X-Git-Url: http://git.osdn.net/view?p=bytom%2Fvapor.git;a=blobdiff_plain;f=vendor%2Fgonum.org%2Fv1%2Fgonum%2Flapack%2Fgonum%2Fdlanv2.go;fp=vendor%2Fgonum.org%2Fv1%2Fgonum%2Flapack%2Fgonum%2Fdlanv2.go;h=0000000000000000000000000000000000000000;hp=e5dcfb7522d18096f0c517d3aab50768ed8059dc;hb=54373c1a3efe0e373ec1605840a4363e4b246c46;hpb=ee01d543fdfe1fd0a4d548965c66f7923ea7b062 diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dlanv2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dlanv2.go deleted file mode 100644 index e5dcfb75..00000000 --- a/vendor/gonum.org/v1/gonum/lapack/gonum/dlanv2.go +++ /dev/null @@ -1,132 +0,0 @@ -// 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" - -// Dlanv2 computes the Schur factorization of a real 2×2 matrix: -// [ a b ] = [ cs -sn ] * [ aa bb ] * [ cs sn ] -// [ c d ] [ sn cs ] [ cc dd ] * [-sn cs ] -// If cc is zero, aa and dd are real eigenvalues of the matrix. Otherwise it -// holds that aa = dd and bb*cc < 0, and aa ± sqrt(bb*cc) are complex conjugate -// eigenvalues. The real and imaginary parts of the eigenvalues are returned in -// (rt1r,rt1i) and (rt2r,rt2i). -func (impl Implementation) Dlanv2(a, b, c, d float64) (aa, bb, cc, dd float64, rt1r, rt1i, rt2r, rt2i float64, cs, sn float64) { - switch { - case c == 0: // Matrix is already upper triangular. - aa = a - bb = b - cc = 0 - dd = d - cs = 1 - sn = 0 - case b == 0: // Matrix is lower triangular, swap rows and columns. - aa = d - bb = -c - cc = 0 - dd = a - cs = 0 - sn = 1 - case a == d && math.Signbit(b) != math.Signbit(c): // Matrix is already in the standard Schur form. - aa = a - bb = b - cc = c - dd = d - cs = 1 - sn = 0 - default: - temp := a - d - p := temp / 2 - bcmax := math.Max(math.Abs(b), math.Abs(c)) - bcmis := math.Min(math.Abs(b), math.Abs(c)) - if b*c < 0 { - bcmis *= -1 - } - scale := math.Max(math.Abs(p), bcmax) - z := p/scale*p + bcmax/scale*bcmis - eps := dlamchP - - if z >= 4*eps { - // Real eigenvalues. Compute aa and dd. - if p > 0 { - z = p + math.Sqrt(scale)*math.Sqrt(z) - } else { - z = p - math.Sqrt(scale)*math.Sqrt(z) - } - aa = d + z - dd = d - bcmax/z*bcmis - // Compute bb and the rotation matrix. - tau := impl.Dlapy2(c, z) - cs = z / tau - sn = c / tau - bb = b - c - cc = 0 - } else { - // Complex eigenvalues, or real (almost) equal eigenvalues. - // Make diagonal elements equal. - sigma := b + c - tau := impl.Dlapy2(sigma, temp) - cs = math.Sqrt((1 + math.Abs(sigma)/tau) / 2) - sn = -p / (tau * cs) - if sigma < 0 { - sn *= -1 - } - // Compute [ aa bb ] = [ a b ] [ cs -sn ] - // [ cc dd ] [ c d ] [ sn cs ] - aa = a*cs + b*sn - bb = -a*sn + b*cs - cc = c*cs + d*sn - dd = -c*sn + d*cs - // Compute [ a b ] = [ cs sn ] [ aa bb ] - // [ c d ] [-sn cs ] [ cc dd ] - a = aa*cs + cc*sn - b = bb*cs + dd*sn - c = -aa*sn + cc*cs - d = -bb*sn + dd*cs - - temp = (a + d) / 2 - aa = temp - bb = b - cc = c - dd = temp - - if cc != 0 { - if bb != 0 { - if math.Signbit(bb) == math.Signbit(cc) { - // Real eigenvalues, reduce to - // upper triangular form. - sab := math.Sqrt(math.Abs(bb)) - sac := math.Sqrt(math.Abs(cc)) - p = sab * sac - if cc < 0 { - p *= -1 - } - tau = 1 / math.Sqrt(math.Abs(bb+cc)) - aa = temp + p - bb = bb - cc - cc = 0 - dd = temp - p - cs1 := sab * tau - sn1 := sac * tau - cs, sn = cs*cs1-sn*sn1, cs*sn1+sn+cs1 - } - } else { - bb = -cc - cc = 0 - cs, sn = -sn, cs - } - } - } - } - - // Store eigenvalues in (rt1r,rt1i) and (rt2r,rt2i). - rt1r = aa - rt2r = dd - if cc != 0 { - rt1i = math.Sqrt(math.Abs(bb)) * math.Sqrt(math.Abs(cc)) - rt2i = -rt1i - } - return -}