lapack/gonum: add Dptcon

lapack/testlapack/dptcon.go

@@ -0,0 +1,81 @@
+// Copyright ©2023 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/floats"
+	"gonum.org/v1/gonum/lapack"
+)
+
+type Dptconer interface {
+	Dptcon(n int, d, e []float64, anorm float64, work []float64) (rcond float64)
+
+	Dpttrf(n int, d, e []float64) (ok bool)
+	Dpttrs(n, nrhs int, d, e []float64, b []float64, ldb int)
+}
+
+func DptconTest(t *testing.T, impl Dptconer) {
+	rnd := rand.New(rand.NewSource(1))
+	for _, n := range []int{0, 1, 2, 3, 4, 5, 10, 20, 50, 51, 52, 53, 54, 100} {
+		dptconTest(t, impl, rnd, n)
+	}
+}
+
+func dptconTest(t *testing.T, impl Dptconer, rnd *rand.Rand, n int) {
+	const tol = 1e-15
+
+	name := fmt.Sprintf("n=%v", n)
+
+	// Generate a random diagonally dominant symmetric tridiagonal matrix A.
+	d, e := newRandomSymTridiag(n, rnd)
+	aNorm := dlanst(lapack.MaxColumnSum, n, d, e)
+
+	// Compute the Cholesky factorization of A.
+	ok := impl.Dpttrf(n, d, e)
+	if !ok {
+		t.Errorf("%v: bad test matrix, Dpttrf failed", name)
+		return
+	}
+
+	// Compute the reciprocal of the condition number of A.
+	dCopy := make([]float64, len(d))
+	copy(dCopy, d)
+	eCopy := make([]float64, len(e))
+	copy(eCopy, e)
+	work := make([]float64, 3*n)
+	rcondGot := impl.Dptcon(n, d, e, aNorm, work)
+
+	// Check that Dptcon didn't modify d and e.
+	if !floats.Equal(d, dCopy) {
+		t.Errorf("%v: unexpected modification of d", name)
+	}
+	if !floats.Equal(e, eCopy) {
+		t.Errorf("%v: unexpected modification of e", name)
+	}
+
+	// Compute the norm of A⁻¹.
+	aInv, lda := make([]float64, n*n), max(1, n)
+	for i := 0; i < n; i++ {
+		aInv[i*lda+i] = 1
+	}
+	impl.Dpttrs(n, n, d, e, aInv, lda)
+	aInvNorm := dlange(lapack.MaxColumnSum, n, n, aInv, lda)
+
+	rcondWant := 1.0
+	if aNorm > 0 && aInvNorm > 0 {
+		rcondWant = 1 / aNorm / aInvNorm
+	}
+
+	diff := math.Abs(rcondGot - rcondWant)
+	if diff > tol {
+		t.Errorf("%v: unexpected value of rcond. got=%v, want=%v (diff=%v)", name, rcondGot, rcondWant, diff)
+	}
+}