func RosenbrockDf(x *vector.GslVector, params interface{}, j *matrix.GslMatrix) int {
rp := params.(*Rparams)
x0 := vector.Get(x, 0)
matrix.Set(j, 0, 0, -rp.A)
matrix.Set(j, 0, 1, 0)
matrix.Set(j, 1, 0, -2*rp.B*x0)
matrix.Set(j, 1, 1, rp.B)
return int(gogsl.GSL_SUCCESS)
}
func Df(t float64, y []float64, dfdy []float64, dfdt []float64, params interface{}) int {
mu := *params.(*float64)
dfdyMat := matrix.ViewArray(dfdy, 2, 2)
m := dfdyMat.Matrix()
matrix.Set(m, 0, 0, 0.0)
matrix.Set(m, 0, 1, 1.0)
matrix.Set(m, 1, 0, -2.0*mu*y[0]*y[1]-1.0)
matrix.Set(m, 1, 1, -mu*(y[0]*y[0]-1.0))
dfdt[0] = 0.0
dfdt[1] = 0.0
return int(gogsl.GSL_SUCCESS)
}
func TestWeightedQuadtricFit(t *testing.T) {
var n int = 19
data := MakeData(0.1, 2.0, 0.1)
X := matrix.MatrixAlloc(n, 3)
y := vector.VectorAlloc(n)
w := vector.VectorAlloc(n)
c := vector.VectorAlloc(3)
cov := matrix.MatrixAlloc(3, 3)
for i := 0; i < n; i++ {
xi := data[i*3]
yi := data[i*3+1]
ei := data[i*3+2]
fmt.Printf("%g %g +/- %g\n", xi, yi, ei)
matrix.Set(X, i, 0, 1.0)
matrix.Set(X, i, 1, xi)
matrix.Set(X, i, 2, xi*xi)
vector.Set(y, i, yi)
vector.Set(w, i, 1.0/(ei*ei))
}
work := multifit.LinearAlloc(n, 3)
_, chisq := multifit.Wlinear(X, w, y, c, cov, work)
fmt.Printf("# best fit: Y = %g + %g X + %g X^2\n",
vector.Get(c, 0), vector.Get(c, 1), vector.Get(c, 2))
fmt.Printf("# covariance matrix:\n")
fmt.Printf("[ %+.5e, %+.5e, %+.5e \n",
matrix.Get(cov, 0, 0), matrix.Get(cov, 0, 1), matrix.Get(cov, 0, 2))
fmt.Printf(" %+.5e, %+.5e, %+.5e \n",
matrix.Get(cov, 1, 0), matrix.Get(cov, 1, 1), matrix.Get(cov, 1, 2))
fmt.Printf(" %+.5e, %+.5e, %+.5e ]\n",
matrix.Get(cov, 2, 0), matrix.Get(cov, 2, 1), matrix.Get(cov, 2, 2))
fmt.Printf("# chisq = %g\n", chisq)
}
func TestRobust(t *testing.T) {
var p int = 2 // linear fit
var a float64 = 1.45 // data slope
var b float64 = 3.88 // data intercept
var n int = 20
X := matrix.MatrixAlloc(n, p)
x := vector.VectorAlloc(n)
y := vector.VectorAlloc(n)
c := vector.VectorAlloc(p)
cOls := vector.VectorAlloc(p)
cov := matrix.MatrixAlloc(p, p)
r := rng.RngAlloc(rng.DefaultRngType())
// generate linear dataset
for i := 0; i < n-3; i++ {
dx := 10.0 / (float64(n) - 1.0)
ei := rng.Uniform(r)
xi := -5.0 + float64(i)*dx
yi := a*xi + b
vector.Set(x, i, xi)
vector.Set(y, i, yi+ei)
}
// add a few outliers
vector.Set(x, n-3, 4.7)
vector.Set(y, n-3, -8.3)
vector.Set(x, n-2, 3.5)
vector.Set(y, n-2, -6.7)
vector.Set(x, n-1, 4.1)
vector.Set(y, n-1, -6.0)
// construct design matrix X for linear fit
for i := 0; i < n; i++ {
xi := vector.Get(x, i)
matrix.Set(X, i, 0, 1.0)
matrix.Set(X, i, 1, xi)
}
// perform robust and OLS fit
DoFit(multifit.GSL_MULTIFIT_ROBUST_OLS, X, y, cOls, cov)
DoFit(multifit.GSL_MULTIFIT_ROBUST_BISQUARE, X, y, c, cov)
// output data and model
for i := 0; i < n; i++ {
xi := vector.Get(x, i)
yi := vector.Get(y, i)
v := matrix.Row(X, i).Vector()
_, yRob, _ := multifit.RobustEst(v, c, cov)
_, yOls, _ := multifit.RobustEst(v, cOls, cov)
fmt.Printf("%g %g %g %g\n", xi, yi, yRob, yOls)
}
fmt.Printf("# best fit: Y = %g + %g X\n", vector.Get(c, 0), vector.Get(c, 1))
fmt.Printf("# covariance matrix:\n")
fmt.Printf("# [ %+.5e, %+.5e\n", matrix.Get(cov, 0, 0), matrix.Get(cov, 0, 1))
fmt.Printf("# %+.5e, %+.5e\n", matrix.Get(cov, 1, 0), matrix.Get(cov, 1, 1))
}
func TestBspline(t *testing.T) {
var n int = 200
var ncoeffs int = 12
var nbreak int = ncoeffs - 2
rng.EnvSetup()
r := rng.RngAlloc(rng.DefaultRngType())
// allocate a cubic bspline workspace (k = 4)
bw := bspline.Alloc(4, nbreak)
B := vector.VectorAlloc(ncoeffs)
x := vector.VectorAlloc(n)
y := vector.VectorAlloc(n)
X := matrix.MatrixAlloc(n, ncoeffs)
c := vector.VectorAlloc(ncoeffs)
w := vector.VectorAlloc(n)
cov := matrix.MatrixAlloc(ncoeffs, ncoeffs)
mw := multifit.LinearAlloc(n, ncoeffs)
fmt.Printf("#m=0,S=0\n")
// this is the data to be fitted
for i := 0; i < n; i++ {
xi := (15.0 / (float64(n) - 1)) * float64(i)
yi := math.Cos(xi) * math.Exp(-0.1*xi)
sigma := 0.1 * yi
dy := randist.Gaussian(r, sigma)
vector.Set(x, i, xi)
vector.Set(y, i, yi+dy)
vector.Set(w, i, 1.0/(sigma*sigma))
fmt.Printf("%f %f\n", xi, yi+dy)
}
// use uniform breakpoints on [0, 15]
bspline.KnotsUniform(0.0, 15.0, bw)
// construct the fit matrix X
for i := 0; i < n; i++ {
xi := vector.Get(x, i)
// compute B_j(xi) for all j
bspline.Eval(xi, B, bw)
// fill in row i of X
for j := 0; j < ncoeffs; j++ {
matrix.Set(X, i, j, vector.Get(B, j))
}
}
// do the fit
_, chisq := multifit.Wlinear(X, w, y, c, cov, mw)
dof := float64(n - ncoeffs)
tss := stats.Wtss(w.Data_(), w.Stride(), y.Data_(), y.Stride(), n)
rsq := 1.0 - chisq/tss
fmt.Printf("chisq/dof = %e, Rsq = %f\n", chisq/dof, rsq)
fmt.Printf("#m=1,S=0\n")
for xi := 0.0; xi < 15.0; xi += 0.1 {
bspline.Eval(xi, B, bw)
_, yi, _ := multifit.LinearEst(B, c, cov)
fmt.Printf("%f %f\n", xi, yi)
}
}