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interp: add a DerivativePredictor interface and implement it in AkimaSpline and PiecewiseCubic

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This commit is contained in:
Roman Werpachowski
2020-08-10 23:14:54 +01:00
committed by GitHub
parent 755716c143
commit 41a8e221d0
2 changed files with 96 additions and 22 deletions
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79
interp/interp_test.go
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@@ -231,16 +231,31 @@ func TestPiecewiseCubic(t *testing.T) {
var pc PiecewiseCubic
pc.FitWithDerivatives(test.xs, ys, dydxs)
n := len(test.xs)
got := pc.Predict(test.xs[0] - 0.1)
m := n - 1
x0 := test.xs[0]
x1 := test.xs[m]
x := x0 - 0.1
got := pc.Predict(x)
want := ys[0]
if got != want {
t.Errorf("Mismatch in value extrapolated to the left for test case %d: got %v, want %g", i, got, want)
}
got = pc.Predict(test.xs[n-1] + 0.1)
want = ys[n-1]
got = pc.PredictDerivative(x)
want = dydxs[0]
if got != want {
t.Errorf("Mismatch in derivative extrapolated to the left for test case %d: got %v, want %g", i, got, want)
}
x = x1 + 0.1
got = pc.Predict(x)
want = ys[m]
if got != want {
t.Errorf("Mismatch in value extrapolated to the right for test case %d: got %v, want %g", i, got, want)
}
got = pc.PredictDerivative(x)
want = dydxs[m]
if got != want {
t.Errorf("Mismatch in derivative extrapolated to the right for test case %d: got %v, want %g", i, got, want)
}
for j := 0; j < n; j++ {
x := test.xs[j]
got := pc.Predict(x)
@@ -248,7 +263,7 @@ func TestPiecewiseCubic(t *testing.T) {
if math.Abs(got-want) > valueTol {
t.Errorf("Mismatch in interpolated value at x == %g for test case %d: got %v, want %g", x, i, got, want)
}
if j < n-1 {
if j < m {
got = pc.coeffs.At(j, 0)
if math.Abs(got-want) > valueTol {
t.Errorf("Mismatch in 0-th order interpolation coefficient in %d-th node for test case %d: got %v, want %g", j, i, got, want)
@@ -261,6 +276,11 @@ func TestPiecewiseCubic(t *testing.T) {
if math.Abs(got-want) > valueTol {
t.Errorf("Mismatch in interpolated value at x == %g for test case %d: got %v, want %g", x, i, got, want)
}
got = pc.PredictDerivative(xk)
want = discrDerivPredict(&pc, x0, x1, xk, h)
if math.Abs(got-want) > derivTol {
t.Errorf("Mismatch in interpolated derivative at x == %g for test case %d: got %v, want %g", x, i, got, want)
}
}
} else {
got = pc.lastY
@@ -276,24 +296,15 @@ func TestPiecewiseCubic(t *testing.T) {
t.Errorf("Interpolation coefficients in %d-th node produce mismatch in interpolated value at %g for test case %d: got %v, want %g", j-1, x, i, got, want)
}
}
got = discrDerivPredict(&pc, x, h, j, n)
got = discrDerivPredict(&pc, x0, x1, x, h)
want = test.df(x)
if math.Abs(got-want) > derivTol {
t.Errorf("Mismatch in numerical derivative of interpolated function at x == %g for test case %d: got %v, want %g", x, i, got, want)
}
got = pc.PredictDerivative(x)
if math.Abs(got-want) > valueTol {
t.Errorf("Mismatch in interpolated derivative value at x == %g for test case %d: got %v, want %g", x, i, got, want)
}
if j < n-1 {
got = pc.coeffs.At(j, 1)
if math.Abs(got-want) > valueTol {
t.Errorf("Mismatch in 1-st order interpolation coefficient in %d-th node for test case %d: got %v, want %g", j, i, got, want)
}
}
if j > 0 {
dx := test.xs[j] - test.xs[j-1]
got = (3*pc.coeffs.At(j-1, 3)*dx+2*pc.coeffs.At(j-1, 2))*dx + pc.coeffs.At(j-1, 1)
if math.Abs(got-want) > valueTol {
t.Errorf("Interpolation coefficients in %d-th node produce mismatch in interpolated derivative value at %g for test case %d: got %v, want %g", j-1, x, i, got, want)
}
}
}
}
}
@@ -327,6 +338,10 @@ func TestPiecewiseCubicFitWithDerivatives(t *testing.T) {
if pc.lastY != lastY {
t.Errorf("Mismatch in lastY: got %v, want %g", pc.lastY, lastY)
}
lastDyDx := rightPolyDerivative(xs[2])
if pc.lastDyDx != lastDyDx {
t.Errorf("Mismatch in lastDxDy: got %v, want %g", pc.lastDyDx, lastDyDx)
}
if !floats.Equal(pc.xs, xs) {
t.Errorf("Mismatch in xs: got %v, want %v", pc.xs, xs)
}
@@ -371,7 +386,13 @@ func TestPiecewiseCubicFitWithDerivativesErrors(t *testing.T) {
func TestAkimaSpline(t *testing.T) {
t.Parallel()
const tol = 1e-14
const (
derivAbsTol = 1e-8
derivRelTol = 1e-7
h = 1e-8
nPts = 100
tol = 1e-14
)
for i, test := range []struct {
xs []float64
f func(float64) float64
@@ -403,6 +424,9 @@ func TestAkimaSpline(t *testing.T) {
} {
var as AkimaSpline
n := len(test.xs)
m := n - 1
x0 := test.xs[0]
x1 := test.xs[m]
ys := applyFunc(test.xs, test.f)
err := as.Fit(test.xs, ys)
if err != nil {
@@ -415,6 +439,17 @@ func TestAkimaSpline(t *testing.T) {
if math.Abs(got-want) > tol {
t.Errorf("Mismatch in interpolated value at x == %g for test case %d: got %v, want %g", x, i, got, want)
}
if j < m {
dx := (test.xs[j+1] - x) / nPts
for k := 1; k < nPts; k++ {
xk := x + float64(k)*dx
got = as.PredictDerivative(xk)
want = discrDerivPredict(&as, x0, x1, xk, h)
if math.Abs(got-want) > derivRelTol*math.Abs(want)+derivAbsTol {
t.Errorf("Mismatch in interpolated derivative at x == %g for test case %d: got %v, want %g", x, i, got, want)
}
}
}
}
if n == 2 {
got := as.cubic.coeffs.At(0, 1)
@@ -643,10 +678,10 @@ func panics(fun func()) (b bool) {
return
}
func discrDerivPredict(p Predictor, x, h float64, j, n int) float64 {
if j == 0 {
func discrDerivPredict(p Predictor, x0, x1, x, h float64) float64 {
if x <= x0+h {
return (p.Predict(x+h) - p.Predict(x)) / h
} else if j == n-1 {
} else if x >= x1-h {
return (p.Predict(x) - p.Predict(x-h)) / h
} else {
return (p.Predict(x+h) - p.Predict(x-h)) / (2 * h)