From f08ea468d690b524286d156324f8795b7e64b198 Mon Sep 17 00:00:00 2001
From: Vladimir Chalupecky <vladimir.chalupecky@gmail.com>
Date: Wed, 19 Dec 2018 17:22:32 +0100
Subject: [PATCH] lapack/testlapack: add tests for Dlauu2 and Dlauum

---
 lapack/gonum/lapack_test.go |   8 +++
 lapack/testlapack/dlauu2.go | 112 ++++++++++++++++++++++++++++++++++++
 lapack/testlapack/dlauum.go |  30 ++++++++++
 3 files changed, 150 insertions(+)
 create mode 100644 lapack/testlapack/dlauu2.go
 create mode 100644 lapack/testlapack/dlauum.go

diff --git a/lapack/gonum/lapack_test.go b/lapack/gonum/lapack_test.go
index eab28cef8d..5f51bf1e81 100644
--- a/lapack/gonum/lapack_test.go
+++ b/lapack/gonum/lapack_test.go
@@ -296,6 +296,14 @@ func TestDlatrs(t *testing.T) {
 	testlapack.DlatrsTest(t, impl)
 }
 
+func TestDlauu2(t *testing.T) {
+	testlapack.Dlauu2Test(t, impl)
+}
+
+func TestDlauum(t *testing.T) {
+	testlapack.DlauumTest(t, impl)
+}
+
 func TestDorg2r(t *testing.T) {
 	testlapack.Dorg2rTest(t, impl)
 }
diff --git a/lapack/testlapack/dlauu2.go b/lapack/testlapack/dlauu2.go
new file mode 100644
index 0000000000..66e04ec34d
--- /dev/null
+++ b/lapack/testlapack/dlauu2.go
@@ -0,0 +1,112 @@
+// Copyright ©2018 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"
+	"testing"
+
+	"golang.org/x/exp/rand"
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/blas/blas64"
+)
+
+type Dlauu2er interface {
+	Dlauu2(uplo blas.Uplo, n int, a []float64, lda int)
+}
+
+func Dlauu2Test(t *testing.T, impl Dlauu2er) {
+	for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+		name := "Upper"
+		if uplo == blas.Lower {
+			name = "Lower"
+		}
+		t.Run(name, func(t *testing.T) {
+			ns := []int{0, 1, 2, 3, 4, 5, 10, 25}
+			dlauuTest(t, impl.Dlauu2, uplo, ns)
+		})
+	}
+}
+
+func dlauuTest(t *testing.T, dlauu func(blas.Uplo, int, []float64, int), uplo blas.Uplo, ns []int) {
+	const tol = 1e-13
+
+	bi := blas64.Implementation()
+	rnd := rand.New(rand.NewSource(1))
+
+	for _, n := range ns {
+	loop:
+		for _, lda := range []int{max(1, n), n + 11} {
+			prefix := fmt.Sprintf("n=%v,lda=%v", n, lda)
+
+			// Allocate n×n matrix A and fill it with random numbers.
+			// Only its uplo triangle will be used below.
+			a := make([]float64, n*lda)
+			for i := range a {
+				a[i] = rnd.NormFloat64()
+			}
+			// Create a copy of A.
+			aCopy := make([]float64, len(a))
+			copy(aCopy, a)
+
+			// Compute U*U^T or L^T*L using Dlauu?.
+			dlauu(uplo, n, a, lda)
+
+			if n == 0 {
+				continue
+			}
+
+			// * Check that the triangle opposite to uplo has not been modified.
+			// * Convert the result of Dlauu? into a dense symmetric matrix.
+			// * Zero out the triangle in aCopy opposite to uplo.
+			if uplo == blas.Upper {
+				for i := 1; i < n; i++ {
+					for j := 0; j < i; j++ {
+						if aCopy[i*lda+j] != a[i*lda+j] {
+							t.Errorf("%v: unexpected modification in upper triangle", prefix)
+							break loop
+						}
+						a[i*lda+j] = a[j*lda+i]
+						aCopy[i*lda+j] = 0
+					}
+				}
+			} else {
+				for i := 0; i < n-1; i++ {
+					for j := i + 1; j < n; j++ {
+						if aCopy[i*lda+j] != a[i*lda+j] {
+							t.Errorf("%v: unexpected modification in lower triangle", prefix)
+							break loop
+						}
+						a[i*lda+j] = a[j*lda+i]
+						aCopy[i*lda+j] = 0
+					}
+				}
+			}
+
+			// Compute U*U^T or L^T*L using Dgemm with U and L
+			// represented as dense triangular matrices.
+			ldwant := n
+			want := make([]float64, n*ldwant)
+			if uplo == blas.Upper {
+				// Use aCopy as a dense representation of the upper triangular U.
+				u := aCopy
+				ldu := lda
+				// Compute U * U^T and store the result into want.
+				bi.Dgemm(blas.NoTrans, blas.Trans, n, n, n,
+					1, u, ldu, u, ldu, 0, want, ldwant)
+			} else {
+				// Use aCopy as a dense representation of the lower triangular L.
+				l := aCopy
+				ldl := lda
+				// Compute L^T * L and store the result into want.
+				bi.Dgemm(blas.Trans, blas.NoTrans, n, n, n,
+					1, l, ldl, l, ldl, 0, want, ldwant)
+			}
+			if !equalApprox(n, n, a, lda, want, tol) {
+				t.Errorf("%v: unexpected result", prefix)
+			}
+		}
+	}
+}
diff --git a/lapack/testlapack/dlauum.go b/lapack/testlapack/dlauum.go
new file mode 100644
index 0000000000..604ae7d878
--- /dev/null
+++ b/lapack/testlapack/dlauum.go
@@ -0,0 +1,30 @@
+// Copyright ©2018 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 (
+	"testing"
+
+	"gonum.org/v1/gonum/blas"
+)
+
+type Dlauumer interface {
+	Dlauum(uplo blas.Uplo, n int, a []float64, lda int)
+}
+
+func DlauumTest(t *testing.T, impl Dlauumer) {
+	for _, uplo := range []blas.Uplo{blas.Upper, blas.Lower} {
+		name := "Upper"
+		if uplo == blas.Lower {
+			name = "Lower"
+		}
+		t.Run(name, func(t *testing.T) {
+			// Include small and large sizes to make sure that both
+			// unblocked and blocked paths are taken.
+			ns := []int{0, 1, 2, 3, 4, 5, 10, 25, 31, 32, 33, 63, 64, 65, 127, 128, 129}
+			dlauuTest(t, impl.Dlauum, uplo, ns)
+		})
+	}
+}