatal(err)
+			}
+			// The last sample row holds the final state. The ends are
+			// Dirichlet zeros, so heat drains out of the rod once the
+			// pulse reaches them; by the last time printed it has not,
+			// which is why the interior mean barely moves.
+			row, err = tensor.Slice(u, 0, 4, 5)
+			if err != nil {
+				log.Fatal(err)
+			}
+		}
+		mx, err := tensor.Max(row)
+		if err != nil {
+			log.Fatal(err)
+		}
+		mean, err := tensor.Mean(row)
+		if err != nil {
+			log.Fatal(err)
+		}
+		fmt.Printf("  %.2f s   %7.4f   %7.4f\n", tf, mx.Float(), mean)
+	}
+
+	fmt.Println()
+	fmt.Println("wave equation (velocity Verlet, fixed ends):")
+	fmt.Println("  time     peak     position of the peak")
+	rest, err := tensor.Zeros(tensor.Float, n)
+	if err != nil {
+		log.Fatal(err)
+	}
+	for _, tf := range []float64{0, 0.5, 1.0, 1.5} {
+		var row *tensor.Array
+		if tf == 0 {
+			row = u0
+		} else {
+			u, err := tensor.IntegrateWave1D(u0, rest, c, dx, tf, tf/600, 5)
+			if err != nil {
+				log.Fatal(err)
+			}
+			row, err = tensor.Slice(u, 0, 4, 5)
+			if err != nil {
+				log.Fatal(err)
+			}
+		}
+		mx, err := tensor.Max(row)
+		if err != nil {
+			log.Fatal(err)
+		}
+		peak, peakVal := 0, -1.0
+		for i := range n {
+			if v := row.FloatAt(i); v > peakVal {
+				peak, peakVal = i, v
+			}
+		}
+		fmt.Printf("  %.2f s   %6.4f   x = %.2f m\n",
+			tf, mx.Float(), float64(peak)*dx-1.0)
+	}
+}