lapack: imported lapack as a subtree

lapack/native/dgecon.go

@@ -0,0 +1,81 @@
+// 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/blas"
+	"github.com/gonum/blas/blas64"
+	"github.com/gonum/lapack"
+)
+
+// Dgecon estimates the reciprocal of the condition number of the n×n matrix A
+// given the LU decomposition of the matrix. The condition number computed may
+// be based on the 1-norm or the ∞-norm.
+//
+// The slice a contains the result of the LU decomposition of A as computed by Dgetrf.
+//
+// anorm is the corresponding 1-norm or ∞-norm of the original matrix A.
+//
+// work is a temporary data slice of length at least 4*n and Dgecon will panic otherwise.
+//
+// iwork is a temporary data slice of length at least n and Dgecon will panic otherwise.
+func (impl Implementation) Dgecon(norm lapack.MatrixNorm, n int, a []float64, lda int, anorm float64, work []float64, iwork []int) float64 {
+	checkMatrix(n, n, a, lda)
+	if norm != lapack.MaxColumnSum && norm != lapack.MaxRowSum {
+		panic(badNorm)
+	}
+	if len(work) < 4*n {
+		panic(badWork)
+	}
+	if len(iwork) < n {
+		panic(badWork)
+	}
+
+	if n == 0 {
+		return 1
+	} else if anorm == 0 {
+		return 0
+	}
+
+	bi := blas64.Implementation()
+	var rcond, ainvnm float64
+	var kase int
+	var normin bool
+	isave := new([3]int)
+	onenrm := norm == lapack.MaxColumnSum
+	smlnum := dlamchS
+	kase1 := 2
+	if onenrm {
+		kase1 = 1
+	}
+	for {
+		ainvnm, kase = impl.Dlacn2(n, work[n:], work, iwork, ainvnm, kase, isave)
+		if kase == 0 {
+			if ainvnm != 0 {
+				rcond = (1 / ainvnm) / anorm
+			}
+			return rcond
+		}
+		var sl, su float64
+		if kase == kase1 {
+			sl = impl.Dlatrs(blas.Lower, blas.NoTrans, blas.Unit, normin, n, a, lda, work, work[2*n:])
+			su = impl.Dlatrs(blas.Upper, blas.NoTrans, blas.NonUnit, normin, n, a, lda, work, work[3*n:])
+		} else {
+			su = impl.Dlatrs(blas.Upper, blas.Trans, blas.NonUnit, normin, n, a, lda, work, work[3*n:])
+			sl = impl.Dlatrs(blas.Lower, blas.Trans, blas.Unit, normin, n, a, lda, work, work[2*n:])
+		}
+		scale := sl * su
+		normin = true
+		if scale != 1 {
+			ix := bi.Idamax(n, work, 1)
+			if scale == 0 || scale < math.Abs(work[ix])*smlnum {
+				return rcond
+			}
+			impl.Drscl(n, scale, work, 1)
+		}
+	}
+}