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3fa9374bd4
This merges the three packages, matrix, mat64, and cmat128. It then renames this big package to mat. It fixes the import statements and corresponding code
124 lines
3.2 KiB
Go
124 lines
3.2 KiB
Go
// Copyright ©2015 The gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package mat_test
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import (
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"fmt"
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"gonum.org/v1/gonum/mat"
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)
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func ExampleCholesky() {
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// Construct a symmetric positive definite matrix.
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tmp := mat.NewDense(4, 4, []float64{
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2, 6, 8, -4,
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1, 8, 7, -2,
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2, 2, 1, 7,
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8, -2, -2, 1,
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})
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var a mat.SymDense
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a.SymOuterK(1, tmp)
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fmt.Printf("a = %0.4v\n", mat.Formatted(&a, mat.Prefix(" ")))
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// Compute the cholesky factorization.
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var chol mat.Cholesky
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if ok := chol.Factorize(&a); !ok {
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fmt.Println("a matrix is not positive semi-definite.")
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}
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// Find the determinant.
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fmt.Printf("\nThe determinant of a is %0.4g\n\n", chol.Det())
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// Use the factorization to solve the system of equations a * x = b.
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b := mat.NewVector(4, []float64{1, 2, 3, 4})
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var x mat.Vector
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if err := x.SolveCholeskyVec(&chol, b); err != nil {
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fmt.Println("Matrix is near singular: ", err)
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}
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fmt.Println("Solve a * x = b")
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fmt.Printf("x = %0.4v\n", mat.Formatted(&x, mat.Prefix(" ")))
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// Extract the factorization and check that it equals the original matrix.
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var t mat.TriDense
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t.LFromCholesky(&chol)
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var test mat.Dense
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test.Mul(&t, t.T())
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fmt.Println()
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fmt.Printf("L * L^T = %0.4v\n", mat.Formatted(&a, mat.Prefix(" ")))
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// Output:
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// a = ⎡120 114 -4 -16⎤
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// ⎢114 118 11 -24⎥
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// ⎢ -4 11 58 17⎥
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// ⎣-16 -24 17 73⎦
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//
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// The determinant of a is 1.543e+06
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//
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// Solve a * x = b
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// x = ⎡ -0.239⎤
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// ⎢ 0.2732⎥
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// ⎢-0.04681⎥
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// ⎣ 0.1031⎦
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//
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// L * L^T = ⎡120 114 -4 -16⎤
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// ⎢114 118 11 -24⎥
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// ⎢ -4 11 58 17⎥
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// ⎣-16 -24 17 73⎦
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}
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func ExampleCholeskySymRankOne() {
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a := mat.NewSymDense(4, []float64{
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1, 1, 1, 1,
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0, 2, 3, 4,
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0, 0, 6, 10,
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0, 0, 0, 20,
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})
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fmt.Printf("A = %0.4v\n", mat.Formatted(a, mat.Prefix(" ")))
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// Compute the Cholesky factorization.
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var chol mat.Cholesky
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if ok := chol.Factorize(a); !ok {
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fmt.Println("matrix a is not positive definite.")
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}
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x := mat.NewVector(4, []float64{0, 0, 0, 1})
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fmt.Printf("\nx = %0.4v\n", mat.Formatted(x, mat.Prefix(" ")))
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// Rank-1 update the factorization.
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chol.SymRankOne(&chol, 1, x)
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// Rank-1 update the matrix a.
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a.SymRankOne(a, 1, x)
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var au mat.SymDense
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au.FromCholesky(&chol)
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// Print the matrix that was updated directly.
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fmt.Printf("\nA' = %0.4v\n", mat.Formatted(a, mat.Prefix(" ")))
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// Print the matrix recovered from the factorization.
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fmt.Printf("\nU'^T * U' = %0.4v\n", mat.Formatted(&au, mat.Prefix(" ")))
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// Output:
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// A = ⎡ 1 1 1 1⎤
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// ⎢ 1 2 3 4⎥
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// ⎢ 1 3 6 10⎥
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// ⎣ 1 4 10 20⎦
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//
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// x = ⎡0⎤
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// ⎢0⎥
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// ⎢0⎥
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// ⎣1⎦
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//
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// A' = ⎡ 1 1 1 1⎤
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// ⎢ 1 2 3 4⎥
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// ⎢ 1 3 6 10⎥
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// ⎣ 1 4 10 21⎦
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//
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// U'^T * U' = ⎡ 1 1 1 1⎤
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// ⎢ 1 2 3 4⎥
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// ⎢ 1 3 6 10⎥
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// ⎣ 1 4 10 21⎦
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}
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