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[bytom/vapor.git] / vendor / gonum.org / v1 / gonum / mat / cholesky_example_test.go

diff --git a/vendor/gonum.org/v1/gonum/mat/cholesky_example_test.go b/vendor/gonum.org/v1/gonum/mat/cholesky_example_test.go
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+++ b/vendor/gonum.org/v1/gonum/mat/cholesky_example_test.go
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+// Copyright ©2015 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 ExampleCholesky() {
+       // Construct a symmetric positive definite matrix.
+       tmp := mat.NewDense(4, 4, []float64{
+               2, 6, 8, -4,
+               1, 8, 7, -2,
+               2, 2, 1, 7,
+               8, -2, -2, 1,
+       })
+       var a mat.SymDense
+       a.SymOuterK(1, tmp)
+
+       fmt.Printf("a = %0.4v\n", mat.Formatted(&a, mat.Prefix("    ")))
+
+       // Compute the cholesky factorization.
+       var chol mat.Cholesky
+       if ok := chol.Factorize(&a); !ok {
+               fmt.Println("a matrix is not positive semi-definite.")
+       }
+
+       // Find the determinant.
+       fmt.Printf("\nThe determinant of a is %0.4g\n\n", chol.Det())
+
+       // Use the factorization to solve the system of equations a * x = b.
+       b := mat.NewVecDense(4, []float64{1, 2, 3, 4})
+       var x mat.VecDense
+       if err := chol.SolveVec(&x, b); err != nil {
+               fmt.Println("Matrix is near singular: ", err)
+       }
+       fmt.Println("Solve a * x = b")
+       fmt.Printf("x = %0.4v\n", mat.Formatted(&x, mat.Prefix("    ")))
+
+       // Extract the factorization and check that it equals the original matrix.
+       t := chol.LTo(nil)
+       var test mat.Dense
+       test.Mul(t, t.T())
+       fmt.Println()
+       fmt.Printf("L * L^T = %0.4v\n", mat.Formatted(&a, mat.Prefix("          ")))
+
+       // Output:
+       // a = ⎡120  114   -4  -16⎤
+       //     ⎢114  118   11  -24⎥
+       //     ⎢ -4   11   58   17⎥
+       //     ⎣-16  -24   17   73⎦
+       //
+       // The determinant of a is 1.543e+06
+       //
+       // Solve a * x = b
+       // x = ⎡  -0.239⎤
+       //     ⎢  0.2732⎥
+       //     ⎢-0.04681⎥
+       //     ⎣  0.1031⎦
+       //
+       // L * L^T = ⎡120  114   -4  -16⎤
+       //           ⎢114  118   11  -24⎥
+       //           ⎢ -4   11   58   17⎥
+       //           ⎣-16  -24   17   73⎦
+}
+
+func ExampleCholesky_SymRankOne() {
+       a := mat.NewSymDense(4, []float64{
+               1, 1, 1, 1,
+               0, 2, 3, 4,
+               0, 0, 6, 10,
+               0, 0, 0, 20,
+       })
+       fmt.Printf("A = %0.4v\n", mat.Formatted(a, mat.Prefix("    ")))
+
+       // Compute the Cholesky factorization.
+       var chol mat.Cholesky
+       if ok := chol.Factorize(a); !ok {
+               fmt.Println("matrix a is not positive definite.")
+       }
+
+       x := mat.NewVecDense(4, []float64{0, 0, 0, 1})
+       fmt.Printf("\nx = %0.4v\n", mat.Formatted(x, mat.Prefix("    ")))
+
+       // Rank-1 update the factorization.
+       chol.SymRankOne(&chol, 1, x)
+       // Rank-1 update the matrix a.
+       a.SymRankOne(a, 1, x)
+
+       au := chol.ToSym(nil)
+
+       // Print the matrix that was updated directly.
+       fmt.Printf("\nA' =        %0.4v\n", mat.Formatted(a, mat.Prefix("            ")))
+       // Print the matrix recovered from the factorization.
+       fmt.Printf("\nU'^T * U' = %0.4v\n", mat.Formatted(au, mat.Prefix("            ")))
+
+       // Output:
+       // A = ⎡ 1   1   1   1⎤
+       //     ⎢ 1   2   3   4⎥
+       //     ⎢ 1   3   6  10⎥
+       //     ⎣ 1   4  10  20⎦
+       //
+       // x = ⎡0⎤
+       //     ⎢0⎥
+       //     ⎢0⎥
+       //     ⎣1⎦
+       //
+       // A' =        ⎡ 1   1   1   1⎤
+       //             ⎢ 1   2   3   4⎥
+       //             ⎢ 1   3   6  10⎥
+       //             ⎣ 1   4  10  21⎦
+       //
+       // U'^T * U' = ⎡ 1   1   1   1⎤
+       //             ⎢ 1   2   3   4⎥
+       //             ⎢ 1   3   6  10⎥
+       //             ⎣ 1   4  10  21⎦
+}