lapack: add Dgtsv

lapack/testlapack/locallapack.go

@@ -0,0 +1,162 @@
+// Copyright ©2020 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"
+
+	"gonum.org/v1/gonum/blas"
+	"gonum.org/v1/gonum/lapack"
+)
+
+func dlagtm(trans blas.Transpose, m, n int, alpha float64, dl, d, du []float64, b []float64, ldb int, beta float64, c []float64, ldc int) {
+	if m == 0 || n == 0 {
+		return
+	}
+
+	if beta != 1 {
+		if beta == 0 {
+			for i := 0; i < m; i++ {
+				ci := c[i*ldc : i*ldc+n]
+				for j := range ci {
+					ci[j] = 0
+				}
+			}
+		} else {
+			for i := 0; i < m; i++ {
+				ci := c[i*ldc : i*ldc+n]
+				for j := range ci {
+					ci[j] *= beta
+				}
+			}
+		}
+	}
+
+	if alpha == 0 {
+		return
+	}
+
+	if m == 1 {
+		if alpha == 1 {
+			for j := 0; j < n; j++ {
+				c[j] += d[0] * b[j]
+			}
+		} else {
+			for j := 0; j < n; j++ {
+				c[j] += alpha * d[0] * b[j]
+			}
+		}
+		return
+	}
+
+	if trans != blas.NoTrans {
+		dl, du = du, dl
+	}
+
+	if alpha == 1 {
+		for j := 0; j < n; j++ {
+			c[j] += d[0]*b[j] + du[0]*b[ldb+j]
+		}
+		for i := 1; i < m-1; i++ {
+			for j := 0; j < n; j++ {
+				c[i*ldc+j] += dl[i-1]*b[(i-1)*ldb+j] + d[i]*b[i*ldb+j] + du[i]*b[(i+1)*ldb+j]
+			}
+		}
+		for j := 0; j < n; j++ {
+			c[(m-1)*ldc+j] += dl[m-2]*b[(m-2)*ldb+j] + d[m-1]*b[(m-1)*ldb+j]
+		}
+	} else {
+		for j := 0; j < n; j++ {
+			c[j] += alpha * (d[0]*b[j] + du[0]*b[ldb+j])
+		}
+		for i := 1; i < m-1; i++ {
+			for j := 0; j < n; j++ {
+				c[i*ldc+j] += alpha * (dl[i-1]*b[(i-1)*ldb+j] + d[i]*b[i*ldb+j] + du[i]*b[(i+1)*ldb+j])
+			}
+		}
+		for j := 0; j < n; j++ {
+			c[(m-1)*ldc+j] += alpha * (dl[m-2]*b[(m-2)*ldb+j] + d[m-1]*b[(m-1)*ldb+j])
+		}
+	}
+}
+
+func dlangt(norm lapack.MatrixNorm, n int, dl, d, du []float64) float64 {
+	if n == 0 {
+		return 0
+	}
+
+	dl = dl[:n-1]
+	d = d[:n]
+	du = du[:n-1]
+
+	var anorm float64
+	switch norm {
+	case lapack.MaxAbs:
+		for _, diag := range [][]float64{dl, d, du} {
+			for _, di := range diag {
+				if math.IsNaN(di) {
+					return di
+				}
+				di = math.Abs(di)
+				if di > anorm {
+					anorm = di
+				}
+			}
+		}
+	case lapack.MaxColumnSum:
+		if n == 1 {
+			return math.Abs(d[0])
+		}
+		anorm = math.Abs(d[0]) + math.Abs(dl[0])
+		if math.IsNaN(anorm) {
+			return anorm
+		}
+		tmp := math.Abs(du[n-2]) + math.Abs(d[n-1])
+		if math.IsNaN(tmp) {
+			return tmp
+		}
+		if tmp > anorm {
+			anorm = tmp
+		}
+		for i := 1; i < n-1; i++ {
+			tmp = math.Abs(du[i-1]) + math.Abs(d[i]) + math.Abs(dl[i])
+			if math.IsNaN(tmp) {
+				return tmp
+			}
+			if tmp > anorm {
+				anorm = tmp
+			}
+		}
+	case lapack.MaxRowSum:
+		if n == 1 {
+			return math.Abs(d[0])
+		}
+		anorm = math.Abs(d[0]) + math.Abs(du[0])
+		if math.IsNaN(anorm) {
+			return anorm
+		}
+		tmp := math.Abs(dl[n-2]) + math.Abs(d[n-1])
+		if math.IsNaN(tmp) {
+			return tmp
+		}
+		if tmp > anorm {
+			anorm = tmp
+		}
+		for i := 1; i < n-1; i++ {
+			tmp = math.Abs(dl[i-1]) + math.Abs(d[i]) + math.Abs(du[i])
+			if math.IsNaN(tmp) {
+				return tmp
+			}
+			if tmp > anorm {
+				anorm = tmp
+			}
+		}
+	case lapack.Frobenius:
+		panic("not implemented")
+	default:
+		panic("invalid norm")
+	}
+	return anorm
+}