lapack/testlapack/dtrexc.go

// Copyright ©2016 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"
	"testing"

	"golang.org/x/exp/rand"

	"gonum.org/v1/gonum/blas"
	"gonum.org/v1/gonum/blas/blas64"
	"gonum.org/v1/gonum/lapack"
)

type Dtrexcer interface {
	Dtrexc(compq lapack.UpdateSchurComp, n int, t []float64, ldt int, q []float64, ldq int, ifst, ilst int, work []float64) (ifstOut, ilstOut int, ok bool)
}

func DtrexcTest(t *testing.T, impl Dtrexcer) {
	rnd := rand.New(rand.NewSource(1))

	for _, n := range []int{0, 1, 2, 3, 4, 5, 6, 10, 18, 31, 53} {
		for _, extra := range []int{0, 3} {
			for cas := 0; cas < 100; cas++ {
				var ifst, ilst int
				if n > 0 {
					ifst = rnd.Intn(n)
					ilst = rnd.Intn(n)
				}
				dtrexcTest(t, impl, rnd, n, ifst, ilst, extra)
			}
		}
	}
}

func dtrexcTest(t *testing.T, impl Dtrexcer, rnd *rand.Rand, n, ifst, ilst, extra int) {
	const tol = 1e-13

	tmat, _, _ := randomSchurCanonical(n, n+extra, true, rnd)
	tmatCopy := cloneGeneral(tmat)

	fstSize, fstFirst := schurBlockSize(tmat, ifst)
	lstSize, lstFirst := schurBlockSize(tmat, ilst)

	name := fmt.Sprintf("Case n=%v,ifst=%v,nbfst=%v,ilst=%v,nblst=%v,extra=%v",
		n, ifst, fstSize, ilst, lstSize, extra)

	// 1. Test without accumulating Q.

	compq := lapack.UpdateSchurNone

	work := nanSlice(n)

	ifstGot, ilstGot, ok := impl.Dtrexc(compq, n, tmat.Data, tmat.Stride, nil, 1, ifst, ilst, work)

	if !generalOutsideAllNaN(tmat) {
		t.Errorf("%v: out-of-range write to T", name)
	}

	// 2. Test with accumulating Q.

	compq = lapack.UpdateSchur

	tmat2 := cloneGeneral(tmatCopy)
	q := eye(n, n+extra)
	qCopy := cloneGeneral(q)
	work = nanSlice(n)

	ifstGot2, ilstGot2, ok2 := impl.Dtrexc(compq, n, tmat2.Data, tmat2.Stride, q.Data, q.Stride, ifst, ilst, work)

	if !generalOutsideAllNaN(tmat2) {
		t.Errorf("%v: out-of-range write to T2", name)
	}
	if !generalOutsideAllNaN(q) {
		t.Errorf("%v: out-of-range write to Q", name)
	}

	// Check that outputs from cases 1. and 2. are exactly equal, then check one of them.
	if ifstGot != ifstGot2 {
		t.Errorf("%v: ifstGot != ifstGot2", name)
	}
	if ilstGot != ilstGot2 {
		t.Errorf("%v: ilstGot != ilstGot2", name)
	}
	if ok != ok2 {
		t.Errorf("%v: ok != ok2", name)
	}
	if !equalGeneral(tmat, tmat2) {
		t.Errorf("%v: T != T2", name)
	}

	// Check that the index of the first block was correctly updated (if
	// necessary).
	ifstWant := ifst
	if !fstFirst {
		ifstWant = ifst - 1
	}
	if ifstWant != ifstGot {
		t.Errorf("%v: unexpected ifst=%v, want %v", name, ifstGot, ifstWant)
	}

	// Check that the index of the last block is as expected when ok=true.
	// When ok=false, we don't know at which block the algorithm failed, so
	// we don't check.
	ilstWant := ilst
	if !lstFirst {
		ilstWant--
	}
	if ok {
		if ifstWant < ilstWant {
			// If the blocks are swapped backwards, these
			// adjustments are not necessary, the first row of the
			// last block will end up at ifst.
			switch {
			case fstSize == 2 && lstSize == 1:
				ilstWant--
			case fstSize == 1 && lstSize == 2:
				ilstWant++
			}
		}
		if ilstWant != ilstGot {
			t.Errorf("%v: unexpected ilst=%v, want %v", name, ilstGot, ilstWant)
		}
	}

	if n <= 1 || ifstGot == ilstGot {
		// Too small matrix or no swapping.
		// Check that T was not modified.
		if !equalGeneral(tmat, tmatCopy) {
			t.Errorf("%v: unexpected modification of T when no swapping", name)
		}
		// Check that Q was not modified.
		if !equalGeneral(q, qCopy) {
			t.Errorf("%v: unexpected modification of Q when no swapping", name)
		}
		// Nothing more to check
		return
	}

	if !isSchurCanonicalGeneral(tmat) {
		t.Errorf("%v: T is not in Schur canonical form", name)
	}

	// Check that T was not modified except above the second subdiagonal in
	// rows and columns [modMin,modMax].
	modMin := min(ifstGot, ilstGot)
	modMax := max(ifstGot, ilstGot) + fstSize
	for i := 0; i < n; i++ {
		for j := 0; j < n; j++ {
			if modMin <= i && i < modMax && j+1 >= i {
				continue
			}
			if modMin <= j && j < modMax && j+1 >= i {
				continue
			}
			diff := tmat.Data[i*tmat.Stride+j] - tmatCopy.Data[i*tmatCopy.Stride+j]
			if diff != 0 {
				t.Errorf("%v: unexpected modification at T[%v,%v]", name, i, j)
			}
		}
	}

	// Check that Q is orthogonal.
	resid := residualOrthogonal(q, false)
	if resid > tol {
		t.Errorf("%v: Q is not orthogonal; resid=%v, want<=%v", name, resid, tol)
	}

	// Check that Q is unchanged outside of columns [modMin,modMax].
	for i := 0; i < n; i++ {
		for j := 0; j < n; j++ {
			if modMin <= j && j < modMax {
				continue
			}
			if q.Data[i*q.Stride+j]-qCopy.Data[i*qCopy.Stride+j] != 0 {
				t.Errorf("%v: unexpected modification of Q[%v,%v]", name, i, j)
			}
		}
	}

	// Check that Qᵀ * TOrig * Q == T
	qt := zeros(n, n, n)
	blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, tmatCopy, 0, qt)
	qtq := cloneGeneral(tmat)
	blas64.Gemm(blas.NoTrans, blas.NoTrans, -1, qt, q, 1, qtq)
	resid = dlange(lapack.MaxColumnSum, n, n, qtq.Data, qtq.Stride)
	if resid > tol {
		t.Errorf("%v: mismatch between Qᵀ*(initial T)*Q and (final T); resid=%v, want<=%v",
			name, resid, tol)
	}
}