Merge from master

testlapack/dgecon.go

@@ -1,9 +1,10 @@
 package testlapack
 
 import (
-	"math"
+	"log"
 	"testing"
 
+	"github.com/gonum/floats"
 	"github.com/gonum/lapack"
 )
 
@@ -44,6 +45,18 @@ func DgeconTest(t *testing.T, impl Dgeconer) {
 			condOne: 0.024740155174938,
 			condInf: 0.012034465570035,
 		},
+		// Dgecon does not match Dpocon for this case. https://github.com/xianyi/OpenBLAS/issues/664.
+		{
+			a: []float64{
+				2.9995576045549965, -2.0898894566158663, 3.965560740124006,
+				-2.0898894566158663, 1.9634729526261008, -2.8681002706874104,
+				3.965560740124006, -2.8681002706874104, 5.502416670471008,
+			},
+			m:       3,
+			n:       3,
+			condOne: 0.024054837369015203,
+			condInf: 0.024054837369015203,
+		},
 	} {
 		m := test.m
 		n := test.n
@@ -64,11 +77,17 @@ func DgeconTest(t *testing.T, impl Dgeconer) {
 		iwork := make([]int, n)
 		condOne := impl.Dgecon(lapack.MaxColumnSum, n, a, lda, oneNorm, work, iwork)
 		condInf := impl.Dgecon(lapack.MaxRowSum, n, a, lda, infNorm, work, iwork)
-		if math.Abs(condOne-test.condOne) > 1e-13 {
+
+		// Error if not the same order, otherwise log the difference.
+		if !floats.EqualWithinAbsOrRel(condOne, test.condOne, 1e0, 1e0) {
 			t.Errorf("One norm mismatch. Want %v, got %v.", test.condOne, condOne)
+		} else if !floats.EqualWithinAbsOrRel(condOne, test.condOne, 1e-14, 1e-14) {
+			log.Printf("Dgecon one norm mismatch. Want %v, got %v.", test.condOne, condOne)
 		}
-		if math.Abs(condInf-test.condInf) > 1e-13 {
-			t.Errorf("Inf norm mismatch. Want %v, got %v.", test.condInf, condInf)
+		if !floats.EqualWithinAbsOrRel(condInf, test.condInf, 1e0, 1e0) {
+			t.Errorf("One norm mismatch. Want %v, got %v.", test.condInf, condInf)
+		} else if !floats.EqualWithinAbsOrRel(condInf, test.condInf, 1e-14, 1e-14) {
+			log.Printf("Dgecon one norm mismatch. Want %v, got %v.", test.condInf, condInf)
 		}
 	}
 }

testlapack/dlartg.go

@@ -0,0 +1,32 @@
+// Copyright ©2015 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 (
+	"math"
+	"math/rand"
+	"testing"
+)
+
+type Dlartger interface {
+	Dlartg(f, g float64) (cs, sn, r float64)
+}
+
+func DlartgTest(t *testing.T, impl Dlartger) {
+	for i := 0; i < 100; i++ {
+		f := rand.NormFloat64()
+		g := rand.NormFloat64()
+		cs, sn, r := impl.Dlartg(f, g)
+
+		rTest := cs*f + sn*g
+		zeroTest := -sn*f + cs*g
+		if math.Abs(rTest-r) > 1e-14 {
+			t.Errorf("R result mismatch. Computed %v, found %v", r, rTest)
+		}
+		if math.Abs(zeroTest) > 1e-14 {
+			t.Errorf("Zero result mismatch. Found %v", zeroTest)
+		}
+	}
+}

testlapack/dlas2.go

@@ -0,0 +1,34 @@
+// Copyright ©2015 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 (
+	"math"
+	"testing"
+)
+
+type Dlas2er interface {
+	Dlas2(f, g, h float64) (min, max float64)
+}
+
+func Dlas2Test(t *testing.T, impl Dlas2er) {
+	for i, test := range []struct {
+		f, g, h, ssmin, ssmax float64
+	}{
+		// Singular values computed from Octave.
+		{10, 30, 12, 3.567778859365365, 33.634371616111189},
+		{10, 30, -12, 3.567778859365365, 33.634371616111189},
+		{2, 30, -12, 0.741557056404952, 32.364333658088754},
+		{-2, 5, 12, 1.842864429909778, 13.023204317408728},
+	} {
+		ssmin, ssmax := impl.Dlas2(test.f, test.g, test.h)
+		if math.Abs(ssmin-test.ssmin) > 1e-12 {
+			t.Errorf("Case %d, minimal singular value mismatch. Want %v, got %v", i, test.ssmin, ssmin)
+		}
+		if math.Abs(ssmax-test.ssmax) > 1e-12 {
+			t.Errorf("Case %d, minimal singular value mismatch. Want %v, got %v", i, test.ssmin, ssmin)
+		}
+	}
+}

testlapack/dlasr.go

@@ -0,0 +1,147 @@
+// Copyright ©2015 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 (
+	"math"
+	"math/rand"
+	"testing"
+
+	"github.com/gonum/blas"
+	"github.com/gonum/blas/blas64"
+	"github.com/gonum/floats"
+	"github.com/gonum/lapack"
+)
+
+type Dlasrer interface {
+	Dlasr(side blas.Side, pivot lapack.Pivot, direct lapack.Direct, m, n int, c, s, a []float64, lda int)
+}
+
+func DlasrTest(t *testing.T, impl Dlasrer) {
+	for _, side := range []blas.Side{blas.Left, blas.Right} {
+		for _, pivot := range []lapack.Pivot{lapack.Variable, lapack.Top, lapack.Bottom} {
+			for _, direct := range []lapack.Direct{lapack.Forward, lapack.Backward} {
+				for _, test := range []struct {
+					m, n, lda int
+				}{
+					{5, 5, 0},
+					{5, 10, 0},
+					{10, 5, 0},
+
+					{5, 5, 20},
+					{5, 10, 20},
+					{10, 5, 20},
+				} {
+					m := test.m
+					n := test.n
+					lda := test.lda
+					if lda == 0 {
+						lda = n
+					}
+					a := make([]float64, m*lda)
+					for i := range a {
+						a[i] = rand.Float64()
+					}
+					var s, c []float64
+					if side == blas.Left {
+						s = make([]float64, m-1)
+						c = make([]float64, m-1)
+					} else {
+						s = make([]float64, n-1)
+						c = make([]float64, n-1)
+					}
+					for k := range s {
+						theta := rand.Float64() * 2 * math.Pi
+						s[k] = math.Sin(theta)
+						c[k] = math.Cos(theta)
+					}
+					aCopy := make([]float64, len(a))
+					copy(a, aCopy)
+					impl.Dlasr(side, pivot, direct, m, n, c, s, a, lda)
+
+					pSize := m
+					if side == blas.Right {
+						pSize = n
+					}
+					p := blas64.General{
+						Rows:   pSize,
+						Cols:   pSize,
+						Stride: pSize,
+						Data:   make([]float64, pSize*pSize),
+					}
+					pk := blas64.General{
+						Rows:   pSize,
+						Cols:   pSize,
+						Stride: pSize,
+						Data:   make([]float64, pSize*pSize),
+					}
+					ptmp := blas64.General{
+						Rows:   pSize,
+						Cols:   pSize,
+						Stride: pSize,
+						Data:   make([]float64, pSize*pSize),
+					}
+					for i := 0; i < pSize; i++ {
+						p.Data[i*p.Stride+i] = 1
+						ptmp.Data[i*p.Stride+i] = 1
+					}
+					// Compare to direct computation.
+					for k := range s {
+						for i := range p.Data {
+							pk.Data[i] = 0
+						}
+						for i := 0; i < pSize; i++ {
+							pk.Data[i*p.Stride+i] = 1
+						}
+						if pivot == lapack.Variable {
+							pk.Data[k*p.Stride+k] = c[k]
+							pk.Data[k*p.Stride+k+1] = s[k]
+							pk.Data[(k+1)*p.Stride+k] = -s[k]
+							pk.Data[(k+1)*p.Stride+k+1] = c[k]
+						} else if pivot == lapack.Top {
+							pk.Data[0] = c[k]
+							pk.Data[k+1] = s[k]
+							pk.Data[(k+1)*p.Stride] = -s[k]
+							pk.Data[(k+1)*p.Stride+k+1] = c[k]
+						} else {
+							pk.Data[(pSize-1-k)*p.Stride+pSize-k-1] = c[k]
+							pk.Data[(pSize-1-k)*p.Stride+pSize-1] = s[k]
+							pk.Data[(pSize-1)*p.Stride+pSize-1-k] = -s[k]
+							pk.Data[(pSize-1)*p.Stride+pSize-1] = c[k]
+						}
+						if direct == lapack.Forward {
+							blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, pk, ptmp, 0, p)
+						} else {
+							blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, ptmp, pk, 0, p)
+						}
+						copy(ptmp.Data, p.Data)
+					}
+
+					aMat := blas64.General{
+						Rows:   m,
+						Cols:   n,
+						Stride: lda,
+						Data:   make([]float64, m*lda),
+					}
+					copy(a, aCopy)
+					newA := blas64.General{
+						Rows:   m,
+						Cols:   n,
+						Stride: lda,
+						Data:   make([]float64, m*lda),
+					}
+					if side == blas.Left {
+						blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, p, aMat, 0, newA)
+					} else {
+						blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, aMat, p, 0, newA)
+					}
+					if !floats.EqualApprox(newA.Data, a, 1e-12) {
+						t.Errorf("A update mismatch")
+					}
+				}
+			}
+		}
+	}
+}

testlapack/dpocon.go

@@ -1,12 +1,13 @@
 package testlapack
 
 import (
-	"math"
+	"log"
 	"math/rand"
 	"testing"
 
 	"github.com/gonum/blas"
 	"github.com/gonum/blas/blas64"
+	"github.com/gonum/floats"
 	"github.com/gonum/lapack"
 )
 
@@ -44,6 +45,17 @@ func DpoconTest(t *testing.T, impl Dpoconer) {
 			n:    3,
 			cond: 0.050052137643379,
 		},
+		// Dgecon does not match Dpocon for this case. https://github.com/xianyi/OpenBLAS/issues/664.
+		{
+			a: []float64{
+				2.9995576045549965, -2.0898894566158663, 3.965560740124006,
+				0, 1.9634729526261008, -2.8681002706874104,
+				0, 0, 5.502416670471008,
+			},
+			uplo: blas.Upper,
+			n:    3,
+			cond: 0.024054837369015203,
+		},
 	} {
 		n := test.n
 		a := make([]float64, len(test.a))
@@ -60,8 +72,11 @@ func DpoconTest(t *testing.T, impl Dpoconer) {
 		}
 		iwork := make([]int, n)
 		cond := impl.Dpocon(uplo, n, a, lda, anorm, work, iwork)
-		if math.Abs(cond-test.cond) > 1e-14 {
+		// Error if not the same order, otherwise log the difference.
+		if !floats.EqualWithinAbsOrRel(cond, test.cond, 1e0, 1e0) {
 			t.Errorf("Cond mismatch. Want %v, got %v.", test.cond, cond)
+		} else if !floats.EqualWithinAbsOrRel(cond, test.cond, 1e-14, 1e-14) {
+			log.Printf("Dpocon cond mismatch. Want %v, got %v.", test.cond, cond)
 		}
 	}
 	bi := blas64.Implementation()
@@ -89,6 +104,9 @@ func DpoconTest(t *testing.T, impl Dpoconer) {
 				copy(aCopy, a)
 				bi.Dgemm(blas.Trans, blas.NoTrans, n, n, n, 1, aCopy, lda, aCopy, lda, 0, a, lda)
 
+				aDat := make([]float64, len(aCopy))
+				copy(aDat, a)
+
 				aDense := make([]float64, len(a))
 				if uplo == blas.Upper {
 					for i := 0; i < n; i++ {
@@ -122,8 +140,11 @@ func DpoconTest(t *testing.T, impl Dpoconer) {
 				ipiv := make([]int, n)
 				impl.Dgetrf(n, n, aDense, lda, ipiv)
 				want := impl.Dgecon(lapack.MaxColumnSum, n, aDense, lda, denseNorm, work, iwork)
-				if math.Abs(got-want) > 1e-14 {
-					t.Errorf("Cond mismatch. Want %v, got %v.", want, got)
+				// Error if not the same order, otherwise log the difference.
+				if !floats.EqualWithinAbsOrRel(want, got, 1e0, 1e0) {
+					t.Errorf("Dpocon and Dgecon mismatch. Dpocon %v, Dgecon %v.", got, want)
+				} else if !floats.EqualWithinAbsOrRel(want, got, 1e-14, 1e-14) {
+					log.Printf("Dpocon and Dgecon mismatch. Dpocon %v, Dgecon %v.", got, want)
 				}
 			}
 		}