| // 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 testlapack |
| |
| import ( |
| "math/rand" |
| "testing" |
| |
| "gonum.org/v1/gonum/blas" |
| "gonum.org/v1/gonum/blas/blas64" |
| "gonum.org/v1/gonum/floats" |
| ) |
| |
| type Dgetf2er interface { |
| Dgetf2(m, n int, a []float64, lda int, ipiv []int) bool |
| } |
| |
| func Dgetf2Test(t *testing.T, impl Dgetf2er) { |
| rnd := rand.New(rand.NewSource(1)) |
| for _, test := range []struct { |
| m, n, lda int |
| }{ |
| {10, 10, 0}, |
| {10, 5, 0}, |
| {10, 5, 0}, |
| |
| {10, 10, 20}, |
| {5, 10, 20}, |
| {10, 5, 20}, |
| } { |
| m := test.m |
| n := test.n |
| lda := test.lda |
| if lda == 0 { |
| lda = n |
| } |
| a := make([]float64, m*lda) |
| for i := range a { |
| a[i] = rnd.Float64() |
| } |
| aCopy := make([]float64, len(a)) |
| copy(aCopy, a) |
| |
| mn := min(m, n) |
| ipiv := make([]int, mn) |
| for i := range ipiv { |
| ipiv[i] = rnd.Int() |
| } |
| ok := impl.Dgetf2(m, n, a, lda, ipiv) |
| checkPLU(t, ok, m, n, lda, ipiv, a, aCopy, 1e-14, true) |
| } |
| |
| // Test with singular matrices (random matrices are almost surely non-singular). |
| for _, test := range []struct { |
| m, n, lda int |
| a []float64 |
| }{ |
| { |
| m: 2, |
| n: 2, |
| lda: 2, |
| a: []float64{ |
| 1, 0, |
| 0, 0, |
| }, |
| }, |
| { |
| m: 2, |
| n: 2, |
| lda: 2, |
| a: []float64{ |
| 1, 5, |
| 2, 10, |
| }, |
| }, |
| { |
| m: 3, |
| n: 3, |
| lda: 3, |
| // row 3 = row1 + 2 * row2 |
| a: []float64{ |
| 1, 5, 7, |
| 2, 10, -3, |
| 5, 25, 1, |
| }, |
| }, |
| { |
| m: 3, |
| n: 4, |
| lda: 4, |
| // row 3 = row1 + 2 * row2 |
| a: []float64{ |
| 1, 5, 7, 9, |
| 2, 10, -3, 11, |
| 5, 25, 1, 31, |
| }, |
| }, |
| } { |
| if impl.Dgetf2(test.m, test.n, test.a, test.lda, make([]int, min(test.m, test.n))) { |
| t.Log("Returned ok with singular matrix.") |
| } |
| } |
| } |
| |
| // checkPLU checks that the PLU factorization contained in factorize matches |
| // the original matrix contained in original. |
| func checkPLU(t *testing.T, ok bool, m, n, lda int, ipiv []int, factorized, original []float64, tol float64, print bool) { |
| var hasZeroDiagonal bool |
| for i := 0; i < min(m, n); i++ { |
| if factorized[i*lda+i] == 0 { |
| hasZeroDiagonal = true |
| break |
| } |
| } |
| if hasZeroDiagonal && ok { |
| t.Error("Has a zero diagonal but returned ok") |
| } |
| if !hasZeroDiagonal && !ok { |
| t.Error("Non-zero diagonal but returned !ok") |
| } |
| |
| // Check that the LU decomposition is correct. |
| mn := min(m, n) |
| l := make([]float64, m*mn) |
| ldl := mn |
| u := make([]float64, mn*n) |
| ldu := n |
| for i := 0; i < m; i++ { |
| for j := 0; j < n; j++ { |
| v := factorized[i*lda+j] |
| switch { |
| case i == j: |
| l[i*ldl+i] = 1 |
| u[i*ldu+i] = v |
| case i > j: |
| l[i*ldl+j] = v |
| case i < j: |
| u[i*ldu+j] = v |
| } |
| } |
| } |
| |
| LU := blas64.General{ |
| Rows: m, |
| Cols: n, |
| Stride: n, |
| Data: make([]float64, m*n), |
| } |
| U := blas64.General{ |
| Rows: mn, |
| Cols: n, |
| Stride: ldu, |
| Data: u, |
| } |
| L := blas64.General{ |
| Rows: m, |
| Cols: mn, |
| Stride: ldl, |
| Data: l, |
| } |
| blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, L, U, 0, LU) |
| |
| p := make([]float64, m*m) |
| ldp := m |
| for i := 0; i < m; i++ { |
| p[i*ldp+i] = 1 |
| } |
| for i := len(ipiv) - 1; i >= 0; i-- { |
| v := ipiv[i] |
| blas64.Swap(m, blas64.Vector{Inc: 1, Data: p[i*ldp:]}, blas64.Vector{Inc: 1, Data: p[v*ldp:]}) |
| } |
| P := blas64.General{ |
| Rows: m, |
| Cols: m, |
| Stride: m, |
| Data: p, |
| } |
| aComp := blas64.General{ |
| Rows: m, |
| Cols: n, |
| Stride: lda, |
| Data: make([]float64, m*lda), |
| } |
| copy(aComp.Data, factorized) |
| blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, P, LU, 0, aComp) |
| if !floats.EqualApprox(aComp.Data, original, tol) { |
| if print { |
| t.Errorf("PLU multiplication does not match original matrix.\nWant: %v\nGot: %v", original, aComp.Data) |
| return |
| } |
| t.Error("PLU multiplication does not match original matrix.") |
| } |
| } |