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 // Copyright ©2019 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 ( "fmt" "math" "testing" "golang.org/x/exp/rand" "gonum.org/v1/gonum/blas" "gonum.org/v1/gonum/blas/blas64" "gonum.org/v1/gonum/floats" ) type Dpbtrser interface { Dpbtrs(uplo blas.Uplo, n, kd, nrhs int, ab []float64, ldab int, b []float64, ldb int) Dpbtrfer } // DpbtrsTest tests Dpbtrs by comparing the computed and known, generated solutions of // a linear system with a random symmetric positive definite band matrix. func DpbtrsTest(t *testing.T, impl Dpbtrser) { rnd := rand.New(rand.NewSource(1)) for _, n := range []int{0, 1, 2, 3, 4, 5, 65, 100, 129} { for _, kd := range []int{0, (n + 1) / 4, (3*n - 1) / 4, (5*n + 1) / 4} { for _, nrhs := range []int{0, 1, 2, 5} { for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} { for _, ldab := range []int{kd + 1, kd + 1 + 3} { for _, ldb := range []int{max(1, nrhs), nrhs + 4} { dpbtrsTest(t, impl, rnd, uplo, n, kd, nrhs, ldab, ldb) } } } } } } } func dpbtrsTest(t *testing.T, impl Dpbtrser, rnd *rand.Rand, uplo blas.Uplo, n, kd, nrhs int, ldab, ldb int) { const tol = 1e-12 name := fmt.Sprintf("uplo=%v,n=%v,kd=%v,nrhs=%v,ldab=%v,ldb=%v", string(uplo), n, kd, nrhs, ldab, ldb) // Generate a random symmetric positive definite band matrix. ab := randSymBand(uplo, n, kd, ldab, rnd) // Compute the Cholesky decomposition of A. abFac := make([]float64, len(ab)) copy(abFac, ab) ok := impl.Dpbtrf(uplo, n, kd, abFac, ldab) if !ok { t.Fatalf("%v: bad test matrix, Dpbtrs failed", name) } abFacCopy := make([]float64, len(abFac)) copy(abFacCopy, abFac) // Generate a random solution. xWant := make([]float64, n*ldb) for i := range xWant { xWant[i] = rnd.NormFloat64() } // Compute the corresponding right-hand side. bi := blas64.Implementation() b := make([]float64, len(xWant)) if n > 0 { for j := 0; j < nrhs; j++ { bi.Dsbmv(uplo, n, kd, 1, ab, ldab, xWant[j:], ldb, 0, b[j:], ldb) } } // Solve Uᵀ * U * X = B or L * Lᵀ * X = B. impl.Dpbtrs(uplo, n, kd, nrhs, abFac, ldab, b, ldb) xGot := b // Check that the Cholesky factorization matrix has not been modified. if !floats.Equal(abFac, abFacCopy) { t.Errorf("%v: unexpected modification of ab", name) } // Compute and check the max-norm difference between the computed and generated solutions. var diff float64 for i := 0; i < n; i++ { for j := 0; j < nrhs; j++ { diff = math.Max(diff, math.Abs(xWant[i*ldb+j]-xGot[i*ldb+j])) } } if diff > tol { t.Errorf("%v: unexpected result, diff=%v", name, diff) } }