Merge pull request #245 from gonum/dlatm1

testlapack: add Dlatm1

testlapack/matgen.go

@@ -0,0 +1,118 @@
+// Copyright ©2017 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"
+)
+
+// Dlatm1 computes the entries of dst as specified by mode, cond and rsign.
+//
+// mode describes how dst will be computed:
+//  |mode| == 1: dst[0] = 1 and dst[1:n] = 1/cond
+//  |mode| == 2: dst[:n-1] = 1/cond and dst[n-1] = 1
+//  |mode| == 3: dst[i] = cond^{-i/(n-1)}, i=0,...,n-1
+//  |mode| == 4: dst[i] = 1 - i*(1-1/cond)/(n-1)
+//  |mode| == 5: dst[i] = random number in the range (1/cond, 1) such that
+//                    their logarithms are uniformly distributed
+//  |mode| == 6: dst[i] = random number from the distribution given by dist
+// If mode is negative, the order of the elements of dst will be reversed.
+// For other values of mode Dlatm1 will panic.
+//
+// If rsign is true and mode is not ±6, each entry of dst will be multiplied by 1
+// or -1 with probability 0.5
+//
+// dist specifies the type of distribution to be used when mode == ±6:
+//  dist == 1: Uniform[0,1)
+//  dist == 2: Uniform[-1,1)
+//  dist == 3: Normal(0,1)
+// For other values of dist Dlatm1 will panic.
+//
+// rnd is used as a source of random numbers.
+func Dlatm1(dst []float64, mode int, cond float64, rsign bool, dist int, rnd *rand.Rand) {
+	amode := mode
+	if amode < 0 {
+		amode = -amode
+	}
+	if amode < 1 || 6 < amode {
+		panic("testlapack: invalid mode")
+	}
+	if cond < 1 {
+		panic("testlapack: cond < 1")
+	}
+	if amode == 6 && (dist < 1 || 3 < dist) {
+		panic("testlapack: invalid dist")
+	}
+
+	n := len(dst)
+	if n == 0 {
+		return
+	}
+
+	switch amode {
+	case 1:
+		dst[0] = 1
+		for i := 1; i < n; i++ {
+			dst[i] = 1 / cond
+		}
+	case 2:
+		for i := 0; i < n-1; i++ {
+			dst[i] = 1
+		}
+		dst[n-1] = 1 / cond
+	case 3:
+		dst[0] = 1
+		if n > 1 {
+			alpha := math.Pow(cond, -1/float64(n-1))
+			for i := 1; i < n; i++ {
+				dst[i] = math.Pow(alpha, float64(i))
+			}
+		}
+	case 4:
+		dst[0] = 1
+		if n > 1 {
+			condInv := 1 / cond
+			alpha := (1 - condInv) / float64(n-1)
+			for i := 1; i < n; i++ {
+				dst[i] = float64(n-i-1)*alpha + condInv
+			}
+		}
+	case 5:
+		alpha := math.Log(1 / cond)
+		for i := range dst {
+			dst[i] = math.Exp(alpha * rnd.Float64())
+		}
+	case 6:
+		switch dist {
+		case 1:
+			for i := range dst {
+				dst[i] = rnd.Float64()
+			}
+		case 2:
+			for i := range dst {
+				dst[i] = 2*rnd.Float64() - 1
+			}
+		case 3:
+			for i := range dst {
+				dst[i] = rnd.NormFloat64()
+			}
+		}
+	}
+
+	if rsign && amode != 6 {
+		for i, v := range dst {
+			if rnd.Float64() < 0.5 {
+				dst[i] = -v
+			}
+		}
+	}
+
+	if mode < 0 {
+		for i := 0; i < n/2; i++ {
+			dst[i], dst[n-i-1] = dst[n-i-1], dst[i]
+		}
+	}
+}