MATLAB: How to calculate spline of the function

spline

Hi. How can i obtain a cubic spline coefficients, if i know values and derivatives of the function? For example:

args = [-1, 0, 1];
vals = [-1, 0, 1];
derivs = [3, 0, 3];
subic_spline_coefs = ...?

I'd like obtain coefs using derivatives information.

Best Answer

X = [args;args]
Y = [vals;derivs]
P = spapi(4,X(:),Y(:))

after comment

ppp = csape([-1 1],[3 -1 1 3],[1 1])

polyval(ppp.coefs,1)

Related Solutions

MATLAB: A*A’=C

One solution can be found by using SVD

>> C = [2/3 -1/3 -1/3;-1/3 2/3 -1/3;-1/3 -1/3 2/3]
C =
    0.6667   -0.3333   -0.3333
   -0.3333    0.6667   -0.3333
   -0.3333   -0.3333    0.6667
>> rank(C) % check if C can be factorized with 3x2 matrix
ans =
     2
>> [U,S,V]=svd(C);
>> A = U(:,1:2)*S(1:2,1:2)
A =
   -0.8165    0.0000
    0.4082   -0.7071
    0.4082    0.7071
>> A*A'
ans =
    0.6667   -0.3333   -0.3333
   -0.3333    0.6667   -0.3333
   -0.3333   -0.3333    0.6667

The solution is not uique since you can multiply on the right side of A by any Hermitian matrix of size 2 x 2

MATLAB: How to find the derivative of a spline curve in MATLAB 7.9 (R2009b)

The POLYDER function is meant to be used to differentiate polynomials, and not piece-wise polynomials, such as splines.

If you have Spline Toolbox, you can use FNDER function to find the derivative of a spline:

pp=spline(x,y);
p_der=fnder(pp,1);
y_prime=ppval(p_der,x);

For more information on the FNDER function, please refer to the documentation by executing the following in the MATLAB command prompt:

doc fnder

If you do not have access to the Spline Toolbox, you can use UNMKPP function to break down your polynomial and then use MKPP function to assemble a new polynomial that will be a derivative of the first polynomial as in the following example:

% create points we will use to construct the spline
x = 0:10;
y = (x-5).^3+3*3+x+5;
% points the spline will be plotted at
xx = linspace(0,10,20);
% create the spline
pp = spline(x,y);
% plot the spline and the initial points used to create it
figure
plot(x,y,'o',xx,ppval(pp,xx))
hold on
% extract details from piece-wise polynomial by breaking it apart
[breaks,coefs,l,k,d] = unmkpp(pp);
% make the polynomial that describes the derivative
pp2 = mkpp(breaks,repmat(k-1:-1:1,d*l,1).*coefs(:,1:k-1),d);
% plot the derivative of the polynomial
plot(xx,ppval(pp2,xx),'-r')
% to calculate 2nd derivative differentiate the 1st derivative
[breaks,coefs,l,k,d] = unmkpp(pp2);
pp3 = mkpp(breaks,repmat(k-1:-1:1,d*l,1).*coefs(:,1:k-1),d);
plot(xx,ppval(pp3,xx),'-g')

For more information on the UNMKPP and MKPP functions please refer to the documentation by executing the following in the MATLAB command prompt:

doc unmkpp
doc mkpp

Best Answer

Related Solutions

MATLAB: A*A’=C

MATLAB: How to find the derivative of a spline curve in MATLAB 7.9 (R2009b)

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