cgo,native: implement dgeqp3 and test

testlapack/dgeqp3.go

@@ -0,0 +1,135 @@
+// 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"
+)
+
+type Dgeqp3er interface {
+	Dlapmter
+	Dgeqp3(m, n int, a []float64, lda int, jpvt []int, tau, work []float64, lwork int)
+}
+
+func Dgeqp3Test(t *testing.T, impl Dgeqp3er) {
+	rnd := rand.New(rand.NewSource(1))
+	for c, test := range []struct {
+		m, n, lda int
+	}{
+		{1, 1, 0},
+		{2, 2, 0},
+		{3, 2, 0},
+		{2, 3, 0},
+		{1, 12, 0},
+		{2, 6, 0},
+		{3, 4, 0},
+		{4, 3, 0},
+		{6, 2, 0},
+		{12, 1, 0},
+		{1, 1, 20},
+		{2, 2, 20},
+		{3, 2, 20},
+		{2, 3, 20},
+		{1, 12, 20},
+		{2, 6, 20},
+		{3, 4, 20},
+		{4, 3, 20},
+		{6, 2, 20},
+		{12, 1, 20},
+		{129, 256, 0},
+		{256, 129, 0},
+		{129, 256, 266},
+		{256, 129, 266},
+	} {
+		n := test.n
+		m := test.m
+		lda := test.lda
+		if lda == 0 {
+			lda = test.n
+		}
+		const (
+			all = iota
+			some
+			none
+		)
+		for _, free := range []int{all, some, none} {
+			a := make([]float64, m*lda)
+			for i := range a {
+				a[i] = rnd.Float64()
+			}
+			aCopy := make([]float64, len(a))
+			copy(aCopy, a)
+			jpvt := make([]int, n)
+			for j := range jpvt {
+				switch free {
+				case all:
+					jpvt[j] = -1
+				case some:
+					jpvt[j] = rnd.Intn(2) - 1
+				case none:
+					jpvt[j] = 0
+				default:
+					panic("bad freedom")
+				}
+			}
+			k := min(m, n)
+			tau := make([]float64, k)
+			for i := range tau {
+				tau[i] = rnd.Float64()
+			}
+			work := make([]float64, 1)
+			impl.Dgeqp3(m, n, a, lda, jpvt, tau, work, -1)
+			lwork := int(work[0])
+			work = make([]float64, lwork)
+			for i := range work {
+				work[i] = rnd.Float64()
+			}
+			impl.Dgeqp3(m, n, a, lda, jpvt, tau, work, lwork)
+
+			// Test that the QR factorization has completed successfully. Compute
+			// Q based on the vectors.
+			q := constructQ("QR", m, n, a, lda, tau)
+
+			// Check that q is orthonormal
+			for i := 0; i < m; i++ {
+				nrm := blas64.Nrm2(m, blas64.Vector{Inc: 1, Data: q.Data[i*m:]})
+				if math.Abs(nrm-1) > 1e-13 {
+					t.Errorf("Case %v, q not normal", c)
+				}
+				for j := 0; j < i; j++ {
+					dot := blas64.Dot(m, blas64.Vector{Inc: 1, Data: q.Data[i*m:]}, blas64.Vector{Inc: 1, Data: q.Data[j*m:]})
+					if math.Abs(dot) > 1e-14 {
+						t.Errorf("Case %v, q not orthogonal", c)
+					}
+				}
+			}
+			// Check that A * P = Q * R
+			r := blas64.General{
+				Rows:   m,
+				Cols:   n,
+				Stride: n,
+				Data:   make([]float64, m*n),
+			}
+			for i := 0; i < m; i++ {
+				for j := i; j < n; j++ {
+					r.Data[i*n+j] = a[i*lda+j]
+				}
+			}
+			got := nanGeneral(m, n, lda)
+			blas64.Gemm(blas.NoTrans, blas.NoTrans, 1, q, r, 0, got)
+
+			want := blas64.General{Rows: m, Cols: n, Stride: lda, Data: aCopy}
+			impl.Dlapmt(true, want.Rows, want.Cols, want.Data, want.Stride, jpvt)
+			if !equalApproxGeneral(got, want, 1e-13) {
+				t.Errorf("Case %v,  Q*R != A*P\nQ*R=%v\nA*P=%v", c, got, want)
+			}
+		}
+	}
+}