2d Lagrange interpolation

Please choose your input case:

synthetic data

Please specify the boundaries on the x and y axis: x-axis : from to y-axis : from to Specify the case you want to see, and, accordingly, either the function or the node point: Interpolating polynomial Interpolation error sqrt( x^2 + y^2) sin(pi*x)*cos(pi*y) 1 / (x^2+y^2+1) Input of a function of your own: Please type the evaluation program of your function here using FORTRAN rules. Your final statement must be fu= You may use the constants pi, e(=exp(1)), sqrt2(=1.414...), the integer variables i,j,k, the logicals bool1,bool2,bool3 and the double precision variables sum,h1,h2,h3,h4,u(100),v(100),a(100,100) which are all intialized with zero resp. .false. . The routine has the parameters x, y (double, input) and must return fu (double out). never change x or y!. first is a local integer and set 0 before calling the function the first time. You may use this in order to initialize some local data and set it 1 afterwards to avoid multiple such initialization. Your settings of the local variables are preserved during program execution. C**** it computes the truncated McLaurin series of sin(pi*x)-cos(pi*y) if ( first .ne. 0 ) goto 100 u(1)=1.d0 do 50 i=2,80 c****** coefficients of exp(pi*z) series u(i)=u(i-1)*pi/dble(i-1) 50 continue 100 continue first=1 fu=0.d0 h1=1.d0 do 200 i=40,1,-1 k=i+i fu=fu+h1*(u(k)*x**(k-1)-u(k-1)*y**(k-2)) h1=-h1 200 continue Lagrange basis function node i (in x direction): attention: 0 <= i <= n ! node j (in y direction): attention: 0 <= j <= m ! Specify the interpolation degrees here: Important: both degrees between 0 and 20 ! degree in x: n= degree in y: m=

own (x,y,z)-data

Please specify the interpolation degrees n (for x) and m (for y) here: n= m= Please type the input data here in the textarea, in array form like x0 ... xn y0 z0,0 ... z0,n ... ... ... ... ym zm,0 ... zm,n Each row of this array must begin on a new line, but may extend over several lines. 0,1, 0,1,3, 1,4,6, type the number of evalution points in this field , 0 <= num <= 20 num = and the (x,y) coordinates as a list of 2*num numbers in this textarea : 0.5,0.5,

Specify the two rotation angles of the x and z axis for the 3D projected plot:

for the x axis (in degrees [0:180], 0= screen horizontally)
for the z axis (in degrees [0:360], 0= orthogonal to the screen)

Click on "evaluate", in order to submit your input.