lapack: imported lapack as a subtree

lapack/native/dlarfx.go

@@ -0,0 +1,535 @@
+// Copyright ©2016 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 native
+
+import "github.com/gonum/blas"
+
+// Dlarfx applies an elementary reflector H to a real m×n matrix C, from either
+// the left or the right, with loop unrolling when the reflector has order less
+// than 11.
+//
+// H is represented in the form
+//  H = I - tau * v * v^T,
+// where tau is a real scalar and v is a real vector. If tau = 0, then H is
+// taken to be the identity matrix.
+//
+// v must have length equal to m if side == blas.Left, and equal to n if side ==
+// blas.Right, otherwise Dlarfx will panic.
+//
+// c and ldc represent the m×n matrix C. On return, C is overwritten by the
+// matrix H * C if side == blas.Left, or C * H if side == blas.Right.
+//
+// work must have length at least n if side == blas.Left, and at least m if side
+// == blas.Right, otherwise Dlarfx will panic. work is not referenced if H has
+// order < 11.
+//
+// Dlarfx is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dlarfx(side blas.Side, m, n int, v []float64, tau float64, c []float64, ldc int, work []float64) {
+	checkMatrix(m, n, c, ldc)
+	switch side {
+	case blas.Left:
+		checkVector(m, v, 1)
+		if m > 10 && len(work) < n {
+			panic(badWork)
+		}
+	case blas.Right:
+		checkVector(n, v, 1)
+		if n > 10 && len(work) < m {
+			panic(badWork)
+		}
+	default:
+		panic(badSide)
+	}
+
+	if tau == 0 {
+		return
+	}
+
+	if side == blas.Left {
+		// Form H * C, where H has order m.
+		switch m {
+		default: // Code for general m.
+			impl.Dlarf(side, m, n, v, 1, tau, c, ldc, work)
+			return
+
+		case 0: // No-op for zero size matrix.
+			return
+
+		case 1: // Special code for 1×1 Householder matrix.
+			t0 := 1 - tau*v[0]*v[0]
+			for j := 0; j < n; j++ {
+				c[j] *= t0
+			}
+			return
+
+		case 2: // Special code for 2×2 Householder matrix.
+			v0 := v[0]
+			t0 := tau * v0
+			v1 := v[1]
+			t1 := tau * v1
+			for j := 0; j < n; j++ {
+				sum := v0*c[j] + v1*c[ldc+j]
+				c[j] -= sum * t0
+				c[ldc+j] -= sum * t1
+			}
+			return
+
+		case 3: // Special code for 3×3 Householder matrix.
+			v0 := v[0]
+			t0 := tau * v0
+			v1 := v[1]
+			t1 := tau * v1
+			v2 := v[2]
+			t2 := tau * v2
+			for j := 0; j < n; j++ {
+				sum := v0*c[j] + v1*c[ldc+j] + v2*c[2*ldc+j]
+				c[j] -= sum * t0
+				c[ldc+j] -= sum * t1
+				c[2*ldc+j] -= sum * t2
+			}
+			return
+
+		case 4: // Special code for 4×4 Householder matrix.
+			v0 := v[0]
+			t0 := tau * v0
+			v1 := v[1]
+			t1 := tau * v1
+			v2 := v[2]
+			t2 := tau * v2
+			v3 := v[3]
+			t3 := tau * v3
+			for j := 0; j < n; j++ {
+				sum := v0*c[j] + v1*c[ldc+j] + v2*c[2*ldc+j] + v3*c[3*ldc+j]
+				c[j] -= sum * t0
+				c[ldc+j] -= sum * t1
+				c[2*ldc+j] -= sum * t2
+				c[3*ldc+j] -= sum * t3
+			}
+			return
+
+		case 5: // Special code for 5×5 Householder matrix.
+			v0 := v[0]
+			t0 := tau * v0
+			v1 := v[1]
+			t1 := tau * v1
+			v2 := v[2]
+			t2 := tau * v2
+			v3 := v[3]
+			t3 := tau * v3
+			v4 := v[4]
+			t4 := tau * v4
+			for j := 0; j < n; j++ {
+				sum := v0*c[j] + v1*c[ldc+j] + v2*c[2*ldc+j] + v3*c[3*ldc+j] + v4*c[4*ldc+j]
+				c[j] -= sum * t0
+				c[ldc+j] -= sum * t1
+				c[2*ldc+j] -= sum * t2
+				c[3*ldc+j] -= sum * t3
+				c[4*ldc+j] -= sum * t4
+			}
+			return
+
+		case 6: // Special code for 6×6 Householder matrix.
+			v0 := v[0]
+			t0 := tau * v0
+			v1 := v[1]
+			t1 := tau * v1
+			v2 := v[2]
+			t2 := tau * v2
+			v3 := v[3]
+			t3 := tau * v3
+			v4 := v[4]
+			t4 := tau * v4
+			v5 := v[5]
+			t5 := tau * v5
+			for j := 0; j < n; j++ {
+				sum := v0*c[j] + v1*c[ldc+j] + v2*c[2*ldc+j] + v3*c[3*ldc+j] + v4*c[4*ldc+j] +
+					v5*c[5*ldc+j]
+				c[j] -= sum * t0
+				c[ldc+j] -= sum * t1
+				c[2*ldc+j] -= sum * t2
+				c[3*ldc+j] -= sum * t3
+				c[4*ldc+j] -= sum * t4
+				c[5*ldc+j] -= sum * t5
+			}
+			return
+
+		case 7: // Special code for 7×7 Householder matrix.
+			v0 := v[0]
+			t0 := tau * v0
+			v1 := v[1]
+			t1 := tau * v1
+			v2 := v[2]
+			t2 := tau * v2
+			v3 := v[3]
+			t3 := tau * v3
+			v4 := v[4]
+			t4 := tau * v4
+			v5 := v[5]
+			t5 := tau * v5
+			v6 := v[6]
+			t6 := tau * v6
+			for j := 0; j < n; j++ {
+				sum := v0*c[j] + v1*c[ldc+j] + v2*c[2*ldc+j] + v3*c[3*ldc+j] + v4*c[4*ldc+j] +
+					v5*c[5*ldc+j] + v6*c[6*ldc+j]
+				c[j] -= sum * t0
+				c[ldc+j] -= sum * t1
+				c[2*ldc+j] -= sum * t2
+				c[3*ldc+j] -= sum * t3
+				c[4*ldc+j] -= sum * t4
+				c[5*ldc+j] -= sum * t5
+				c[6*ldc+j] -= sum * t6
+			}
+			return
+
+		case 8: // Special code for 8×8 Householder matrix.
+			v0 := v[0]
+			t0 := tau * v0
+			v1 := v[1]
+			t1 := tau * v1
+			v2 := v[2]
+			t2 := tau * v2
+			v3 := v[3]
+			t3 := tau * v3
+			v4 := v[4]
+			t4 := tau * v4
+			v5 := v[5]
+			t5 := tau * v5
+			v6 := v[6]
+			t6 := tau * v6
+			v7 := v[7]
+			t7 := tau * v7
+			for j := 0; j < n; j++ {
+				sum := v0*c[j] + v1*c[ldc+j] + v2*c[2*ldc+j] + v3*c[3*ldc+j] + v4*c[4*ldc+j] +
+					v5*c[5*ldc+j] + v6*c[6*ldc+j] + v7*c[7*ldc+j]
+				c[j] -= sum * t0
+				c[ldc+j] -= sum * t1
+				c[2*ldc+j] -= sum * t2
+				c[3*ldc+j] -= sum * t3
+				c[4*ldc+j] -= sum * t4
+				c[5*ldc+j] -= sum * t5
+				c[6*ldc+j] -= sum * t6
+				c[7*ldc+j] -= sum * t7
+			}
+			return
+
+		case 9: // Special code for 9×9 Householder matrix.
+			v0 := v[0]
+			t0 := tau * v0
+			v1 := v[1]
+			t1 := tau * v1
+			v2 := v[2]
+			t2 := tau * v2
+			v3 := v[3]
+			t3 := tau * v3
+			v4 := v[4]
+			t4 := tau * v4
+			v5 := v[5]
+			t5 := tau * v5
+			v6 := v[6]
+			t6 := tau * v6
+			v7 := v[7]
+			t7 := tau * v7
+			v8 := v[8]
+			t8 := tau * v8
+			for j := 0; j < n; j++ {
+				sum := v0*c[j] + v1*c[ldc+j] + v2*c[2*ldc+j] + v3*c[3*ldc+j] + v4*c[4*ldc+j] +
+					v5*c[5*ldc+j] + v6*c[6*ldc+j] + v7*c[7*ldc+j] + v8*c[8*ldc+j]
+				c[j] -= sum * t0
+				c[ldc+j] -= sum * t1
+				c[2*ldc+j] -= sum * t2
+				c[3*ldc+j] -= sum * t3
+				c[4*ldc+j] -= sum * t4
+				c[5*ldc+j] -= sum * t5
+				c[6*ldc+j] -= sum * t6
+				c[7*ldc+j] -= sum * t7
+				c[8*ldc+j] -= sum * t8
+			}
+			return
+
+		case 10: // Special code for 10×10 Householder matrix.
+			v0 := v[0]
+			t0 := tau * v0
+			v1 := v[1]
+			t1 := tau * v1
+			v2 := v[2]
+			t2 := tau * v2
+			v3 := v[3]
+			t3 := tau * v3
+			v4 := v[4]
+			t4 := tau * v4
+			v5 := v[5]
+			t5 := tau * v5
+			v6 := v[6]
+			t6 := tau * v6
+			v7 := v[7]
+			t7 := tau * v7
+			v8 := v[8]
+			t8 := tau * v8
+			v9 := v[9]
+			t9 := tau * v9
+			for j := 0; j < n; j++ {
+				sum := v0*c[j] + v1*c[ldc+j] + v2*c[2*ldc+j] + v3*c[3*ldc+j] + v4*c[4*ldc+j] +
+					v5*c[5*ldc+j] + v6*c[6*ldc+j] + v7*c[7*ldc+j] + v8*c[8*ldc+j] + v9*c[9*ldc+j]
+				c[j] -= sum * t0
+				c[ldc+j] -= sum * t1
+				c[2*ldc+j] -= sum * t2
+				c[3*ldc+j] -= sum * t3
+				c[4*ldc+j] -= sum * t4
+				c[5*ldc+j] -= sum * t5
+				c[6*ldc+j] -= sum * t6
+				c[7*ldc+j] -= sum * t7
+				c[8*ldc+j] -= sum * t8
+				c[9*ldc+j] -= sum * t9
+			}
+			return
+		}
+	}
+
+	// Form C * H, where H has order n.
+	switch n {
+	default: // Code for general n.
+		impl.Dlarf(side, m, n, v, 1, tau, c, ldc, work)
+		return
+
+	case 0: // No-op for zero size matrix.
+		return
+
+	case 1: // Special code for 1×1 Householder matrix.
+		t0 := 1 - tau*v[0]*v[0]
+		for j := 0; j < m; j++ {
+			c[j*ldc] *= t0
+		}
+		return
+
+	case 2: // Special code for 2×2 Householder matrix.
+		v0 := v[0]
+		t0 := tau * v0
+		v1 := v[1]
+		t1 := tau * v1
+		for j := 0; j < m; j++ {
+			cs := c[j*ldc:]
+			sum := v0*cs[0] + v1*cs[1]
+			cs[0] -= sum * t0
+			cs[1] -= sum * t1
+		}
+		return
+
+	case 3: // Special code for 3×3 Householder matrix.
+		v0 := v[0]
+		t0 := tau * v0
+		v1 := v[1]
+		t1 := tau * v1
+		v2 := v[2]
+		t2 := tau * v2
+		for j := 0; j < m; j++ {
+			cs := c[j*ldc:]
+			sum := v0*cs[0] + v1*cs[1] + v2*cs[2]
+			cs[0] -= sum * t0
+			cs[1] -= sum * t1
+			cs[2] -= sum * t2
+		}
+		return
+
+	case 4: // Special code for 4×4 Householder matrix.
+		v0 := v[0]
+		t0 := tau * v0
+		v1 := v[1]
+		t1 := tau * v1
+		v2 := v[2]
+		t2 := tau * v2
+		v3 := v[3]
+		t3 := tau * v3
+		for j := 0; j < m; j++ {
+			cs := c[j*ldc:]
+			sum := v0*cs[0] + v1*cs[1] + v2*cs[2] + v3*cs[3]
+			cs[0] -= sum * t0
+			cs[1] -= sum * t1
+			cs[2] -= sum * t2
+			cs[3] -= sum * t3
+		}
+		return
+
+	case 5: // Special code for 5×5 Householder matrix.
+		v0 := v[0]
+		t0 := tau * v0
+		v1 := v[1]
+		t1 := tau * v1
+		v2 := v[2]
+		t2 := tau * v2
+		v3 := v[3]
+		t3 := tau * v3
+		v4 := v[4]
+		t4 := tau * v4
+		for j := 0; j < m; j++ {
+			cs := c[j*ldc:]
+			sum := v0*cs[0] + v1*cs[1] + v2*cs[2] + v3*cs[3] + v4*cs[4]
+			cs[0] -= sum * t0
+			cs[1] -= sum * t1
+			cs[2] -= sum * t2
+			cs[3] -= sum * t3
+			cs[4] -= sum * t4
+		}
+		return
+
+	case 6: // Special code for 6×6 Householder matrix.
+		v0 := v[0]
+		t0 := tau * v0
+		v1 := v[1]
+		t1 := tau * v1
+		v2 := v[2]
+		t2 := tau * v2
+		v3 := v[3]
+		t3 := tau * v3
+		v4 := v[4]
+		t4 := tau * v4
+		v5 := v[5]
+		t5 := tau * v5
+		for j := 0; j < m; j++ {
+			cs := c[j*ldc:]
+			sum := v0*cs[0] + v1*cs[1] + v2*cs[2] + v3*cs[3] + v4*cs[4] + v5*cs[5]
+			cs[0] -= sum * t0
+			cs[1] -= sum * t1
+			cs[2] -= sum * t2
+			cs[3] -= sum * t3
+			cs[4] -= sum * t4
+			cs[5] -= sum * t5
+		}
+		return
+
+	case 7: // Special code for 7×7 Householder matrix.
+		v0 := v[0]
+		t0 := tau * v0
+		v1 := v[1]
+		t1 := tau * v1
+		v2 := v[2]
+		t2 := tau * v2
+		v3 := v[3]
+		t3 := tau * v3
+		v4 := v[4]
+		t4 := tau * v4
+		v5 := v[5]
+		t5 := tau * v5
+		v6 := v[6]
+		t6 := tau * v6
+		for j := 0; j < m; j++ {
+			cs := c[j*ldc:]
+			sum := v0*cs[0] + v1*cs[1] + v2*cs[2] + v3*cs[3] + v4*cs[4] +
+				v5*cs[5] + v6*cs[6]
+			cs[0] -= sum * t0
+			cs[1] -= sum * t1
+			cs[2] -= sum * t2
+			cs[3] -= sum * t3
+			cs[4] -= sum * t4
+			cs[5] -= sum * t5
+			cs[6] -= sum * t6
+		}
+		return
+
+	case 8: // Special code for 8×8 Householder matrix.
+		v0 := v[0]
+		t0 := tau * v0
+		v1 := v[1]
+		t1 := tau * v1
+		v2 := v[2]
+		t2 := tau * v2
+		v3 := v[3]
+		t3 := tau * v3
+		v4 := v[4]
+		t4 := tau * v4
+		v5 := v[5]
+		t5 := tau * v5
+		v6 := v[6]
+		t6 := tau * v6
+		v7 := v[7]
+		t7 := tau * v7
+		for j := 0; j < m; j++ {
+			cs := c[j*ldc:]
+			sum := v0*cs[0] + v1*cs[1] + v2*cs[2] + v3*cs[3] + v4*cs[4] +
+				v5*cs[5] + v6*cs[6] + v7*cs[7]
+			cs[0] -= sum * t0
+			cs[1] -= sum * t1
+			cs[2] -= sum * t2
+			cs[3] -= sum * t3
+			cs[4] -= sum * t4
+			cs[5] -= sum * t5
+			cs[6] -= sum * t6
+			cs[7] -= sum * t7
+		}
+		return
+
+	case 9: // Special code for 9×9 Householder matrix.
+		v0 := v[0]
+		t0 := tau * v0
+		v1 := v[1]
+		t1 := tau * v1
+		v2 := v[2]
+		t2 := tau * v2
+		v3 := v[3]
+		t3 := tau * v3
+		v4 := v[4]
+		t4 := tau * v4
+		v5 := v[5]
+		t5 := tau * v5
+		v6 := v[6]
+		t6 := tau * v6
+		v7 := v[7]
+		t7 := tau * v7
+		v8 := v[8]
+		t8 := tau * v8
+		for j := 0; j < m; j++ {
+			cs := c[j*ldc:]
+			sum := v0*cs[0] + v1*cs[1] + v2*cs[2] + v3*cs[3] + v4*cs[4] +
+				v5*cs[5] + v6*cs[6] + v7*cs[7] + v8*cs[8]
+			cs[0] -= sum * t0
+			cs[1] -= sum * t1
+			cs[2] -= sum * t2
+			cs[3] -= sum * t3
+			cs[4] -= sum * t4
+			cs[5] -= sum * t5
+			cs[6] -= sum * t6
+			cs[7] -= sum * t7
+			cs[8] -= sum * t8
+		}
+		return
+
+	case 10: // Special code for 10×10 Householder matrix.
+		v0 := v[0]
+		t0 := tau * v0
+		v1 := v[1]
+		t1 := tau * v1
+		v2 := v[2]
+		t2 := tau * v2
+		v3 := v[3]
+		t3 := tau * v3
+		v4 := v[4]
+		t4 := tau * v4
+		v5 := v[5]
+		t5 := tau * v5
+		v6 := v[6]
+		t6 := tau * v6
+		v7 := v[7]
+		t7 := tau * v7
+		v8 := v[8]
+		t8 := tau * v8
+		v9 := v[9]
+		t9 := tau * v9
+		for j := 0; j < m; j++ {
+			cs := c[j*ldc:]
+			sum := v0*cs[0] + v1*cs[1] + v2*cs[2] + v3*cs[3] + v4*cs[4] +
+				v5*cs[5] + v6*cs[6] + v7*cs[7] + v8*cs[8] + v9*cs[9]
+			cs[0] -= sum * t0
+			cs[1] -= sum * t1
+			cs[2] -= sum * t2
+			cs[3] -= sum * t3
+			cs[4] -= sum * t4
+			cs[5] -= sum * t5
+			cs[6] -= sum * t6
+			cs[7] -= sum * t7
+			cs[8] -= sum * t8
+			cs[9] -= sum * t9
+		}
+		return
+	}
+}