Merge pull request #44 from gonum/adddtrcon

Add Dtrcon and test

cgo/lapack.go

@@ -524,6 +524,33 @@ func (impl Implementation) Dormqr(side blas.Side, trans blas.Transpose, m, n, k
 	clapack.Dormqr(side, trans, m, n, k, a, lda, tau, c, ldc)
 }
 
+// Dtrcon estimates the reciprocal of the condition number of a triangular matrix A.
+// The condition number computed may be based on the 1-norm or the ∞-norm.
+//
+// work is a temporary data slice of length at least 3*n and Dtrcon will panic otherwise.
+//
+// iwork is a temporary data slice of length at least n and Dtrcon will panic otherwise.
+func (impl Implementation) Dtrcon(norm lapack.MatrixNorm, uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int, work []float64, iwork []int) float64 {
+	if norm != lapack.MaxColumnSum && norm != lapack.MaxRowSum {
+		panic(badNorm)
+	}
+	if uplo != blas.Upper && uplo != blas.Lower {
+		panic(badUplo)
+	}
+	if diag != blas.NonUnit && diag != blas.Unit {
+		panic(badDiag)
+	}
+	if len(work) < 3*n {
+		panic(badWork)
+	}
+	if len(iwork) < n {
+		panic(badWork)
+	}
+	rcond := []float64{0}
+	clapack.Dtrcon(byte(norm), uplo, diag, n, a, lda, rcond)
+	return rcond[0]
+}
+
 // Dtrtrs solves a triangular system of the form A * X = B or A^T * X = B. Dtrtrs
 // returns whether the solve completed successfully. If A is singular, no solve is performed.
 func (impl Implementation) Dtrtrs(uplo blas.Uplo, trans blas.Transpose, diag blas.Diag, n, nrhs int, a []float64, lda int, b []float64, ldb int) (ok bool) {

cgo/lapack_test.go

@@ -86,3 +86,7 @@ func TestDormlq(t *testing.T) {
 	testlapack.Dorml2Test(t, blockedTranslate{impl})
 }
 */
+
+func TestDtrcon(t *testing.T) {
+	testlapack.DtrconTest(t, impl)
+}

native/dtrcon.go

@@ -0,0 +1,78 @@
+package native
+
+import (
+	"math"
+
+	"github.com/gonum/blas"
+	"github.com/gonum/blas/blas64"
+	"github.com/gonum/lapack"
+)
+
+// Dtrcon estimates the reciprocal of the condition number of a triangular matrix A.
+// The condition number computed may be based on the 1-norm or the ∞-norm.
+//
+// work is a temporary data slice of length at least 3*n and Dtrcon will panic otherwise.
+//
+// iwork is a temporary data slice of length at least n and Dtrcon will panic otherwise.
+func (impl Implementation) Dtrcon(norm lapack.MatrixNorm, uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int, work []float64, iwork []int) float64 {
+	if norm != lapack.MaxColumnSum && norm != lapack.MaxRowSum {
+		panic(badNorm)
+	}
+	if uplo != blas.Upper && uplo != blas.Lower {
+		panic(badUplo)
+	}
+	if diag != blas.NonUnit && diag != blas.Unit {
+		panic(badDiag)
+	}
+	if len(work) < 3*n {
+		panic(badWork)
+	}
+	if len(iwork) < n {
+		panic(badWork)
+	}
+	if n == 0 {
+		return 1
+	}
+	bi := blas64.Implementation()
+
+	var rcond float64
+	smlnum := dlamchS * float64(n)
+
+	anorm := impl.Dlantr(norm, uplo, diag, n, n, a, lda, work)
+
+	if anorm <= 0 {
+		return rcond
+	}
+	var ainvnm float64
+	var normin bool
+	kase1 := 2
+	if norm == lapack.MaxColumnSum {
+		kase1 = 1
+	}
+	var kase int
+	isave := new([3]int)
+	var scale float64
+	for {
+		ainvnm, kase = impl.Dlacn2(n, work[n:], work, iwork, ainvnm, kase, isave)
+		if kase == 0 {
+			if ainvnm != 0 {
+				rcond = (1 / anorm) / ainvnm
+			}
+			return rcond
+		}
+		if kase == kase1 {
+			scale = impl.Dlatrs(uplo, blas.NoTrans, diag, normin, n, a, lda, work, work[2*n:])
+		} else {
+			scale = impl.Dlatrs(uplo, blas.Trans, diag, normin, n, a, lda, work, work[2*n:])
+		}
+		normin = true
+		if scale != 1 {
+			ix := bi.Idamax(n, work, 1)
+			xnorm := math.Abs(work[ix])
+			if scale == 0 || scale < xnorm*smlnum {
+				return rcond
+			}
+			impl.Drscl(n, scale, work, 1)
+		}
+	}
+}

native/lapack_test.go

@@ -104,6 +104,10 @@ func TestDrscl(t *testing.T) {
 	testlapack.DrsclTest(t, impl)
 }
 
+func TestDtrcon(t *testing.T) {
+	testlapack.DtrconTest(t, impl)
+}
+
 func TestIladlc(t *testing.T) {
 	testlapack.IladlcTest(t, impl)
 }

testlapack/dtrcon.go

@@ -0,0 +1,179 @@
+package testlapack
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"github.com/gonum/blas"
+	"github.com/gonum/floats"
+	"github.com/gonum/lapack"
+)
+
+type Dtrconer interface {
+	Dgeconer
+	Dtrcon(norm lapack.MatrixNorm, uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int, work []float64, iwork []int) float64
+}
+
+func DtrconTest(t *testing.T, impl Dtrconer) {
+	// Hand crafted tests.
+	for _, test := range []struct {
+		a       []float64
+		n       int
+		uplo    blas.Uplo
+		diag    blas.Diag
+		condOne float64
+		condInf float64
+	}{
+		{
+			a: []float64{
+				8, 5, 6,
+				0, 7, 8,
+				0, 0, 6,
+			},
+			n:       3,
+			uplo:    blas.Upper,
+			diag:    blas.Unit,
+			condOne: 1.0 / 645,
+			condInf: 1.0 / 480,
+		},
+		{
+			a: []float64{
+				8, 5, 6,
+				0, 7, 8,
+				0, 0, 6,
+			},
+			n:       3,
+			uplo:    blas.Upper,
+			diag:    blas.NonUnit,
+			condOne: 0.137704918032787,
+			condInf: 0.157894736842105,
+		},
+		{
+			a: []float64{
+				8, 0, 0,
+				5, 7, 0,
+				6, 8, 6,
+			},
+			n:       3,
+			uplo:    blas.Lower,
+			diag:    blas.Unit,
+			condOne: 1.0 / 480,
+			condInf: 1.0 / 645,
+		},
+		{
+			a: []float64{
+				8, 0, 0,
+				5, 7, 0,
+				6, 8, 6,
+			},
+			n:       3,
+			uplo:    blas.Lower,
+			diag:    blas.NonUnit,
+			condOne: 0.157894736842105,
+			condInf: 0.137704918032787,
+		},
+	} {
+		lda := test.n
+		work := make([]float64, 3*test.n)
+		for i := range work {
+			work[i] = rand.Float64()
+		}
+		iwork := make([]int, test.n)
+		for i := range iwork {
+			iwork[i] = rand.Int()
+		}
+		aCopy := make([]float64, len(test.a))
+		copy(aCopy, test.a)
+		condOne := impl.Dtrcon(lapack.MaxColumnSum, test.uplo, test.diag, test.n, test.a, lda, work, iwork)
+		if math.Abs(condOne-test.condOne) > 1e-14 {
+			t.Errorf("One norm mismatch. Want %v, got %v.", test.condOne, condOne)
+		}
+		if !floats.Equal(aCopy, test.a) {
+			t.Errorf("a modified during call")
+		}
+		condInf := impl.Dtrcon(lapack.MaxRowSum, test.uplo, test.diag, test.n, test.a, lda, work, iwork)
+		if math.Abs(condInf-test.condInf) > 1e-14 {
+			t.Errorf("Inf norm mismatch. Want %v, got %v.", test.condInf, condInf)
+		}
+		if !floats.Equal(aCopy, test.a) {
+			t.Errorf("a modified during call")
+		}
+	}
+
+	// Dtrcon does not match the Dgecon output in many cases. See
+	// https://github.com/xianyi/OpenBLAS/issues/636
+	// TODO(btracey): Uncomment this when the mismatch between Dgecon and Dtrcon
+	// is understood.
+	/*
+		// Randomized tests against Dgecon.
+		for _, uplo := range []blas.Uplo{blas.Lower, blas.Upper} {
+			for _, diag := range []blas.Diag{blas.NonUnit, blas.Unit} {
+				for _, test := range []struct {
+					n, lda int
+				}{
+					{3, 0},
+					{4, 9},
+				} {
+					for trial := 0; trial < 1; trial++ {
+						n := test.n
+						lda := test.lda
+						if lda == 0 {
+							lda = n
+						}
+						a := make([]float64, n*lda)
+						if trial == 0 {
+							for i := range a {
+								a[i] = float64(i + 2)
+							}
+						} else {
+							for i := range a {
+								a[i] = rand.NormFloat64()
+							}
+						}
+
+						aDense := make([]float64, len(a))
+						if uplo == blas.Upper {
+							for i := 0; i < n; i++ {
+								for j := i; j < n; j++ {
+									aDense[i*lda+j] = a[i*lda+j]
+								}
+							}
+						} else {
+							for i := 0; i < n; i++ {
+								for j := 0; j <= i; j++ {
+									aDense[i*lda+j] = a[i*lda+j]
+								}
+							}
+						}
+						if diag == blas.Unit {
+							for i := 0; i < n; i++ {
+								aDense[i*lda+i] = 1
+							}
+						}
+
+						ipiv := make([]int, n)
+						work := make([]float64, 4*n)
+						denseOne := impl.Dlange(lapack.MaxColumnSum, n, n, aDense, lda, work)
+						denseInf := impl.Dlange(lapack.MaxRowSum, n, n, aDense, lda, work)
+
+						aDenseLU := make([]float64, len(aDense))
+						copy(aDenseLU, aDense)
+						impl.Dgetrf(n, n, aDenseLU, lda, ipiv)
+						iwork := make([]int, n)
+						want := impl.Dgecon(lapack.MaxColumnSum, n, aDenseLU, lda, denseOne, work, iwork)
+						got := impl.Dtrcon(lapack.MaxColumnSum, uplo, diag, n, a, lda, work, iwork)
+						if math.Abs(want-got) > 1e-14 {
+							t.Errorf("One norm mismatch. Upper = %v, unit = %v, want %v, got %v", uplo == blas.Upper, diag == blas.Unit, want, got)
+						}
+						want = impl.Dgecon(lapack.MaxRowSum, n, aDenseLU, lda, denseInf, work, iwork)
+						got = impl.Dtrcon(lapack.MaxRowSum, uplo, diag, n, a, lda, work, iwork)
+						if math.Abs(want-got) > 1e-14 {
+							t.Errorf("Inf norm mismatch. Upper = %v, unit = %v, want %v, got %v", uplo == blas.Upper, diag == blas.Unit, want, got)
+						}
+					}
+				}
+			}
+		}
+	*/
+}