gonum/mat/dense_example_test.go

// Copyright ©2017 The gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package mat_test

import (
	"fmt"

	"gonum.org/v1/gonum/mat"
)

func ExampleDense_Add() {
	// Initialize two matrices, a and b.
	a := mat.NewDense(2, 2, []float64{1, 0, 1, 0})
	b := mat.NewDense(2, 2, []float64{0, 1, 0, 1})

	// Add a and b, placing the result into c.
	// ...Notice that the size is automatically adjusted when the receiver has zero size.
	var c mat.Dense
	c.Add(a, b)

	// Print the result using the formatter.
	fc := mat.Formatted(&c, mat.Prefix("    "), mat.Squeeze())
	fmt.Printf("Result:\nc = %v\n\n", fc)
	// Output:
	// Result:
	// c = ⎡1  1⎤
	//     ⎣1  1⎦
	//
}

func ExampleDense_Sub() {
	// Initialize two matrices, a and b.
	a := mat.NewDense(2, 2, []float64{1, 1, 1, 1})
	b := mat.NewDense(2, 2, []float64{1, 0, 0, 1})

	// Subtract b from a, placing the result into a.
	a.Sub(a, b)

	// Print the result using the formatter.
	fa := mat.Formatted(a, mat.Prefix("    "), mat.Squeeze())
	fmt.Printf("Result:\na = %v\n\n", fa)
	// Output:
	// Result:
	// a = ⎡0  1⎤
	//     ⎣1  0⎦
	//
}

func ExampleDense_MulElem() {
	// Initialize two matrices, a and b.
	a := mat.NewDense(2, 2, []float64{1, 2, 3, 4})
	b := mat.NewDense(2, 2, []float64{1, 2, 3, 4})

	// Multiply the elements of a and b, placing the result into a.
	a.MulElem(a, b)

	// Print the result using the formatter.
	fa := mat.Formatted(a, mat.Prefix("    "), mat.Squeeze())
	fmt.Printf("Result:\na = %v\n\n", fa)
	// Output:
	// Result:
	// a = ⎡1   4⎤
	//     ⎣9  16⎦
	//
}

func ExampleDense_DivElem() {
	// Initialize two matrices, a and b.
	a := mat.NewDense(2, 2, []float64{5, 10, 15, 20})
	b := mat.NewDense(2, 2, []float64{5, 5, 5, 5})

	// Divide the elements of a by b, placing the result into a.
	a.DivElem(a, b)

	// Print the result using the formatter.
	fa := mat.Formatted(a, mat.Prefix("    "), mat.Squeeze())
	fmt.Printf("Result:\na = %v\n\n", fa)
	// Output:
	// Result:
	// a = ⎡1  2⎤
	//     ⎣3  4⎦
	//
}

func ExampleDense_Inverse() {
	// Initialize two matrices, a and ia.
	a := mat.NewDense(2, 2, []float64{4, 0, 0, 4})
	var ia mat.Dense

	// Take the inverse of a and place the result in ia.
	ia.Inverse(a)

	// Print the result using the formatter.
	fa := mat.Formatted(&ia, mat.Prefix("     "), mat.Squeeze())
	fmt.Printf("Result:\nia = %.2g\n\n", fa)

	// Confirm that A * A^-1 = I
	var r mat.Dense
	r.Mul(a, &ia)
	fr := mat.Formatted(&r, mat.Prefix("    "), mat.Squeeze())
	fmt.Printf("Result:\nr = %v\n\n", fr)

	// The Inverse operation, however, is numerically unstable, and should typically be avoided.
	// For example, a common need is to find x = A^-1 * b. In this case, the SolveVec method of VecDense
	// (if b is a Vector) or Solve method of Dense (if b is a matrix) should used instead of computing
	// the Inverse of A.
	b := mat.NewDense(2, 2, []float64{2, 0, 0, 2})
	var x mat.Dense
	x.Solve(a, b)

	// Print the result using the formatter.
	fx := mat.Formatted(&x, mat.Prefix("    "), mat.Squeeze())
	fmt.Printf("Result:\nx = %v\n\n", fx)

	// Output:
	// Result:
	// ia = ⎡0.25    -0⎤
	//      ⎣   0  0.25⎦
	//
	// Result:
	// r = ⎡1  0⎤
	//     ⎣0  1⎦
	//
	// Result:
	// x = ⎡0.5    0⎤
	//     ⎣  0  0.5⎦
	//
}

func ExampleDense_Mul() {
	// Initialize two matrices, a and b.
	a := mat.NewDense(2, 2, []float64{4, 0, 0, 4})
	b := mat.NewDense(2, 3, []float64{4, 0, 0, 0, 0, 4})

	// Take the matrix product of a and b and place the result in c.
	var c mat.Dense
	c.Mul(a, b)

	// Print the result using the formatter.
	fc := mat.Formatted(&c, mat.Prefix("    "), mat.Squeeze())
	fmt.Printf("Result:\nc = %v\n\n", fc)
	// Output:
	// Result:
	// c = ⎡16  0   0⎤
	//     ⎣ 0  0  16⎦
	//
}

func ExampleDense_Exp() {
	// Initialize a matrix a with some data.
	a := mat.NewDense(2, 2, []float64{1, 0, 0, 1})

	// Take the exponential of the matrix and place the result in m.
	var m mat.Dense
	m.Exp(a)

	// Print the result using the formatter.
	fm := mat.Formatted(&m, mat.Prefix("    "), mat.Squeeze())
	fmt.Printf("Result:\nm = %4.2f\n\n", fm)
	// Output:
	// Result:
	// m = ⎡2.72  0.00⎤
	//     ⎣0.00  2.72⎦
	//
}

func ExampleDense_Pow() {
	// Initialize a matrix with some data.
	a := mat.NewDense(2, 2, []float64{4, 4, 4, 4})

	// Take the second power of matrix a and place the result in m.
	var m mat.Dense
	m.Pow(a, 2)

	// Print the result using the formatter.
	fm := mat.Formatted(&m, mat.Prefix("    "), mat.Squeeze())
	fmt.Printf("Result:\nm = %v\n\n", fm)

	// Take the zeroth power of matrix a and place the result in n.
	// We expect an identity matrix of the same size as matrix a.
	var n mat.Dense
	n.Pow(a, 0)

	// Print the result using the formatter.
	fn := mat.Formatted(&n, mat.Prefix("    "), mat.Squeeze())
	fmt.Printf("Result:\nn = %v\n\n", fn)
	// Output:
	// Result:
	// m = ⎡32  32⎤
	//     ⎣32  32⎦
	//
	// Result:
	// n = ⎡1  0⎤
	//     ⎣0  1⎦
	//
}

func ExampleDense_Scale() {
	// Initialize a matrix with some data.
	a := mat.NewDense(2, 2, []float64{4, 4, 4, 4})

	// Scale the matrix by a factor of 0.25 and place the result in m.
	var m mat.Dense
	m.Scale(0.25, a)

	// Print the result using the formatter.
	fm := mat.Formatted(&m, mat.Prefix("    "), mat.Squeeze())
	fmt.Printf("Result:\nm = %4.3f\n\n", fm)
	// Output:
	// Result:
	// m = ⎡1.000  1.000⎤
	//     ⎣1.000  1.000⎦
	//
}