lapack: imported lapack as a subtree

lapack/testlapack/dtrexc.go

@@ -0,0 +1,219 @@
+// 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"
+	"math/cmplx"
+	"math/rand"
+	"testing"
+
+	"github.com/gonum/blas"
+	"github.com/gonum/blas/blas64"
+	"github.com/gonum/lapack"
+)
+
+type Dtrexcer interface {
+	Dtrexc(compq lapack.EVComp, 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 _, compq := range []lapack.EVComp{lapack.None, lapack.UpdateSchur} {
+		for _, n := range []int{1, 2, 3, 4, 5, 6, 10, 18, 31, 53} {
+			for _, extra := range []int{0, 1, 11} {
+				for cas := 0; cas < 100; cas++ {
+					tmat := randomSchurCanonical(n, n+extra, rnd)
+					ifst := rnd.Intn(n)
+					ilst := rnd.Intn(n)
+					testDtrexc(t, impl, compq, tmat, ifst, ilst, extra, rnd)
+				}
+			}
+		}
+	}
+
+	for _, compq := range []lapack.EVComp{lapack.None, lapack.UpdateSchur} {
+		for _, extra := range []int{0, 1, 11} {
+			tmat := randomSchurCanonical(0, extra, rnd)
+			testDtrexc(t, impl, compq, tmat, 0, 0, extra, rnd)
+		}
+	}
+}
+
+func testDtrexc(t *testing.T, impl Dtrexcer, compq lapack.EVComp, tmat blas64.General, ifst, ilst, extra int, rnd *rand.Rand) {
+	const tol = 1e-13
+
+	n := tmat.Rows
+	fstSize, fstFirst := schurBlockSize(tmat, ifst)
+	lstSize, lstFirst := schurBlockSize(tmat, ilst)
+
+	tmatCopy := cloneGeneral(tmat)
+
+	var wantq bool
+	var q, qCopy blas64.General
+	if compq == lapack.UpdateSchur {
+		wantq = true
+		q = eye(n, n+extra)
+		qCopy = cloneGeneral(q)
+	}
+
+	work := nanSlice(n)
+
+	ifstGot, ilstGot, ok := impl.Dtrexc(compq, n, tmat.Data, tmat.Stride, q.Data, q.Stride, ifst, ilst, work)
+
+	prefix := fmt.Sprintf("Case compq=%v, n=%v, ifst=%v, nbf=%v, ilst=%v, nbl=%v, extra=%v",
+		compq, n, ifst, fstSize, ilst, lstSize, extra)
+
+	if !generalOutsideAllNaN(tmat) {
+		t.Errorf("%v: out-of-range write to T", prefix)
+	}
+	if wantq && !generalOutsideAllNaN(q) {
+		t.Errorf("%v: out-of-range write to Q", prefix)
+	}
+
+	if !ok {
+		t.Logf("%v: Dtrexc returned ok=false", prefix)
+	}
+
+	// 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 index. Want %v, got %v ", prefix, ifstWant, ifstGot)
+	}
+
+	// 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 index. Want %v, got %v", prefix, ilstWant, ilstGot)
+		}
+	}
+
+	if n <= 1 || ifstGot == ilstGot {
+		// Too small matrix or no swapping.
+		// Check that T was not modified.
+		for i := 0; i < n; i++ {
+			for j := 0; j < n; j++ {
+				if tmat.Data[i*tmat.Stride+j] != tmatCopy.Data[i*tmatCopy.Stride+j] {
+					t.Errorf("%v: unexpected modification at T[%v,%v]", prefix, i, j)
+				}
+			}
+		}
+		if !wantq {
+			return
+		}
+		// Check that Q was not modified.
+		for i := 0; i < n; i++ {
+			for j := 0; j < n; j++ {
+				if q.Data[i*q.Stride+j] != qCopy.Data[i*qCopy.Stride+j] {
+					t.Errorf("%v: unexpected modification at Q[%v,%v]", prefix, i, j)
+				}
+			}
+		}
+		return
+	}
+
+	if !isSchurCanonicalGeneral(tmat) {
+		t.Errorf("%v: T is not in Schur canonical form", prefix)
+	}
+
+	// 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]", prefix, i, j)
+			}
+		}
+	}
+
+	// Check that the block at ifstGot was delivered to ilstGot correctly.
+	if fstSize == 1 {
+		// 1×1 blocks are swapped exactly.
+		got := tmat.Data[ilstGot*tmat.Stride+ilstGot]
+		want := tmatCopy.Data[ifstGot*tmatCopy.Stride+ifstGot]
+		if want != got {
+			t.Errorf("%v: unexpected 1×1 block at T[%v,%v]. Want %v, got %v",
+				prefix, want, got, ilstGot, ilstGot)
+		}
+	} else {
+		// Check that the swapped 2×2 block is in Schur canonical form.
+		a, b, c, d := extract2x2Block(tmat.Data[ilstGot*tmat.Stride+ilstGot:], tmat.Stride)
+		if !isSchurCanonical(a, b, c, d) {
+			t.Errorf("%v: 2×2 block at T[%v,%v] not in Schur canonical form", prefix, ilstGot, ilstGot)
+		}
+		ev1Got, ev2Got := schurBlockEigenvalues(a, b, c, d)
+
+		// Check that the swapped 2×2 block has the same eigenvalues.
+		// The block was originally located at T[ifstGot,ifstGot].
+		a, b, c, d = extract2x2Block(tmatCopy.Data[ifstGot*tmatCopy.Stride+ifstGot:], tmatCopy.Stride)
+		ev1Want, ev2Want := schurBlockEigenvalues(a, b, c, d)
+		if cmplx.Abs(ev1Got-ev1Want) > tol {
+			t.Errorf("%v: unexpected first eigenvalue of 2×2 block at T[%v,%v]. Want %v, got %v",
+				prefix, ilstGot, ilstGot, ev1Want, ev1Got)
+		}
+		if cmplx.Abs(ev2Got-ev2Want) > tol {
+			t.Errorf("%v: unexpected second eigenvalue of 2×2 block at T[%v,%v]. Want %v, got %v",
+				prefix, ilstGot, ilstGot, ev2Want, ev2Got)
+		}
+	}
+
+	if !wantq {
+		return
+	}
+
+	if !isOrthonormal(q) {
+		t.Errorf("%v: Q is not orthogonal", prefix)
+	}
+	// 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]", prefix, i, j)
+			}
+		}
+	}
+	// Check that Q^T TOrig Q == T.
+	tq := eye(n, n)
+	blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, tmatCopy, q, 0, tq)
+	qtq := eye(n, n)
+	blas64.Gemm(blas.Trans, blas.NoTrans, 1, q, tq, 0, qtq)
+	if !equalApproxGeneral(qtq, tmat, tol) {
+		t.Errorf("%v: Q^T (initial T) Q and (final T) are not equal", prefix)
+	}
+}