lapack: imported lapack as a subtree

lapack/native/dlange.go

@@ -0,0 +1,84 @@
+// 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 native
+
+import (
+	"math"
+
+	"github.com/gonum/lapack"
+)
+
+// Dlange computes the matrix norm of the general m×n matrix a. The input norm
+// specifies the norm computed.
+//  lapack.MaxAbs: the maximum absolute value of an element.
+//  lapack.MaxColumnSum: the maximum column sum of the absolute values of the entries.
+//  lapack.MaxRowSum: the maximum row sum of the absolute values of the entries.
+//  lapack.NormFrob: the square root of the sum of the squares of the entries.
+// If norm == lapack.MaxColumnSum, work must be of length n, and this function will panic otherwise.
+// There are no restrictions on work for the other matrix norms.
+func (impl Implementation) Dlange(norm lapack.MatrixNorm, m, n int, a []float64, lda int, work []float64) float64 {
+	// TODO(btracey): These should probably be refactored to use BLAS calls.
+	checkMatrix(m, n, a, lda)
+	switch norm {
+	case lapack.MaxRowSum, lapack.MaxColumnSum, lapack.NormFrob, lapack.MaxAbs:
+	default:
+		panic(badNorm)
+	}
+	if norm == lapack.MaxColumnSum && len(work) < n {
+		panic(badWork)
+	}
+	if m == 0 && n == 0 {
+		return 0
+	}
+	if norm == lapack.MaxAbs {
+		var value float64
+		for i := 0; i < m; i++ {
+			for j := 0; j < n; j++ {
+				value = math.Max(value, math.Abs(a[i*lda+j]))
+			}
+		}
+		return value
+	}
+	if norm == lapack.MaxColumnSum {
+		if len(work) < n {
+			panic(badWork)
+		}
+		for i := 0; i < n; i++ {
+			work[i] = 0
+		}
+		for i := 0; i < m; i++ {
+			for j := 0; j < n; j++ {
+				work[j] += math.Abs(a[i*lda+j])
+			}
+		}
+		var value float64
+		for i := 0; i < n; i++ {
+			value = math.Max(value, work[i])
+		}
+		return value
+	}
+	if norm == lapack.MaxRowSum {
+		var value float64
+		for i := 0; i < m; i++ {
+			var sum float64
+			for j := 0; j < n; j++ {
+				sum += math.Abs(a[i*lda+j])
+			}
+			value = math.Max(value, sum)
+		}
+		return value
+	}
+	if norm == lapack.NormFrob {
+		var value float64
+		scale := 0.0
+		sum := 1.0
+		for i := 0; i < m; i++ {
+			scale, sum = impl.Dlassq(n, a[i*lda:], 1, scale, sum)
+		}
+		value = scale * math.Sqrt(sum)
+		return value
+	}
+	panic("lapack: bad matrix norm")
+}