Working implementation of blocked QR

Improved function documentation

Fixed dlarfb and dlarft and added full tests

Added dgelq2

Working Dgels

Fix many comments and tests

Many PR comment responses

Responded to more PR comments

Many PR comments

testlapack/dormqr.go

@@ -0,0 +1,150 @@
+// 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 (
+	"fmt"
+	"math/rand"
+	"testing"
+
+	"github.com/gonum/blas"
+	"github.com/gonum/floats"
+)
+
+type Dormqrer interface {
+	Dorm2rer
+	Dormqr(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int)
+}
+
+func DormqrTest(t *testing.T, impl Dormqrer) {
+	for _, side := range []blas.Side{blas.Left, blas.Right} {
+		for _, trans := range []blas.Transpose{blas.NoTrans, blas.Trans} {
+			for _, test := range []struct {
+				common, adim, cdim, lda, ldc int
+			}{
+				{6, 7, 8, 0, 0},
+				{6, 8, 7, 0, 0},
+				{7, 6, 8, 0, 0},
+				{7, 8, 6, 0, 0},
+				{8, 6, 7, 0, 0},
+				{8, 7, 6, 0, 0},
+				{100, 200, 300, 0, 0},
+				{100, 300, 200, 0, 0},
+				{200, 100, 300, 0, 0},
+				{200, 300, 100, 0, 0},
+				{300, 100, 200, 0, 0},
+				{300, 200, 100, 0, 0},
+				{100, 200, 300, 400, 500},
+				{100, 300, 200, 400, 500},
+				{200, 100, 300, 400, 500},
+				{200, 300, 100, 400, 500},
+				{300, 100, 200, 400, 500},
+				{300, 200, 100, 400, 500},
+				{100, 200, 300, 500, 400},
+				{100, 300, 200, 500, 400},
+				{200, 100, 300, 500, 400},
+				{200, 300, 100, 500, 400},
+				{300, 100, 200, 500, 400},
+				{300, 200, 100, 500, 400},
+			} {
+				var ma, na, mc, nc int
+				if side == blas.Left {
+					ma = test.common
+					na = test.adim
+					mc = test.common
+					nc = test.cdim
+				} else {
+					ma = test.common
+					na = test.adim
+					mc = test.cdim
+					nc = test.common
+				}
+				// Generate a random matrix
+				lda := test.lda
+				if lda == 0 {
+					lda = na
+				}
+				a := make([]float64, ma*lda)
+				for i := range a {
+					a[i] = rand.Float64()
+				}
+				// Compute random C matrix
+				ldc := test.ldc
+				if ldc == 0 {
+					ldc = nc
+				}
+				c := make([]float64, mc*ldc)
+				for i := range c {
+					c[i] = rand.Float64()
+				}
+
+				// Compute QR
+				k := min(ma, na)
+				tau := make([]float64, k)
+				work := make([]float64, 1)
+				impl.Dgeqrf(ma, na, a, lda, tau, work, -1)
+				work = make([]float64, int(work[0]))
+				impl.Dgeqrf(ma, na, a, lda, tau, work, len(work))
+
+				cCopy := make([]float64, len(c))
+				copy(cCopy, c)
+				ans := make([]float64, len(c))
+				copy(ans, cCopy)
+
+				if side == blas.Left {
+					work = make([]float64, nc)
+				} else {
+					work = make([]float64, mc)
+				}
+				impl.Dorm2r(side, trans, mc, nc, k, a, lda, tau, ans, ldc, work)
+
+				// Make sure Dorm2r and Dormqr match with small work
+				for i := range work {
+					work[i] = rand.Float64()
+				}
+				lwork := len(work)
+				copy(c, cCopy)
+				impl.Dormqr(side, trans, mc, nc, k, a, lda, tau, c, ldc, work, lwork)
+				if !floats.EqualApprox(c, ans, 1e-12) {
+					t.Errorf("Dormqr and Dorm2r mismatch for small work")
+				}
+
+				// Try with the optimum amount of work
+				copy(c, cCopy)
+				impl.Dormqr(side, trans, mc, nc, k, a, lda, tau, c, ldc, work, -1)
+				work = make([]float64, int(work[0]))
+				lwork = len(work)
+				for i := range work {
+					work[i] = rand.Float64()
+				}
+				_ = lwork
+				impl.Dormqr(side, trans, mc, nc, k, a, lda, tau, c, ldc, work, lwork)
+				if !floats.EqualApprox(c, ans, 1e-12) {
+					t.Errorf("Dormqr and Dorm2r mismatch for full work")
+					fmt.Println("ccopy")
+					for i := 0; i < mc; i++ {
+						fmt.Println(cCopy[i*ldc : (i+1)*ldc])
+					}
+					fmt.Println("ans =")
+					for i := 0; i < mc; i++ {
+						fmt.Println(ans[i*ldc : (i+1)*ldc])
+					}
+					fmt.Println("c =")
+					for i := 0; i < mc; i++ {
+						fmt.Println(c[i*ldc : (i+1)*ldc])
+					}
+				}
+				// Try with less than the optimum amount of work
+				copy(c, cCopy)
+				work = work[1:]
+				lwork--
+				impl.Dormqr(side, trans, mc, nc, k, a, lda, tau, c, ldc, work, lwork)
+				if !floats.EqualApprox(c, ans, 1e-12) {
+					t.Errorf("Dormqr and Dorm2r mismatch for medium work")
+				}
+			}
+		}
+	}
+}