| // 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 ( |
| "testing" |
| |
| "golang.org/x/exp/rand" |
| |
| "gonum.org/v1/gonum/blas" |
| "gonum.org/v1/gonum/blas/blas64" |
| ) |
| |
| type Dtrtrier interface { |
| Dtrtri(uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int) bool |
| } |
| |
| func DtrtriTest(t *testing.T, impl Dtrtrier) { |
| const tol = 1e-10 |
| rnd := rand.New(rand.NewSource(1)) |
| bi := blas64.Implementation() |
| for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} { |
| for _, diag := range []blas.Diag{blas.NonUnit, blas.Unit} { |
| for _, test := range []struct { |
| n, lda int |
| }{ |
| {3, 0}, |
| {70, 0}, |
| {200, 0}, |
| {3, 5}, |
| {70, 92}, |
| {200, 205}, |
| } { |
| n := test.n |
| lda := test.lda |
| if lda == 0 { |
| lda = n |
| } |
| // Allocate n×n matrix A and fill it with random numbers. |
| a := make([]float64, n*lda) |
| for i := range a { |
| a[i] = rnd.Float64() |
| } |
| for i := 0; i < n; i++ { |
| // This keeps the matrices well conditioned. |
| a[i*lda+i] += float64(n) |
| } |
| aCopy := make([]float64, len(a)) |
| copy(aCopy, a) |
| // Compute the inverse of the uplo triangle. |
| impl.Dtrtri(uplo, diag, n, a, lda) |
| // Zero out the opposite triangle. |
| if uplo == blas.Upper { |
| for i := 1; i < n; i++ { |
| for j := 0; j < i; j++ { |
| aCopy[i*lda+j] = 0 |
| a[i*lda+j] = 0 |
| } |
| } |
| } else { |
| for i := 0; i < n; i++ { |
| for j := i + 1; j < n; j++ { |
| aCopy[i*lda+j] = 0 |
| a[i*lda+j] = 0 |
| } |
| } |
| } |
| if diag == blas.Unit { |
| // Set the diagonal explicitly to 1. |
| for i := 0; i < n; i++ { |
| a[i*lda+i] = 1 |
| aCopy[i*lda+i] = 1 |
| } |
| } |
| // Compute A^{-1} * A and store the result in ans. |
| ans := make([]float64, len(a)) |
| bi.Dgemm(blas.NoTrans, blas.NoTrans, n, n, n, 1, a, lda, aCopy, lda, 0, ans, lda) |
| // Check that ans is the identity matrix. |
| dist := distFromIdentity(n, ans, lda) |
| if dist > tol { |
| t.Errorf("|inv(A) * A - I| = %v is too large. Upper = %v, unit = %v, n = %v, lda = %v", |
| dist, uplo == blas.Upper, diag == blas.Unit, n, lda) |
| } |
| } |
| } |
| } |
| } |