.
A .
det:
D = det(A)
inv:
A1 = inv(A)
MATLAB , ,
:
>> A = [1 2 1 4; 2 0 4 3; 4 2 2 1; -3 1 3 2]
:
>> B = [13; 28; 20; 6]
MATLAB \.
:
>> X = A\B
X =
-1
>> A *X
B.
ans =
13.0000
28.0000
20.0000
6.0000
MatLab ,
I = quad(' ', , b)
, ;
, b ,
I .
e :
I = quad('name', , b, e).
,
.
:
.
-, , , fint
------------------------------------------------------------------------------------------------------------------------
function f = fint(x)
f = exp(-x).*sin(x);
------------------------------------------------------------------------------------------------------------------------
, ,
>> I = quad('fint', -1, 1)
long
I =
-0.66349146785310
:
>> I = quad('fint', -1, 1, 1.0e-10)
I =
-0.66349366663001
.
, inline:
>> F = inline('exp(-x).* sin(x)')
F =
Inline function:
F(x) = exp(-x).* sin(x)
quad , :
>> I = quad(F, -1, 1)
I =
-0.66349146785310
.
, @:
>> F = @(x)exp(-x).*sin(x)
F =
@(x)exp(-x).*sin(x)
>> I = quad(F, -1, 1)
I =
-0.6635
, .
,
x , .
|
|
.
.
-, :
------------------------------------------------------------------------------------------------------------------------
function f = fparam(x, par1, par2)
f = par1.*x.^2+par2.*sin(x);
------------------------------------------------------------------------------------------------------------------------
quad,
I = quad('fparam', -1, 1, 1.0e-06, 0, 22.5, -5.9)
I =
, , , quad.
( ''0'' )
.
>> F = inline('par1.*x.^2+par2.* sin(x)','x','par1','par2')
F =
Inline function:
F(x,par1,par2) = par1.*x.^2+par2.* sin(x)
quad
>> I = quad(F, -1, 1,1.0e-10, 0,22.5,-5.9)
I =
15.0000
.
>> f = @(x, par1, par2) par1.*x.^2+par2.* sin(x)
f =
@(x,par1,par2)par1.*x.^2+par2.*sin(x)
>> I = quad(f, -1, 1,1.0e-10, 0,22.5,-5.9)
I =
15.0000
, .
, ( ) :
.. | ||||
.. |
.
- f_simps, MatLab
: F , M , h .
, , 10 , f_simps.
:
M = 10;
a = -1;
b = 1;
h = (b-a)/M;
x = a:h:b;
F = exp(-x).*sin(x);
Int = f_simps(F, M, h)
Int =
-0.6635
1. .
MatLab . ,
p = [1 0 3.2 -5.2 0 0.5 1 -3]
polyval, , :
polyval(p, 1)
, .
2. .
x | .. | |||
y | ... |
,
:
.
.
, , MatLab vander. \.
,
0,5 | |||||
1,5 | 1,2 |
.
- list_12.
:
0.5 1 2 3 4
1.5 0 1 2 1.2
|
|
P_4
0.21905 -2.4905 9.4667 -13.252 6.0571
x_0 = 3.5
P_x_0 =
1.7321
3. - .
1)
, , .
2)
, .
3) .
interp1.
yi = interp1(x, y, xi, method)
x ;
y ;
xi , ;
method :
nearest ;
liner ;
spline .
interp1 yi .
. list_13.
0.5 1 2 3 4
1.5 0 1 2 1.2
. x_0 = 3,5
Near_x_0 =
1.2
Line_x_0 =
1.6
Spline_x_0 =
1.8618
ynear_X1 = 1
4. .
().
.. | ||||
.. |
,
.
, , , MatLab polyfit:
pk = polyfit(x, y, k),
x ;
y ;
k .
pk .
Pk = polyval(pk, t),
t ( ) .
,
x | |||||||
y | 0.5 | 0.5 |
. list_14.
x =
1 2 3 4 5 6 7
y =
0.5 0.5 1 4 3 5 8
P_3
p3 =
0.027778 -0.16071 0.95437 -0.57143
MatLab ode45, - 4-5
[X, Y] = ode45('name',[x0 b], y0),
name , ;
[x0 b] ;
y0 ;
X , ;
Y .
, X Y , .
) 1- :
.
.
- x (, ) y ( ) fprdif:
- list_15 :
) :
,
.
.
- : , , , : , . . fosl.
|
|
, ode45 - list_16.
) :
1. .
2. - .
3. ode45.
4. .
.
. , . :
.
.
fosl_1 , : x , y , :
list_17 ode45 :
.
,
,
, , .
:
- . :
.
- - .
- -, . , :
.
- , .
- bvpinit. bvpinit , , .
- bvp4c . MatLab ( ).
- .
.
, , , , , .
:
.
- rside :
------------------------------------------------------------------------------------------------------------------------
function f = rside(x, y)
f = [y(2); -2*y(2)./(x-2)-(x-2).*y(1)+1];
------------------------------------------------------------------------------------------------------------------------
- bound :
------------------------------------------------------------------------------------------------------------------------
function f = bound(ya, yb)
f = [ya(1)+0.5; yb(1)+1];
------------------------------------------------------------------------------------------------------------------------
-, bvpinit bvp4c , .
|
|
------------------------------------------------------------------------------------------------------------------------
% .
clear all
% 0.1:
X0 = [0:0.1:1];
% :
Y0 = [0 0];
initsol = bvpinit(X0, Y0);
% BVP4C:
sol = bvp4c('rside', 'bound', initsol);
% C sol:
% sol.x ,
% sol.y , ,
% sol.y(1,:) y1
% sol.y(2,:) - y2
plot(sol.x, sol.y(1,:), 'r.')
grid on
------------------------------------------------------------------------------------------------------------------------