Интерполяция функции двух переменных многочленом Лагранжа

function kursovaya
х=[0.05 0.10 0.17 0.25 0.30 0.36]; 
у=[0.0500, 0.1003, 0.1717, 0.2553, 0.3093, 0.3764]; 
xlabel('x'); ylabel('y'); hold on 
plot(x, у, 'rо') 
t =-0.5:.01:0.5; 
c5=polyfit(x,y,5); 
y5=polyval(c5,t); 
plot(t,y5,'r-'| title('Интерполяция','FontName','Courier') 
hl=legend('данные','Интерполяция',0); 
set(hL,'FontName','Courier')

clc
clear all
 
x = 0:1:5; 
y = 3*sin(sqrt(x)) + 0.35*x - 3.8; 
yi = interp1(x,y, x, 'linear');
subplot(2,1,1)
plot(x,y,'-ob')
 
x1 = 0:1:5; % масив х
y1 = 5*sin(sqrt(x)) + 0.5*x - 5; 
y1i = interp1(x1,y1, x1, 'linear');
subplot(2,1,2)
plot(x1,y1,'-or')

x = 0:1:5; 
y = 3*sin(sqrt(x)) + 0.35*x - 3.8; 
xi = 0:0.01:5;
yi = interp1(x,y, xi, 'linear');
plot(x,y,'-ob')

clear ,clc
 
[x,y] = meshgrid( -5:5 );
z = sin( (x.^2 + y.^2)/5 );
 
[xi, yi] = meshgrid( -5:0.1:5 );
zi = interp2(x,y,z, xi,yi);
 
subplot(1,2,1)
surf(x,y,z,'facealpha',0.5)
shading flat
title('до интерполяции')
 
subplot(1,2,2)
surf(xi,yi,zi,'facealpha',0.5)
shading flat
title('после интерполяции')

function zi = lagrange2(x,y,z, xi,yi)
% Интерполяция двумерным многочленом Лагранжа
% xi - массив координат узлов x
% yi - массив координат узлов y
% z - массив значений интерполируемой функции
% x - массив данных х
% y - массив данных y
%
% by Zosima
 
% проверка
if (size(x)~=size(y))|(size(z)~=size(y))|(size(z)~=size(x))
    disp('Размеры матриц данных x,y,z не совпадают!')
    return
elseif size(xi)~=size(yi)
    disp('Размеры узловых xi,yi матриц не совпадают!')
    return
end
 
zi = zeros(size(xi));
for ii = 1:size(x,1)
    for jj = 1:size(x,2)
 
        P = ones(size(xi));
        for i = 1:size(x,1)
            for j = 1:size(x,2)
                if (ii~=i)&(jj~=j)
                    P = P.*( (xi-x(i,j)).*(yi-y(i,j))) ./ ...
                        ( (x(ii,jj)-x(i,j))*(y(ii,jj)-y(i,j)) );
                end
            end
        end
        zi = zi + z(ii,jj).*P;
 
    end
end

clear, clc
 
[x y] = meshgrid( 0:0.25:1 );
z = 2*x.^2 - 3*sqrt(y) + randn(size(x));
 
[xi yi] = meshgrid(0:0.01:1);
 
zi1 = interp2(x,y,z, xi,yi); % встроенная
zi2 = lagrange2(x,y,z, xi,yi); % самодельная
 
surf(x,y,z,'facealpha',0.7), hold on
surf(xi,yi,zi2,'facealpha',0.5)

function kursovaya
x=[0.05 0.10 0.17 0.25 0.30 0.36]; 
y=[0.0500, 0.1003, 0.1717, 0.2553, 0.3093, 0.3764]; 
xlabel('x');
ylabel('y');
hold on 
plot(x,y,'-or')
t =-0.5:.01:0.5; 
c5=polyfit(x,y,5); 
y5=polyval(c5,t); 
plot(t,y5,'r-'); 
title('Интерполяция','FontName','Courier');
hl=legend('Данные','Интерполяция',0); 
set(hl,'FontName','Courier')

clear ,clc
[x,y] = meshgrid( -5:5 ); % сокращенная форма записи функции 
[X, Y] = meshgrid(x, x)
z = sin( (x.^2 + y.^2)/5 );
 
[xi, yi] = meshgrid( -5:0.1:5 );
zi = interp2(x,y,z, xi,yi); % двумерная интерполяция
 
subplot(1,2,1)
surf(x,y,z,'facealpha',0.5)
shading flat % окраска поверхностей
title('До интерполяции')
 
subplot(1,2,2)
surf(xi,yi,zi,'facealpha',0.5)
shading flat
title('После интерполяции')

function varargout = interfeys(varargin)
% INTERFEYS MATLAB code for interfeys.fig
%      INTERFEYS, by itself, creates a new INTERFEYS or raises the existing
%      singleton*.
%
%      H = INTERFEYS returns the handle to a new INTERFEYS or the handle to
%      the existing singleton*.
%
%      INTERFEYS('CALLBACK',hObject,eventData,handles,...) calls the local
%      function named CALLBACK in INTERFEYS.M with the given input arguments.
%
%      INTERFEYS('Property','Value',...) creates a new INTERFEYS or raises
%      the existing singleton*.  Starting from the left, property value pairs are
%      applied to the GUI before interfeys_OpeningFcn gets called.  An
%      unrecognized property name or invalid value makes property application
%      stop.  All inputs are passed to interfeys_OpeningFcn via varargin.
%
%      *See GUI Options on GUIDE's Tools menu.  Choose "GUI allows only one
%      instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLES
 
% Edit the above text to modify the response to help interfeys
 
% Last Modified by GUIDE v2.5 30-May-2013 17:47:37
 
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name',       mfilename, ...
                   'gui_Singleton',  gui_Singleton, ...
                   'gui_OpeningFcn', @interfeys_OpeningFcn, ...
                   'gui_OutputFcn',  @interfeys_OutputFcn, ...
                   'gui_LayoutFcn',  [] , ...
                   'gui_Callback',   []);
if nargin && ischar(varargin{1})
    gui_State.gui_Callback = str2func(varargin{1});
end
 
if nargout
    [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
    gui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT
 
% --- Executes just before interfeys is made visible.
function interfeys_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject    handle to figure
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
% varargin   command line arguments to interfeys (see VARARGIN)
 
% Choose default command line output for interfeys
handles.output = hObject;
 
% Update handles structure
guidata(hObject, handles);
 
initialize_gui(hObject, handles, false);
 
% UIWAIT makes interfeys wait for user response (see UIRESUME)
% uiwait(handles.figure1);
 
 
% --- Outputs from this function are returned to the command line.
function varargout = interfeys_OutputFcn(hObject, eventdata, handles)
% varargout  cell array for returning output args (see VARARGOUT);
% hObject    handle to figure
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
 
% Get default command line output from handles structure
varargout{1} = handles.output;
 
 
% --- Executes during object creation, after setting all properties.
function density_CreateFcn(hObject, eventdata, handles)
% hObject    handle to density (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    empty - handles not created until after all CreateFcns called
 
% Hint: popupmenu controls usually have a white background on Windows.
%       See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end
 
 
 
function density_Callback(hObject, eventdata, handles)
% hObject    handle to density (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
 
% Hints: get(hObject,'String') returns contents of density as text
%        str2double(get(hObject,'String')) returns contents of density as a double
density = str2double(get(hObject, 'String'));
if isnan(density)
    set(hObject, 'String', 0);
    errordlg('Input must be a number','Error');
end
 
% Save the new density value
handles.metricdata.density = density;
guidata(hObject,handles)
 
% --- Executes during object creation, after setting all properties.
function volume_CreateFcn(hObject, eventdata, handles)
% hObject    handle to volume (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    empty - handles not created until after all CreateFcns called
 
% Hint: popupmenu controls usually have a white background on Windows.
%       See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end
 
 
 
function volume_Callback(hObject, eventdata, handles)
% hObject    handle to volume (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
 
% Hints: get(hObject,'String') returns contents of volume as text
%        str2double(get(hObject,'String')) returns contents of volume as a double
volume = str2double(get(hObject, 'String'));
if isnan(volume)
    set(hObject, 'String', 0);
    errordlg('Input must be a number','Error');
end
 
% Save the new volume value
handles.metricdata.volume = volume;
guidata(hObject,handles)
 
% --- Executes on button press in calculate.
function calculate_Callback(hObject, eventdata, handles)
% hObject    handle to calculate (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
 
mass = handles.metricdata.density * handles.metricdata.volume;
set(handles.mass, 'String', mass);
 
% --- Executes on button press in reset.
function reset_Callback(hObject, eventdata, handles)
% hObject    handle to reset (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
 
initialize_gui(gcbf, handles, true);
 
% --- Executes when selected object changed in unitgroup.
function unitgroup_SelectionChangeFcn(hObject, eventdata, handles)
% hObject    handle to the selected object in unitgroup 
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
 
if (hObject == handles.english)
    set(handles.text4, 'String', 'lb/cu.in');
    set(handles.text5, 'String', 'cu.in');
    set(handles.text6, 'String', 'lb');
else
    set(handles.text4, 'String', 'kg/cu.m');
    set(handles.text5, 'String', 'cu.m');
    set(handles.text6, 'String', 'kg');
end
 
% --------------------------------------------------------------------
function initialize_gui(fig_handle, handles, isreset)
% If the metricdata field is present and the reset flag is false, it means
% we are we are just re-initializing a GUI by calling it from the cmd line
% while it is up. So, bail out as we dont want to reset the data.
if isfield(handles, 'metricdata') && ~isreset
    return;
end
 
handles.metricdata.density = 0;
handles.metricdata.volume  = 0;
 
set(handles.density, 'String', handles.metricdata.density);
set(handles.volume,  'String', handles.metricdata.volume);
set(handles.mass, 'String', 0);
 
set(handles.unitgroup, 'SelectedObject', handles.english);
 
set(handles.text4, 'String', 'lb/cu.in');
set(handles.text5, 'String', 'cu.in');
set(handles.text6, 'String', 'lb');
 
% Update handles structure
guidata(handles.figure1, handles);
 
 
% --- Executes on button press in pushbutton11.
function pushbutton11_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton11 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
 
 
 
function edit6_Callback(hObject, eventdata, handles)
% hObject    handle to edit6 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
 
% Hints: get(hObject,'String') returns contents of edit6 as text
%        str2double(get(hObject,'String')) returns contents of edit6 as a double
 
 
% --- Executes during object creation, after setting all properties.
function edit6_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit6 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    empty - handles not created until after all CreateFcns called
 
% Hint: edit controls usually have a white background on Windows.
%       See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

clear ,clc
[x,y] = meshgrid( -5:5 ); % сокращенная форма записи функции 
[X, Y] = meshgrid(x, x)
z = sin( (x.^2 + y.^2)/5 );
 
[xi, yi] = meshgrid( -5:0.1:5 );
zi = interp2(x,y,z, xi,yi); % двумерная интерполяция
 
subplot(1,2,1)
mesh(x,y,z,'facealpha',0.5)
shading flat % окраска поверхностей
title('До интерполяции')
 
subplot(1,2,2)
mesh(xi,yi,zi,'facealpha',0.5)
shading flat
title('После интерполяции')

function zi = lagrange2(x,y,z, xi,yi)
% Интерполяция двумерным многочленом Лагранжа
% xi - массив координат узлов x
% yi - массив координат узлов y
% z - массив значений интерполируемой функции
% x - массив данных х
% y - массив данных y
if (size(x)~=size(y))|(size(z)~=size(y))|(size(z)~=size(x))
    disp('Размеры матриц данных x,y,z не совпадают!')
    return
elseif size(xi)~=size(yi)
    disp('Размеры узловых xi,yi матриц не совпадают!')
    return
end
zi = zeros(size(xi));
z1 = zeros(size(x,1),size(xi,2));
for i = 1:size(z,1)
    z1(i,:) = lagran1(x(i,:),z(i,:), xi(1,:));
end
 
for j = 1:size(yi,2)
    zi(:,j) = lagran1(y(:,1),z1(:,j), yi(:,1));
end
end
 
function yi = lagran1(x,y, xx)
yi = zeros(size(xx));
for k = 1:length(x)
    P = ones(size(xx));
    for i=1:length(x)
        if k~=i
            P = P.*(xx-x(i))./(x(k)-x(i));
        end
    end
    yi = yi + y(k)*P;
end
end