| // 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/floats" |
| "gonum.org/v1/gonum/lapack" |
| ) |
| |
| type Dlansber interface { |
| Dlansb(norm lapack.MatrixNorm, uplo blas.Uplo, n, kd int, ab []float64, ldab int, work []float64) float64 |
| } |
| |
| func DlansbTest(t *testing.T, impl Dlansber) { |
| rnd := rand.New(rand.NewSource(1)) |
| for _, n := range []int{0, 1, 2, 3, 4, 5, 10} { |
| for _, kd := range []int{0, (n + 1) / 4, (3*n - 1) / 4, (5*n + 1) / 4} { |
| for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} { |
| for _, ldab := range []int{kd + 1, kd + 1 + 7} { |
| dlansbTest(t, impl, rnd, uplo, n, kd, ldab) |
| } |
| } |
| } |
| } |
| } |
| |
| func dlansbTest(t *testing.T, impl Dlansber, rnd *rand.Rand, uplo blas.Uplo, n, kd int, ldab int) { |
| const tol = 1e-15 |
| |
| // Generate a random symmetric band matrix and compute all its norms. |
| ab := make([]float64, max(0, (n-1)*ldab+kd+1)) |
| rowsum := make([]float64, n) |
| colsum := make([]float64, n) |
| var frobWant, maxabsWant float64 |
| if uplo == blas.Upper { |
| for i := 0; i < n; i++ { |
| for jb := 0; jb < min(n-i, kd+1); jb++ { |
| aij := 2*rnd.Float64() - 1 |
| ab[i*ldab+jb] = aij |
| |
| j := jb + i |
| colsum[j] += math.Abs(aij) |
| rowsum[i] += math.Abs(aij) |
| maxabsWant = math.Max(maxabsWant, math.Abs(aij)) |
| frobWant += aij * aij |
| if i != j { |
| // Take into account the symmetric elements. |
| colsum[i] += math.Abs(aij) |
| rowsum[j] += math.Abs(aij) |
| frobWant += aij * aij |
| } |
| } |
| } |
| } else { |
| for i := 0; i < n; i++ { |
| for jb := max(0, kd-i); jb < kd+1; jb++ { |
| aij := 2*rnd.Float64() - 1 |
| ab[i*ldab+jb] = aij |
| |
| j := jb - kd + i |
| colsum[j] += math.Abs(aij) |
| rowsum[i] += math.Abs(aij) |
| maxabsWant = math.Max(maxabsWant, math.Abs(aij)) |
| frobWant += aij * aij |
| if i != j { |
| // Take into account the symmetric elements. |
| colsum[i] += math.Abs(aij) |
| rowsum[j] += math.Abs(aij) |
| frobWant += aij * aij |
| } |
| } |
| } |
| } |
| frobWant = math.Sqrt(frobWant) |
| var maxcolsumWant, maxrowsumWant float64 |
| if n > 0 { |
| maxcolsumWant = floats.Max(colsum) |
| maxrowsumWant = floats.Max(rowsum) |
| } |
| |
| abCopy := make([]float64, len(ab)) |
| copy(abCopy, ab) |
| |
| work := make([]float64, n) |
| var maxcolsumGot, maxrowsumGot float64 |
| for _, norm := range []lapack.MatrixNorm{lapack.MaxAbs, lapack.MaxColumnSum, lapack.MaxRowSum, lapack.Frobenius} { |
| name := fmt.Sprintf("norm=%v,uplo=%v,n=%v,kd=%v,ldab=%v", string(norm), string(uplo), n, kd, ldab) |
| |
| normGot := impl.Dlansb(norm, uplo, n, kd, ab, ldab, work) |
| |
| if !floats.Equal(ab, abCopy) { |
| t.Fatalf("%v: unexpected modification of ab", name) |
| } |
| |
| if norm == lapack.MaxAbs { |
| // MaxAbs norm involves no computation, so we expect |
| // exact equality here. |
| if normGot != maxabsWant { |
| t.Errorf("%v: unexpected result; got %v, want %v", name, normGot, maxabsWant) |
| } |
| continue |
| } |
| |
| var normWant float64 |
| switch norm { |
| case lapack.MaxColumnSum: |
| normWant = maxcolsumWant |
| maxcolsumGot = normGot |
| case lapack.MaxRowSum: |
| normWant = maxrowsumWant |
| maxrowsumGot = normGot |
| case lapack.Frobenius: |
| normWant = frobWant |
| } |
| if math.Abs(normGot-normWant) > tol*float64(n) { |
| t.Errorf("%v: unexpected result; got %v, want %v", name, normGot, normWant) |
| } |
| } |
| // MaxColSum and MaxRowSum norms should be exactly equal because the |
| // matrix is symmetric. |
| if maxcolsumGot != maxrowsumGot { |
| name := fmt.Sprintf("uplo=%v,n=%v,kd=%v,ldab=%v", string(uplo), n, kd, ldab) |
| t.Errorf("%v: unexpected mismatch between MaxColSum and MaxRowSum norms of A; MaxColSum %v, MaxRowSum %v", name, maxcolsumGot, maxrowsumGot) |
| } |
| } |