Add dependencies for code generator

vendor/gonum.org/v1/gonum/lapack/gonum/dsterf.go

@@ -0,0 +1,285 @@
+// 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 gonum
+
+import (
+	"math"
+
+	"gonum.org/v1/gonum/lapack"
+)
+
+// Dsterf computes all eigenvalues of a symmetric tridiagonal matrix using the
+// Pal-Walker-Kahan variant of the QL or QR algorithm.
+//
+// d contains the diagonal elements of the tridiagonal matrix on entry, and
+// contains the eigenvalues in ascending order on exit. d must have length at
+// least n, or Dsterf will panic.
+//
+// e contains the off-diagonal elements of the tridiagonal matrix on entry, and is
+// overwritten during the call to Dsterf. e must have length of at least n-1 or
+// Dsterf will panic.
+//
+// Dsterf is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dsterf(n int, d, e []float64) (ok bool) {
+	if n < 0 {
+		panic(nLT0)
+	}
+
+	// Quick return if possible.
+	if n == 0 {
+		return true
+	}
+
+	switch {
+	case len(d) < n:
+		panic(shortD)
+	case len(e) < n-1:
+		panic(shortE)
+	}
+
+	if n == 1 {
+		return true
+	}
+
+	const (
+		none = 0 // The values are not scaled.
+		down = 1 // The values are scaled below ssfmax threshold.
+		up   = 2 // The values are scaled below ssfmin threshold.
+	)
+
+	// Determine the unit roundoff for this environment.
+	eps := dlamchE
+	eps2 := eps * eps
+	safmin := dlamchS
+	safmax := 1 / safmin
+	ssfmax := math.Sqrt(safmax) / 3
+	ssfmin := math.Sqrt(safmin) / eps2
+
+	// Compute the eigenvalues of the tridiagonal matrix.
+	maxit := 30
+	nmaxit := n * maxit
+	jtot := 0
+
+	l1 := 0
+
+	for {
+		if l1 > n-1 {
+			impl.Dlasrt(lapack.SortIncreasing, n, d)
+			return true
+		}
+		if l1 > 0 {
+			e[l1-1] = 0
+		}
+		var m int
+		for m = l1; m < n-1; m++ {
+			if math.Abs(e[m]) <= math.Sqrt(math.Abs(d[m]))*math.Sqrt(math.Abs(d[m+1]))*eps {
+				e[m] = 0
+				break
+			}
+		}
+
+		l := l1
+		lsv := l
+		lend := m
+		lendsv := lend
+		l1 = m + 1
+		if lend == 0 {
+			continue
+		}
+
+		// Scale submatrix in rows and columns l to lend.
+		anorm := impl.Dlanst(lapack.MaxAbs, lend-l+1, d[l:], e[l:])
+		iscale := none
+		if anorm == 0 {
+			continue
+		}
+		if anorm > ssfmax {
+			iscale = down
+			impl.Dlascl(lapack.General, 0, 0, anorm, ssfmax, lend-l+1, 1, d[l:], n)
+			impl.Dlascl(lapack.General, 0, 0, anorm, ssfmax, lend-l, 1, e[l:], n)
+		} else if anorm < ssfmin {
+			iscale = up
+			impl.Dlascl(lapack.General, 0, 0, anorm, ssfmin, lend-l+1, 1, d[l:], n)
+			impl.Dlascl(lapack.General, 0, 0, anorm, ssfmin, lend-l, 1, e[l:], n)
+		}
+
+		el := e[l:lend]
+		for i, v := range el {
+			el[i] *= v
+		}
+
+		// Choose between QL and QR iteration.
+		if math.Abs(d[lend]) < math.Abs(d[l]) {
+			lend = lsv
+			l = lendsv
+		}
+		if lend >= l {
+			// QL Iteration.
+			// Look for small sub-diagonal element.
+			for {
+				if l != lend {
+					for m = l; m < lend; m++ {
+						if math.Abs(e[m]) <= eps2*(math.Abs(d[m]*d[m+1])) {
+							break
+						}
+					}
+				} else {
+					m = lend
+				}
+				if m < lend {
+					e[m] = 0
+				}
+				p := d[l]
+				if m == l {
+					// Eigenvalue found.
+					l++
+					if l > lend {
+						break
+					}
+					continue
+				}
+				// If remaining matrix is 2 by 2, use Dlae2 to compute its eigenvalues.
+				if m == l+1 {
+					d[l], d[l+1] = impl.Dlae2(d[l], math.Sqrt(e[l]), d[l+1])
+					e[l] = 0
+					l += 2
+					if l > lend {
+						break
+					}
+					continue
+				}
+				if jtot == nmaxit {
+					break
+				}
+				jtot++
+
+				// Form shift.
+				rte := math.Sqrt(e[l])
+				sigma := (d[l+1] - p) / (2 * rte)
+				r := impl.Dlapy2(sigma, 1)
+				sigma = p - (rte / (sigma + math.Copysign(r, sigma)))
+
+				c := 1.0
+				s := 0.0
+				gamma := d[m] - sigma
+				p = gamma * gamma
+
+				// Inner loop.
+				for i := m - 1; i >= l; i-- {
+					bb := e[i]
+					r := p + bb
+					if i != m-1 {
+						e[i+1] = s * r
+					}
+					oldc := c
+					c = p / r
+					s = bb / r
+					oldgam := gamma
+					alpha := d[i]
+					gamma = c*(alpha-sigma) - s*oldgam
+					d[i+1] = oldgam + (alpha - gamma)
+					if c != 0 {
+						p = (gamma * gamma) / c
+					} else {
+						p = oldc * bb
+					}
+				}
+				e[l] = s * p
+				d[l] = sigma + gamma
+			}
+		} else {
+			for {
+				// QR Iteration.
+				// Look for small super-diagonal element.
+				for m = l; m > lend; m-- {
+					if math.Abs(e[m-1]) <= eps2*math.Abs(d[m]*d[m-1]) {
+						break
+					}
+				}
+				if m > lend {
+					e[m-1] = 0
+				}
+				p := d[l]
+				if m == l {
+					// Eigenvalue found.
+					l--
+					if l < lend {
+						break
+					}
+					continue
+				}
+
+				// If remaining matrix is 2 by 2, use Dlae2 to compute its eigenvalues.
+				if m == l-1 {
+					d[l], d[l-1] = impl.Dlae2(d[l], math.Sqrt(e[l-1]), d[l-1])
+					e[l-1] = 0
+					l -= 2
+					if l < lend {
+						break
+					}
+					continue
+				}
+				if jtot == nmaxit {
+					break
+				}
+				jtot++
+
+				// Form shift.
+				rte := math.Sqrt(e[l-1])
+				sigma := (d[l-1] - p) / (2 * rte)
+				r := impl.Dlapy2(sigma, 1)
+				sigma = p - (rte / (sigma + math.Copysign(r, sigma)))
+
+				c := 1.0
+				s := 0.0
+				gamma := d[m] - sigma
+				p = gamma * gamma
+
+				// Inner loop.
+				for i := m; i < l; i++ {
+					bb := e[i]
+					r := p + bb
+					if i != m {
+						e[i-1] = s * r
+					}
+					oldc := c
+					c = p / r
+					s = bb / r
+					oldgam := gamma
+					alpha := d[i+1]
+					gamma = c*(alpha-sigma) - s*oldgam
+					d[i] = oldgam + alpha - gamma
+					if c != 0 {
+						p = (gamma * gamma) / c
+					} else {
+						p = oldc * bb
+					}
+				}
+				e[l-1] = s * p
+				d[l] = sigma + gamma
+			}
+		}
+
+		// Undo scaling if necessary
+		switch iscale {
+		case down:
+			impl.Dlascl(lapack.General, 0, 0, ssfmax, anorm, lendsv-lsv+1, 1, d[lsv:], n)
+		case up:
+			impl.Dlascl(lapack.General, 0, 0, ssfmin, anorm, lendsv-lsv+1, 1, d[lsv:], n)
+		}
+
+		// Check for no convergence to an eigenvalue after a total of n*maxit iterations.
+		if jtot >= nmaxit {
+			break
+		}
+	}
+	for _, v := range e[:n-1] {
+		if v != 0 {
+			return false
+		}
+	}
+	impl.Dlasrt(lapack.SortIncreasing, n, d)
+	return true
+}