func MyDf(v *vector.GslVector, params interface{}, df *vector.GslVector) {
p := params.([]float64)
x := vector.Get(v, 0)
y := vector.Get(v, 1)
vector.Set(df, 0, 2.0*p[2]*(x-p[0]))
vector.Set(df, 1, 2.0*p[3]*(y-p[1]))
}
func PrintStateFdf(iter int, s *multiroot.GslMultirootFdfsolver) {
fmt.Printf("iter = %3d x = % .3f % .3f f(x) = % .3e % .3e\n",
iter,
vector.Get(s.X_(), 0),
vector.Get(s.X_(), 1),
vector.Get(s.F_(), 0),
vector.Get(s.F_(), 1))
}
/* Paraboloid centered on (p[0],p[1]), with
scale factors (p[2],p[3]) and minimum p[4] */
func MyF(v *vector.GslVector, params interface{}) float64 {
p := params.([]float64)
x := vector.Get(v, 0)
y := vector.Get(v, 1)
return p[2]*(x-p[0])*(x-p[0]) +
p[3]*(y-p[1])*(y-p[1]) +
p[4]
}
func Rosenbrock(x *vector.GslVector, params interface{}, f *vector.GslVector) int {
rp := params.(*Rparams)
x0 := vector.Get(x, 0)
x1 := vector.Get(x, 1)
y0 := rp.A * (1.0 - x0)
y1 := rp.B * (x1 - x0*x0)
vector.Set(f, 0, y0)
vector.Set(f, 1, y1)
return int(gogsl.GSL_SUCCESS)
}
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 TestMultimin(t *testing.T) {
par := []float64{1.0, 2.0, 10.0, 20.0, 30.0}
f := &multimin.GslMultiminFunction{
Function: MyF,
Dimension: 2,
Params: par,
}
multimin.InitializeGslMultiminFunction(f)
/* Starting point */
x := vector.VectorAlloc(2)
vector.Set(x, 0, 5.0)
vector.Set(x, 1, 7.0)
/* Set initial step sizes to 1 */
ss := vector.VectorAlloc(2)
vector.SetAll(ss, 1.0)
T := multimin.GSL_MULTIMIN_FMINIMIZER_NSIMPLEX2
s := multimin.FminimizerAlloc(T, 2)
multimin.FminimizerSet(s, f, x, ss)
iter := 0
for {
iter += 1
status := gogsl.GslError(multimin.FminimizerIterate(s))
if status != gogsl.GSL_SUCCESS {
break
}
size := multimin.FminimizerSize(s)
status = gogsl.GslError(multimin.TestSize(size, 1e-2))
if status == gogsl.GSL_SUCCESS {
fmt.Printf("converged to minimum at\n")
}
fmt.Printf("%5d %10.3e %10.3e f() = %7.3f size = %.3f\n",
iter, vector.Get(s.X_(), 0), vector.Get(s.X_(), 1), s.Fval(), size)
if status != gogsl.GSL_CONTINUE || iter >= 100 {
break
}
}
}
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 TestMultiminFdf(t *testing.T) {
par := []float64{1.0, 2.0, 10.0, 20.0, 30.0}
f := &multimin.GslMultiminFunctionFdf{
Function: MyF,
Derivative: MyDf,
Fdf: MyFdf,
Dimension: 2,
Params: par,
}
multimin.InitializeGslMultiminFunctionFdf(f)
/* Starting point */
x := vector.VectorAlloc(2)
vector.Set(x, 0, 5.0)
vector.Set(x, 1, 7.0)
T := multimin.GSL_MULTIMIN_FDFMINIMIZER_CONJUGATE_FR
s := multimin.FdfminimizerAlloc(T, 2)
multimin.FdfminimizerSet(s, f, x, 0.01, 1e-4)
iter := 0
for {
iter += 1
status := gogsl.GslError(multimin.FdfminimizerIterate(s))
if status != gogsl.GSL_SUCCESS {
break
}
status = gogsl.GslError(multimin.TestGradient(s.Gradient_(), 1e-3))
if status == gogsl.GSL_SUCCESS {
fmt.Printf("Minimum found at:\n")
}
fmt.Printf("%5d %10.3e %10.3e f() = %7.3f\n",
iter, vector.Get(s.X_(), 0), vector.Get(s.X_(), 1), s.Fval())
if status != gogsl.GSL_CONTINUE || iter >= 100 {
break
}
}
}
func TestSortVectorIndex(t *testing.T) {
var n int = 10000
var k int = 5
v := vector.VectorAlloc(n)
p := permutation.PermutationAlloc(n)
rng.EnvSetup()
T := rng.DefaultRngType()
r := rng.RngAlloc(T)
for i := 0; i < n; i++ {
vector.Set(v, i, rng.Uniform(r))
}
sort.SortVectorIndex(p, v)
pData := p.Slice_().([]int)
for i := 0; i < k; i++ {
vpi := vector.Get(v, pData[i])
fmt.Printf("order = %d, value = %g\n", i, vpi)
}
}
func TestVector(t *testing.T) {
var stopDoingIt bool
gogsl.SetErrorHandler(&gogsl.GslErrorHandler{
Handler: func(reason string, file string, line int, gslError gogsl.GslError) {
fmt.Println("Caught error: " + reason)
stopDoingIt = true
},
})
v := vector.VectorAlloc(3)
for i := 0; i < 3; i++ {
vector.Set(v, i, float64(1.23)+float64(i))
}
for i := 0; i < 100; i++ { // OUT OF RANGE ERROR
fmt.Printf("v_%d = %g\n", i, vector.Get(v, i))
if stopDoingIt {
break
}
}
}
func TestEigen(t *testing.T) {
data := []float64{1.0, 1 / 2.0, 1 / 3.0, 1 / 4.0,
1 / 2.0, 1 / 3.0, 1 / 4.0, 1 / 5.0,
1 / 3.0, 1 / 4.0, 1 / 5.0, 1 / 6.0,
1 / 4.0, 1 / 5.0, 1 / 6.0, 1 / 7.0}
m := matrix.ViewArray(data, 4, 4)
eval := vector.VectorAlloc(4)
evec := matrix.MatrixAlloc(4, 4)
w := eigen.SymmvAlloc(4)
eigen.Symmv(m.Matrix(), eval, evec, w)
eigen.SymmvSort(eval, evec, eigen.EIGEN_SORT_ABS_ASC)
for i := 0; i < 4; i++ {
evalI := vector.Get(eval, i)
evecI := matrix.Column(evec, i)
fmt.Printf("eigenvalue = %g\n", evalI)
fmt.Printf("eigenvector = \n")
vector.Fprintf(os.Stdout, evecI.Vector(), "%g")
}
}
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)
}
}