linterp.sm (21,54 KiB) scaricato 1471 volta(e).

As a temporary solution:



linterp-xyplot-using-defined-argument.sm (21,7 KiB) scaricato 1548 volta(e).

interp(), ... functions from Mathcad Toolbox still have a bug. The implementation used does incorrect interpolation on some intervals. I don't know how to fix this yet, because the algorithm was restored according to the article and perhaps it was done incorrectly.

Благодарствую!
And what is it?

See the 3-d plot in attach without this bug!linterp.sm (21,44 KiB) scaricato 1512 volta(e).

Это и есть баг в численном алгоритме. К сожалению, требуется основательная переработка алгоритма для выяснения причины такого поведения. Я не силён в кубических сплайнах, в их реализации.
Эта проблема также ведёт к неправильной интерполяции в решателях ОДУ, которые кроме табличного решения предлагают и интерполированные функции. Там используется интерполятор из Mathcad Toolbox.
После реализации этих функций я делал только примитивные тесты и ошибка не была вовремя обнаружена.

Wrote

Это и есть баг в численном алгоритме. К сожалению, требуется основательная переработка алгоритма для выяснения причины такого поведения. Я не силён в кубических сплайнах, в их реализации.
Эта проблема также ведёт к неправильной интерполяции в решателях ОДУ, которые кроме табличного решения предлагают и интерполированные функции. Там используется интерполятор из Mathcad Toolbox.
После реализации этих функций я делал только примитивные тесты и ошибка не была вовремя обнаружена.

Это не просто баг. Это, как говаривал ваш катькин Ельцин, какая-то загогулина!

Wrote

Это и есть баг в численном алгоритме. К сожалению, требуется основательная переработка алгоритма для выяснения причины такого поведения. Я не силён в кубических сплайнах, в их реализации.
Эта проблема также ведёт к неправильной интерполяции в решателях ОДУ, которые кроме табличного решения предлагают и интерполированные функции. Там используется интерполятор из Mathcad Toolbox.
После реализации этих функций я делал только примитивные тесты и ошибка не была вовремя обнаружена.

Is that bug only related to non-equidistant points? In that case, the functions would still be good enough for the ode solvers, at least for rkfixed()

Wrote

Is that bug only related to non-equidistant points ?

The lspline(X,Y) produces the wrong vector
k ... [0 3 0 0 0.6629 ...suite OK]
k ... [0 0.6629 ...suite OK]
Put the right vector in interp(k,X,Y,x) fails.
Simply a bug ... reflexive double bug.
My Smath Solver 30405 document is fine,
Interpolate, 1rst Derivative, 2nd Derivative, Integrate.
Jean.

Wrote

The lspline(X,Y) produces the wrong vector

Jean Giraud produces useless messages.

Hi Viacheslav. It seems that the Mathcad lspline actually it is a cubic spline. That as conclusion comparing lspline with the maple spline function. Thus, it has the Martin's restriction: x values must to be equally spaced (but that is not required for maple algorithms). Actually, that's looks like the best option for working with ODE's, especially for boundary conditions about the derivative of the spline function.

Maple spline function.sm (23,01 KiB) scaricato 1499 volta(e).

Best regards.
Alvaro.

Wrote

It seems that the Mathcad lspline actually it is a cubic spline.

I will remind you of this document, which describes how the functions work. My implementation of interpolation has an error, but the coefficients themselves seem to be calculated correctly.
In Mathcad the first three numbers encode the type of spline. Jean doesn't know about this.

Cubic spline interpolation using Mathcad (2009).pdf (256,71 KiB) scaricato 2764 volta(e).

Hi Viacheslav.

Wrote

Wrote

It seems that the Mathcad lspline actually it is a cubic spline.

I will remind you of this document, which describes how the functions work.

Cubic spline interpolation using Mathcad (2009).pdf (256,71 KiB) scaricato 2764 volta(e).

Yes, my comment is about that the lspline and pspline names could be sort of confusing, because, as the report says, mathcad's lspline, pspline and cspline are all "cubic splines". The "l" in "lspline" is not for linear interpolation, but for linear ends conditions, also called natural conditions. The "p" is for parabolic, and the "c" for cubic, all meaning ends conditions too.





Thus, Mathcad lspline is not related with SMath linterp or maple spline(X,Y,x,linear)

Wrote

In Mathcad the first three numbers encode the type of spline. Jean doesn't know about this.

As usual. Yes, I know. You can also find here an adaptive spline interpolation using that encoding.

Best regards.
Alvaro.

Wrote

Yes, my comment is about that the lspline and pspline names could be sort of confusing, because, as the report says, mathcad's lspline, pspline and cspline are all "cubic splines". The "l" in "lspline" is not for linear interpolation, but for linear ends conditions, also called natural conditions. The "p" is for parabolic, and the "c" for cubic, all meaning ends conditions too.

Well tutored Alvaro.
Easy to explore more from late Samples.
l & p have most remarkable effect in the start region.
Under the hood, l_spline is the interpolator ODEsolve.

Wrote

My implementation of interpolation has an error,

Use the Smath code ... visit late Samples.
As an independent Smath document, can be traced
to doctor your original error.
Simply implement the Mathsoft interpolation code.

Wrote

In Mathcad the first three numbers encode the type of spline. Jean doesn't know about this

I myself don't know a lot of things.
Yet I don't post useless messages just to reply.
I guess most people don't, except Jean.
More unacceptable part is, sometimes he posts false information.
Especially on engineering questions/samples.
And insist on that wrong claims like his life depends on it.
I am afraid he will cause something catastrophic in real life.