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[bytom/vapor.git] / vendor / gonum.org / v1 / gonum / lapack / testlapack / dsterf.go

diff --git a/vendor/gonum.org/v1/gonum/lapack/testlapack/dsterf.go b/vendor/gonum.org/v1/gonum/lapack/testlapack/dsterf.go
new file mode 100644 (file)
index 0000000..a6ca01e
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+++ b/vendor/gonum.org/v1/gonum/lapack/testlapack/dsterf.go
@@ -0,0 +1,127 @@
+// Copyright ©2016 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 testlapack
+
+import (
+       "math"
+       "sort"
+       "testing"
+
+       "golang.org/x/exp/rand"
+
+       "gonum.org/v1/gonum/floats"
+)
+
+type Dsterfer interface {
+       Dgetrfer
+       Dsterf(n int, d, e []float64) (ok bool)
+}
+
+func DsterfTest(t *testing.T, impl Dsterfer) {
+       // Hand coded tests.
+       for cas, test := range []struct {
+               d []float64
+               e []float64
+               n int
+
+               ans []float64
+       }{
+               // Computed from Fortran code.
+               {
+                       d:   []float64{1, 3, 4, 6},
+                       e:   []float64{2, 4, 5},
+                       n:   4,
+                       ans: []float64{11.046227528488854, 4.795922173417400, -2.546379458290125, 0.704229756383872},
+               },
+       } {
+               n := test.n
+               d := make([]float64, len(test.d))
+               copy(d, test.d)
+               e := make([]float64, len(test.e))
+               copy(e, test.e)
+               ok := impl.Dsterf(n, d, e)
+               if !ok {
+                       t.Errorf("Case %d, Eigenvalue decomposition failed", cas)
+                       continue
+               }
+               ans := make([]float64, len(test.ans))
+               copy(ans, test.ans)
+               sort.Float64s(ans)
+               if !floats.EqualApprox(ans, d, 1e-10) {
+                       t.Errorf("eigenvalue mismatch")
+               }
+       }
+
+       rnd := rand.New(rand.NewSource(1))
+       // Probabilistic tests.
+       for _, n := range []int{4, 6, 10} {
+               for cas := 0; cas < 10; cas++ {
+                       d := make([]float64, n)
+                       for i := range d {
+                               d[i] = rnd.NormFloat64()
+                       }
+                       dCopy := make([]float64, len(d))
+                       copy(dCopy, d)
+                       e := make([]float64, n-1)
+                       for i := range e {
+                               e[i] = rnd.NormFloat64()
+                       }
+                       eCopy := make([]float64, len(e))
+                       copy(eCopy, e)
+
+                       ok := impl.Dsterf(n, d, e)
+                       if !ok {
+                               t.Errorf("Eigenvalue decomposition failed")
+                               continue
+                       }
+
+                       // Test that the eigenvalues are sorted.
+                       if !sort.Float64sAreSorted(d) {
+                               t.Errorf("Values are not sorted")
+                       }
+
+                       // Construct original tridagional matrix.
+                       lda := n
+                       a := make([]float64, n*lda)
+                       for i := 0; i < n; i++ {
+                               a[i*lda+i] = dCopy[i]
+                               if i != n-1 {
+                                       a[i*lda+i+1] = eCopy[i]
+                                       a[(i+1)*lda+i] = eCopy[i]
+                               }
+                       }
+
+                       asub := make([]float64, len(a))
+                       ipiv := make([]int, n)
+
+                       // Test that they are actually eigenvalues by computing the
+                       // determinant of A - λI.
+                       // TODO(btracey): Replace this test with a more numerically stable
+                       // test.
+                       for _, lambda := range d {
+                               copy(asub, a)
+                               for i := 0; i < n; i++ {
+                                       asub[i*lda+i] -= lambda
+                               }
+
+                               // Compute LU.
+                               ok := impl.Dgetrf(n, n, asub, lda, ipiv)
+                               if !ok {
+                                       // Definitely singular.
+                                       continue
+                               }
+                               // Compute determinant.
+                               var logdet float64
+                               for i := 0; i < n; i++ {
+                                       v := asub[i*lda+i]
+                                       logdet += math.Log(math.Abs(v))
+                               }
+                               if math.Exp(logdet) > 2 {
+                                       t.Errorf("Incorrect singular value. n = %d, cas = %d, det = %v", n, cas, math.Exp(logdet))
+                               }
+                       }
+               }
+       }
+}