floats: match Norm behaviour in Distance

gonum · Oct 25, 2019 · 7e1144f · 7e1144f
1 parent e2ba7f0
commit 7e1144f
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Showing 6 changed files with 117 additions and 7 deletions.
diff --git a/floats/floats.go b/floats/floats.go
@@ -152,14 +152,10 @@ func Distance(s, t []float64, L float64) float64 {
 	if len(s) == 0 {
 		return 0
 	}
-	var norm float64
 	if L == 2 {
-		for i, v := range s {
-			diff := t[i] - v
-			norm = math.Hypot(norm, diff)
-		}
-		return norm
+		return f64.L2DistanceUnitary(s, t)
 	}
+	var norm float64
 	if L == 1 {
 		for i, v := range s {
 			norm += math.Abs(t[i] - v)

diff --git a/floats/floats_test.go b/floats/floats_test.go
@@ -261,7 +261,7 @@ func TestDistance(t *testing.T) {
 			copy(tmp, test.s)
 			Sub(tmp, test.t)
 			norm := Norm(tmp, L)
-			if !EqualWithinAbsOrRel(dist, norm, 1e-15, 1e-15) {
+			if dist != norm { // Use equality because they should be identical.
 				t.Errorf("Distance does not match norm for case %v, %v. Expected %v, Found %v.", i, j, norm, dist)
 			}
 		}

diff --git a/internal/asm/f32/l2norm.go b/internal/asm/f32/l2norm.go
@@ -60,3 +60,31 @@ func L2NormInc(x []float32, n, incX uintptr) (sum float32) {
 	}
 	return scale * math32.Sqrt(sumSquares)
 }
+
+// L2DistanceUnitary is the L2 norm of x-y.
+func L2DistanceUnitary(x, y []float32) (sum float32) {
+	var scale float32
+	var sumSquares float32 = 1
+	for i, v := range x {
+		v -= y[i]
+		if v == 0 {
+			continue
+		}
+		absxi := math32.Abs(v)
+		if math32.IsNaN(absxi) {
+			return math32.NaN()
+		}
+		if scale < absxi {
+			s := scale / absxi
+			sumSquares = 1 + sumSquares*s*s
+			scale = absxi
+		} else {
+			s := absxi / scale
+			sumSquares += s * s
+		}
+	}
+	if math32.IsInf(scale, 1) {
+		return math32.Inf(1)
+	}
+	return scale * math32.Sqrt(sumSquares)
+}
diff --git a/internal/asm/f32/l2norm_test.go b/internal/asm/f32/l2norm_test.go
@@ -58,3 +58,32 @@ func TestL2NormInc(t *testing.T) {
 		checkValidIncGuard(t, v.x, src_gd, v.inc, g_ln)
 	}
 }
+
+func TestL2DistanceUnitary(t *testing.T) {
+	var src_gd float32 = 1
+	for j, v := range []struct {
+		want float32
+		x, y []float32
+	}{
+		{want: 0, x: []float32{}, y: []float32{}},
+		{want: 2, x: []float32{3}, y: []float32{1}},
+		{want: 3.7416573867739413, x: []float32{2, 4, 6}, y: []float32{1, 2, 3}},
+		{want: 3.7416573867739413, x: []float32{1, 2, 3}, y: []float32{2, 4, 6}},
+		{want: nan, x: []float32{nan}, y: []float32{0}},
+		{want: 17.88854381999832, x: []float32{9, -9, 9, -9, 9}, y: []float32{1, -1, 1, -1, 1}},
+		{want: 2.23606797749979, x: []float32{0, 1, 0, -1, 0, 1, 0, -1, 0, 1}, y: []float32{0, 2, 0, -2, 0, 2, 0, -2, 0, 2}},
+	} {
+		g_ln := 4 + j%2
+		v.x = guardVector(v.x, src_gd, g_ln)
+		v.y = guardVector(v.y, src_gd, g_ln)
+		srcX := v.x[g_ln : len(v.x)-g_ln]
+		srcY := v.y[g_ln : len(v.y)-g_ln]
+		ret := L2DistanceUnitary(srcX, srcY)
+		if !within(ret, v.want) {
+			t.Errorf("Test %d L2Distance error Got: %f Expected: %f", j, ret, v.want)
+		}
+		if !isValidGuard(v.x, src_gd, g_ln) {
+			t.Errorf("Test %d Guard violated in src vector %v %v", j, v.x[:g_ln], v.x[len(v.x)-g_ln:])
+		}
+	}
+}
diff --git a/internal/asm/f64/l2norm.go b/internal/asm/f64/l2norm.go
@@ -60,3 +60,31 @@ func L2NormInc(x []float64, n, incX uintptr) (sum float64) {
 	}
 	return scale * math.Sqrt(sumSquares)
 }
+
+// L2DistanceUnitary is the L2 norm of x-y.
+func L2DistanceUnitary(x, y []float64) (sum float64) {
+	var scale float64
+	var sumSquares float64 = 1
+	for i, v := range x {
+		v -= y[i]
+		if v == 0 {
+			continue
+		}
+		absxi := math.Abs(v)
+		if math.IsNaN(absxi) {
+			return math.NaN()
+		}
+		if scale < absxi {
+			s := scale / absxi
+			sumSquares = 1 + sumSquares*s*s
+			scale = absxi
+		} else {
+			s := absxi / scale
+			sumSquares += s * s
+		}
+	}
+	if math.IsInf(scale, 1) {
+		return math.Inf(1)
+	}
+	return scale * math.Sqrt(sumSquares)
+}
diff --git a/internal/asm/f64/l2norm_test.go b/internal/asm/f64/l2norm_test.go
@@ -58,3 +58,32 @@ func TestL2NormInc(t *testing.T) {
 		checkValidIncGuard(t, v.x, src_gd, v.inc, g_ln)
 	}
 }
+
+func TestL2DistanceUnitary(t *testing.T) {
+	var src_gd float64 = 1
+	for j, v := range []struct {
+		want float64
+		x, y []float64
+	}{
+		{want: 0, x: []float64{}, y: []float64{}},
+		{want: 2, x: []float64{3}, y: []float64{1}},
+		{want: 3.7416573867739413, x: []float64{2, 4, 6}, y: []float64{1, 2, 3}},
+		{want: 3.7416573867739413, x: []float64{1, 2, 3}, y: []float64{2, 4, 6}},
+		{want: nan, x: []float64{nan}, y: []float64{0}},
+		{want: 17.88854381999832, x: []float64{9, -9, 9, -9, 9}, y: []float64{1, -1, 1, -1, 1}},
+		{want: 2.23606797749979, x: []float64{0, 1, 0, -1, 0, 1, 0, -1, 0, 1}, y: []float64{0, 2, 0, -2, 0, 2, 0, -2, 0, 2}},
+	} {
+		g_ln := 4 + j%2
+		v.x = guardVector(v.x, src_gd, g_ln)
+		v.y = guardVector(v.y, src_gd, g_ln)
+		srcX := v.x[g_ln : len(v.x)-g_ln]
+		srcY := v.y[g_ln : len(v.y)-g_ln]
+		ret := L2DistanceUnitary(srcX, srcY)
+		if !within(ret, v.want) {
+			t.Errorf("Test %d L2Distance error Got: %f Expected: %f", j, ret, v.want)
+		}
+		if !isValidGuard(v.x, src_gd, g_ln) {
+			t.Errorf("Test %d Guard violated in src vector %v %v", j, v.x[:g_ln], v.x[len(v.x)-g_ln:])
+		}
+	}
+}