1// Copyright ©2019 The Gonum Authors. All rights reserved. 2// Use of this source code is governed by a BSD-style 3// license that can be found in the LICENSE file. 4 5package testlapack 6 7import ( 8 "fmt" 9 "testing" 10 11 "golang.org/x/exp/rand" 12 13 "gonum.org/v1/gonum/blas" 14 "gonum.org/v1/gonum/blas/blas64" 15) 16 17type Dpotrier interface { 18 Dpotri(uplo blas.Uplo, n int, a []float64, lda int) bool 19 20 Dpotrf(uplo blas.Uplo, n int, a []float64, lda int) bool 21} 22 23func DpotriTest(t *testing.T, impl Dpotrier) { 24 for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} { 25 name := "Upper" 26 if uplo == blas.Lower { 27 name = "Lower" 28 } 29 t.Run(name, func(t *testing.T) { 30 // Include small and large sizes to make sure that both 31 // unblocked and blocked paths are taken. 32 ns := []int{0, 1, 2, 3, 4, 5, 10, 25, 31, 32, 33, 63, 64, 65, 127, 128, 129} 33 const tol = 1e-12 34 35 bi := blas64.Implementation() 36 rnd := rand.New(rand.NewSource(1)) 37 for _, n := range ns { 38 for _, lda := range []int{max(1, n), n + 11} { 39 prefix := fmt.Sprintf("n=%v,lda=%v", n, lda) 40 41 // Generate a random diagonal matrix D with positive entries. 42 d := make([]float64, n) 43 Dlatm1(d, 3, 10000, false, 2, rnd) 44 45 // Construct a positive definite matrix A as 46 // A = U * D * U^T 47 // where U is a random orthogonal matrix. 48 a := make([]float64, n*lda) 49 Dlagsy(n, 0, d, a, lda, rnd, make([]float64, 2*n)) 50 // Create a copy of A. 51 aCopy := make([]float64, len(a)) 52 copy(aCopy, a) 53 // Compute the Cholesky factorization of A. 54 ok := impl.Dpotrf(uplo, n, a, lda) 55 if !ok { 56 t.Fatalf("%v: unexpected Cholesky failure", prefix) 57 } 58 59 // Compute the inverse inv(A). 60 ok = impl.Dpotri(uplo, n, a, lda) 61 if !ok { 62 t.Errorf("%v: unexpected failure", prefix) 63 continue 64 } 65 66 // Check that the triangle of A opposite to uplo has not been modified. 67 if uplo == blas.Upper && !sameLowerTri(n, aCopy, lda, a, lda) { 68 t.Errorf("%v: unexpected modification in lower triangle", prefix) 69 continue 70 } 71 if uplo == blas.Lower && !sameUpperTri(n, aCopy, lda, a, lda) { 72 t.Errorf("%v: unexpected modification in upper triangle", prefix) 73 continue 74 } 75 76 // Change notation for the sake of clarity. 77 ainv := a 78 ldainv := lda 79 80 // Expand ainv into a full dense matrix so that we can call Dsymm below. 81 if uplo == blas.Upper { 82 for i := 1; i < n; i++ { 83 for j := 0; j < i; j++ { 84 ainv[i*ldainv+j] = ainv[j*ldainv+i] 85 } 86 } 87 } else { 88 for i := 0; i < n-1; i++ { 89 for j := i + 1; j < n; j++ { 90 ainv[i*ldainv+j] = ainv[j*ldainv+i] 91 } 92 } 93 } 94 95 // Compute A*inv(A) and store the result into want. 96 ldwant := max(1, n) 97 want := make([]float64, n*ldwant) 98 bi.Dsymm(blas.Left, uplo, n, n, 1, aCopy, lda, ainv, ldainv, 0, want, ldwant) 99 100 // Check that want is close to the identity matrix. 101 dist := distFromIdentity(n, want, ldwant) 102 if dist > tol { 103 t.Errorf("%v: |A * inv(A) - I| = %v is too large", prefix, dist) 104 } 105 } 106 } 107 }) 108 } 109} 110