From 5150caf5155452c1f858755f7bf925f1ea5fd474 Mon Sep 17 00:00:00 2001
From: Will Charczuk <will@blendlabs.com>
Date: Mon, 17 Apr 2017 23:08:46 -0700
Subject: [PATCH] lu decomp implementation.

---
 matrix/matrix.go      | 60 +++++++++++++++++++++++++++++++++++++++++++
 matrix/matrix_test.go | 15 +++++++++++
 2 files changed, 75 insertions(+)

diff --git a/matrix/matrix.go b/matrix/matrix.go
index 51a3da0..c94768b 100644
--- a/matrix/matrix.go
+++ b/matrix/matrix.go
@@ -324,8 +324,68 @@ func (m *Matrix) Multiply(m2 *Matrix) (m3 *Matrix, err error) {
 	return
 }
 
+// Pivotize does something i'm not sure what.
+func (m *Matrix) Pivotize() *Matrix {
+	pv := make([]int, m.stride)
+
+	for i := range pv {
+		pv[i] = i
+	}
+
+	for j, dx := 0, 0; j < m.stride; j++ {
+		row := j
+		max := m.elements[dx]
+		for i, ixcj := j, dx; i < m.stride; i++ {
+			if m.elements[ixcj] > max {
+				max = m.elements[ixcj]
+				row = i
+			}
+			ixcj += m.stride
+		}
+		if j != row {
+			pv[row], pv[j] = pv[j], pv[row]
+		}
+		dx += m.stride + 1
+	}
+	p := Zero(m.stride, m.stride)
+	for r, c := range pv {
+		p.elements[r*m.stride+c] = 1
+	}
+	return p
+}
+
 // Decompositions
 
+// LU performs the LU decomposition.
+func (m *Matrix) LU() (l, u, p *Matrix) {
+	l = Zero(m.stride, m.stride)
+	u = Zero(m.stride, m.stride)
+	p = m.Pivotize()
+	m, _ = p.Multiply(m)
+	for j, jxc0 := 0, 0; j < m.stride; j++ {
+		l.elements[jxc0+j] = 1
+		for i, ixc0 := 0, 0; ixc0 <= jxc0; i++ {
+			sum := 0.
+			for k, kxcj := 0, j; k < i; k++ {
+				sum += u.elements[kxcj] * l.elements[ixc0+k]
+				kxcj += m.stride
+			}
+			u.elements[ixc0+j] = m.elements[ixc0+j] - sum
+			ixc0 += m.stride
+		}
+		for ixc0 := jxc0; ixc0 < len(m.elements); ixc0 += m.stride {
+			sum := 0.
+			for k, kxcj := 0, j; k < j; k++ {
+				sum += u.elements[kxcj] * l.elements[ixc0+k]
+				kxcj += m.stride
+			}
+			l.elements[ixc0+j] = (m.elements[ixc0+j] - sum) / u.elements[jxc0+j]
+		}
+		jxc0 += m.stride
+	}
+	return
+}
+
 // QR performs the qr decomposition.
 func (m *Matrix) QR() (q, r *Matrix) {
 	defer func() {
diff --git a/matrix/matrix_test.go b/matrix/matrix_test.go
index c58c5ba..52475f2 100644
--- a/matrix/matrix_test.go
+++ b/matrix/matrix_test.go
@@ -329,6 +329,21 @@ func TestMatrixString(t *testing.T) {
 	assert.Equal("1 2 3 \n4 5 6 \n7 8 9 \n", m.String())
 }
 
+func TestMatrixLU(t *testing.T) {
+	assert := assert.New(t)
+
+	m := NewFromArrays([][]float64{
+		{1, 3, 5},
+		{2, 4, 7},
+		{1, 1, 0},
+	})
+
+	l, u, p := m.LU()
+	assert.NotNil(l)
+	assert.NotNil(u)
+	assert.NotNil(p)
+}
+
 func TestMatrixQR(t *testing.T) {
 	assert := assert.New(t)