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Fix CubicSplineInterpolator integration function #29

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Merged
CD3 merged 2 commits into from
May 16, 2025
Merged

Fix CubicSplineInterpolator integration function #29

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df47148
Fix CubicSplineInterpolator integration function
jamiescottie1 May 7, 2025
b619ab7
Fix copy-paste mistake in CubicSplineInterpolator integration function
jamiescottie1 May 8, 2025
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22 changes: 14 additions & 8 deletions src/libInterpolate/Interpolators/_1D/CubicSplineInterpolator.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -155,7 +155,7 @@ Real CubicSplineInterpolator<Real>::integral(Real _a, Real _b) const {
* I = (x_2 - x_1) \int_t_a^t_b ( 1 - t )*y_1 + t*y_2 + t*( 1 - t )( a*(1 -
* t) + b*t ) dt
*
* = (x_2 - x_1) [ ( t - t^2/2 )*y_1 + t^2/2*y_2 + a*(t^2 - 2*t^3/3 +
* = (x_2 - x_1) [ ( t - t^2/2 )*y_1 + t^2/2*y_2 + a*(t^2/2 - 2*t^3/3 +
* t^4/4) + b*(t^3/3 - t^4/4) ] |_t_a^t_b
*
* if we integrate over the entire element, i.e. x -> [x1,x2], then we will
Expand All @@ -166,7 +166,7 @@ Real CubicSplineInterpolator<Real>::integral(Real _a, Real _b) const {
*
*/

Real x_1, x_2, t;
Real x_1, x_2, t, t2, t3, t4;
Real y_1, y_2;
Real sum = 0;
for (int i = ai; i < bi - 1; i++) {
Expand Down Expand Up @@ -198,13 +198,16 @@ Real CubicSplineInterpolator<Real>::integral(Real _a, Real _b) const {
y_1 = Y[bi - 1];
y_2 = Y[bi];
t = (_b - x_1) / (x_2 - x_1);
t2 = t*t;
t3 = t2*t;
t4 = t2*t2;

// adding area between x_1 and _b
sum += static_cast<Real>(
(x_2 - x_1) *
((t - pow(t, 2) / 2) * y_1 + pow(t, 2) / 2. * y_2 +
a[bi - 1] * (pow(t, 2) - 2. * pow(t, 3) / 3. + pow(t, 4) / 4.) +
b[bi - 1] * (pow(t, 3) / 3. - pow(t, 4) / 4.)));
((t - 0.5 * t2) * y_1 + 0.5 * t2 * y_2 +
a[bi - 1] * (0.5 * t2 - 2. * t3 / 3. + 0.25 * t4) +
b[bi - 1] * (t3 / 3. - 0.25 * t4)));

//
// [_a,X(0)]
Expand All @@ -217,13 +220,16 @@ Real CubicSplineInterpolator<Real>::integral(Real _a, Real _b) const {
y_1 = Y[ai - 1];
y_2 = Y[ai];
t = (_a - x_1) / (x_2 - x_1);
t2 = t*t;
t3 = t2*t;
t4 = t2*t2;

// subtracting area from x_1 to _a
sum -= static_cast<Real>(
(x_2 - x_1) *
((t - pow(t, 2) / 2) * y_1 + pow(t, 2) / 2. * y_2 +
a[ai - 1] * (pow(t, 2) - 2. * pow(t, 3) / 3. + pow(t, 4) / 4.) +
b[ai - 1] * (pow(t, 3) / 3. - pow(t, 4) / 4.)));
((t - 0.5 * t2) * y_1 + 0.5 * t2 * y_2 +
a[ai - 1] * (0.5 * t2 - 2. * t3 / 3. + 0.25 * t4) +
b[ai - 1] * (t3 / 3. - 0.25 * t4)));

if (ai != bi) // _a and _b are not in the in the same element, need to add
// area of element containing _a
Expand Down
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