%-- 2/19/2025 10:31 AM --%
ver
bench
%-- 2/21/2025 1:52 PM --%
peaks
paths
path
which sin
which peaks
type peaks
edit peaks
help plot
doc plot
x = 0:pi/10:2*pi;
y1 = sin(x);
y2 = sin(x-0.25);
y3 = sin(x-0.5);
figure
plot(x,y1,'g',x,y2,'b--o',x,y3,'c*')
ver
demos
%-- 2/24/2025 6:24 PM --%
pwd
%-- 2/28/2025 1:08 PM --%
ver
1+1
path
vibes
edit vibes
travel
truss
pwd
ls
echodemo m01
format compact
whos
x = [1 2 3 4]
x = 1:5
sqrt(x)
tic, sqrt(1:10^6); toc
tic, sqrt(1:10^7); toc
tic, sqrt(1:10^9); toc
whos
help realmin
doc realmin
help
help complex
realmax
realmax*10
1/0
0/0
x=1:4
x
x = [1 -i 1-i 2]
x(1)
x(2)
x(3)
x(1:2)
x(1:4)
whos
x
x(1:5)
size(x)
y = sin(x);
plot(x,y)
grid
1:5
3:1
3:-1:1
fliplr(1:5)
1:5
1:2:5
1:0.5:5
y
x
x = 1:10
y = x^2
y = x.^2
y(2:5)
y([2 3 4 5])
y([3 3 6 5])
which linspace
edit linspace
log10(ans)
10^1.8
a
a,b
a(1:4)+b
a,b
a*b
a.*b
a
a'
a*b'
a'*b
a/b
b/a
b,a
b./a
a.\b
a
a.^2
a.**2
a**2
a, b
1 2 3; 4 5 6]
z = [1 2 3; 4 5 6]
g = [1 2 3
4 5 6
7 8 9]
a, b
[a;b]
z = [a;b]
z(1,3)
z(1,;)
z(1,:)
zeros(4)
zeros(4,3)
rand(4)
history
hist
history
hist
a'*b
QUIT
%-- 3/3/2025 5:14 PM --%
ver
pwd
cdf ..
cd ..
pwd
1:5
x = 1:5
whos
sin(x)
x^2
x*x
x
x.*x
x.^2
x'
1:5
1:2:9
b = 1:2:9
a.*b
x.*b
a,b,b./a
x,b,b./x
format compact
help format
doc format
A = [1 2 3; 4 5 6
7 8 9]
det(A)
eps
1+eps/2 -1
1+eps -1
whos
1:10
linspace(1,10,10)
linspace(1,10,2)
linspace(1,2,20)
x = linspace(0, 2*pi, 30);
size(x)
y = sin(x);
plot(x,y)
plot(x,y, '*-')
grid
plot(x,y, x,y.^2)
xlabel('nezavisle promenna x'
ylabel('zavisle promenna'
title('2sin(x)cos(x) = sin(2x)')
xlabel('nezavisle promenna x')
ls
dir
doc plot
a = 1:9
a>4
b=9-a
a==b
-3:3
x = (-3:3)/3
sin(x)./x
0/0
x = linspace(0, 2*pi, 30);
x = linspace(0, pi/2, 30);
plot(x,x, x,sin(x))
x = (-3:3)/3
x==0
xx = x + (x==0)*eps
sin(xx)./xx
a
a>2
a<6
(a<6) & (a<2)
(a<6) & (a>2)
100^400
realmax
pwd
discont
type discont.m
f01(2)
1:4
f01(1:4)
edit Pi1
rand
rand(2)
rand(1,2)
doc if
Pi1(10)
Pi1(10^5)
Pi1(10^6)
Pi1(10^7)
1:4
sum(1:4)
Pi2(10^5)
tic, Pi1(10^6), roc
tic, Pi1(10^6), toc
tic, Pi1(10^7), toc
tic, Pi2(10^7), toc
edit Pi_err.m
Pi_err
%-- 3/5/2025 5:43 PM --%
PWD
pwdpwd
pwd
doc hilb
edit pi1
N=5; A=hilb(N), bar3(A*inv(A))
N=5; A=hilb(N); bar3(A*inv(A))
N=10; A=hilb(N); bar3(A*inv(A))
N=11; A=hilb(N); bar3(A*inv(A))
N=13; A=hilb(N); bar3(A*inv(A))
Pi2(1000)
(Pi2(10^7)/pi-1)
format compact
tic, Pi1(10^5), toc
tic, Pi1(10^7), toc
tic, (Pi1(10^7)/pi-1), tpc
tic, (Pi1(10^7)/pi-1), t0c
tic, (Pi1(10^7)/pi-1), toc
tic, (Pi1(10^8)/pi-1), toc
tic, (Pi2(10^8)/pi-1), toc
Pi_err
hilb(4)
doc hilb
edit hilb
det(hilb(4)
det(hilb(4))
det(hilb(9))
det(hilb(20))
det(hilb(24))
det(hilb(28))
det(hilb(32))
A = [1 2 3; 4 5 6
7 8 0]
det(A)
b = [366; 804; 351]
x=inv(A)*b
A*x-b
eps
x=A\b
A*x-b
doc \
edit op_vs_inv.m
op_vs_inv
N=8, A =hilb(N); bar3(inv(A)&A)
N=8, A =hilb(N); bar3(inv(A)*A)
N=8, A =hilb(N); pcoloer(inv(A)*A)
N=8, A =hilb(N); pcolor(inv(A)*A)
N=11; A =hilb(N); pcolor(inv(A)*A), colorbar
N=12; A =hilb(N); pcolor(inv(A)*A), colorbar
N=13; A =hilb(N); pcolor(inv(A)*A), colorbar
N=14; A =hilb(N); pcolor(inv(A)*A), colorbar
N=14; A =hilb(N); bar3(inv(A)*A), colorbar
N=12; A =hilb(N); bar3(inv(A)*A), colorbar
ver
Learning HDL Toolbox                             Version 24.1        (R2024a)
Deep Learning Toolbox                                 Version 24.1        (R2024a)
Econometrics T
%-- 3/7/2025 1:16 PM --%
pwd
sin(Pi)
sin(pi)
whos
who
format compact
help format
doc format
clear
10^300 * 10^9
1+eps > 1
eps
1+eps/2 > 1
1+eps/2-1
1+eps-1
format long
1+eps-1
1+eps/2-1
sqrt(4)
sqrt(-1)
format short
0/0
doc imag
sqrt(-1)
imag(sqrt(-1))
conj(sqrt(-1))
help
lookfor complex
a=3, b=4
[1 3 5]
[1,3,5]
1:5
1:2:5
x = 0:0.1:1
x = (0:0.1:1)*pi
sin(Pi)
sin(pi)
sin([pi, pi/3 pi/4])
plot(x,sin(x))
plot(x,sin(x).'*-')
plot(x,sin(x),'*-')
grid
b=1:2:9
size(b)
b(2)
b(6)
b(1)
2:4
b, b(2:4)
b([4 3 1 4 4])
1:7
linspace(1,4,4)
linspace(1,4,6)
linspace(1,5,6)
linspace(0,5,6)
edit linspace
xx = logspace(0,2,11)
log10(xx)
log(xx)
a=1:5
b( = 1:2:9
b = 1:2:9
a
sin(a)
a
a/2
a*2
a*b
a,b
a.*b
b, b'
a*b'
a'*b
a,b
b/a
b./a
b./a, a.\b
a
sqrt(a)
a.^2
a^a
2^a
2.^a
a
a'
c=[1; 2; 3;4;5]
c'
g=[1 2 3; 4 5 6]
g(2,3)
g(2,1:3)
g(2,:)
g(1:end,2:end)
zeros(3)
zeros(2:4)
zeros(2,4)
ones(3)
diaf(3)
diag(3)
diag(3,3)
rand(4)
A = rand(100,4);
sum(1:4)
doc ones
sum(A)
sum(A)/100
sum(rand(1000,5))/1000
sum(rand(10000,5))/10000
clear
peaks
%-- 3/10/2025 5:06 PM --%
1:9
format compact
clc
A = 1:9
A = reshape(A,3,3)
A'
rot90(A)
rot90(A,-1)
fliplr(rot90(A,-1))
rot90(A,2)
rot90(A,3)
A'
A = A'
det(A)
eps
A(3,3)=0
b = [366;804;352]
det(A)
x = inv(A)*b
A*x-b
doc \
x2 = A\b
A*x2-b
eig(A)
V = eig(A)
[V,D] = eig(A)
hilb(4)
hilb(3)
hilb(4)
det(hilb(4))
det(hilb(8))
det(hilb(20))
realmin
det(hilb(22))
det(hilb(24))
det(hilb(28))
det(hilb(31))
det(hilb(30))
doc norm
which norm
edsit norm
edit norm
op_vs_inv
N=5; A=hilb(N); pcolor(A*inv(A)), colorbar
N=10; A=hilb(N); pcolor(A*inv(A)), colorbar
N=12; A=hilb(N); pcolor(A*inv(A)), colorbar
N=12; A=hilb(N); bar3(A*inv(A)), colorbar
N=14; A=hilb(N); bar3(A*inv(A))
fh = @(N) A=hilb(N); bar3(A*inv(A))
fh = @(N) bar3(hilb(N)*inv(hiln(N)))
fh(5)
fh = @(N) bar3(hilb(N)*inv(hilb(N)))
fh(5)
fh(15)
eps
1+eps >1
1+eps/2 >1
calc_eps
EPS-eps
EPS==eps
num_dif
grid
num_dif2
clc
x = linspace(0, 2*pi, 30);
y = sin(x);
z = cos(x);
plot(x,y,x,z)
grid
xlabel( 'Independent Variable X')       % x-axis label
ylabel( 'Dependent Variables Y and Z')  % y-axis label
title(`Sine nad Cosine Curves')         % title the plot
title('Sine nad Cosine Curves')         % title the plot
text(2.5, 0.7, 'sin(x)')
gtext('cos(x)')
axis off
axis on, grid off
axis square
figure(3)
x = linspace(0, 2*pi, 30);
y = sin(x);
z = cos(x);
plot(x,y)
plot(x,z)
hold on
plot(x,y)
hold off
plot(x,y)
which ezplot
doc ezplot
fplot('sin(x)/(1+x^2)')
fplot(@(x) sin(x)./(1+x.^2))
fplot(@(x) sin(x)/(1+x.^2))
fplot(@sin)
fplot(@sin. [0 10])
fplot(@sin, [0 10])
fplot(@sin^2, [0 10])
fplot(@sin*2, [0 10])
fplot(@(x) sin*2, [0 10])
fplot(@(x) sin.*2, [0 10])
fplot(@(x) sin(x)*2, [0 10])
fplot(@(x) sin(x).^2, [0 10])
ezplot('2*cos(t)','2*sin(t)')
ezplot('2*cos(t)','2*sin(t)', [0 1.5*Pi])
ezplot('2*cos(t)','2*sin(t)', [0 1.5*pi])
fplot(@(t) 2*cos(t), @(t) 2*sin(t)), grid
axis equal
ezplot('x^2+y^2-4')
axis([-2 2 -2 2])
axis equal
fimplicit(@(x,y) x.^2 + y.^2 -4)
fimplicit(@(x,y) x.^2 + y.^2 -4), grid, axis equal, axis([-3 3 -3 3])
ezpolar('sin(t)/t', [-6*pi,6*pi])
fplot(@(t) (sin(t)./t).*cos(t), @(t) (sin(t)./t).*sin(t), ...
[-6*pi,6*pi], 'LineWidth', 2), grid
h1 = fplot3( @(t) cos(2*pi*t), @(t) sin(2*pi*t), @(t) t,[0,4])
h1.LineWidth=3
h1.color=red
h1.Color=[2 0 0]
h1.Color=[1 0 0]
h1.color=[1 0 0]
QUIT
%-- 3/12/2025 5:18 PM --%
edit f401
edit f401_d
num_dif
grid
figure(2)
num_dif2
@(x) x^9
f1 = @(x) x^9
f1(2)
f1([1 2])
f1 = @(x) x.^9
f1([1 2])
num_dif2
clc
x = linspace(0, 2*pi, 30);
clear
x = linspace(0, 2*pi, 30);
y = sin(x); z = cos(x);
plot(x,y, x,z)
plot(x,y, x,z, '*-')
doc ezplot
ezplot('x^2')
ezplot('x^2', [-3, 5])
fplot('x^2', [-3, 5])
fplot('x.^2', [-3, 5])
fplot('x^2', [-3, 5])
fplot(@sin, [-3, 5])
fplot(@(x) sin(x)^2, [-3, 5]), grid
fplot(@(x) sin(x).^2, [-3, 5]), grid
fplot(@(t) 2*cos(t), @(t) 2*sin(t)), grid
axis square
fplot(@(t) 2*cos(t), @(t) 2*sin(t), t=[0, 3/2*pi]), grid
fplot(@(t) 2*cos(t), @(t) 2*sin(t), [0, 3/2*pi]), grid
fplot([@(t) 2*cos(t), @(t) 2*sin(t)], [0, 3/2*pi]), grid
fplot({@(t) 2*cos(t), @(t) 2*sin(t)}, [0, 3/2*pi]), grid
fimplicit(@(x,y) x.^2 + y.^2 -4)
grid, axis square
fplot(@(t) (sin(t)./t).*cos(t), @(t) (sin(t)./t).*sin(t), ...
[-6*pi,6*pi], 'LineWidth', 2), grid
h1 = [-6*pi,6*pi], 'LineWidth', 2), grid
h1 = fplot3( @(t) cos(2*pi*t), @(t) sin(2*pi*t), @(t) t,[0,4])
h1.LineWidth = 2;
get(h1
get(h1)
h1.Color = [1 1 0]
h1.ZFunction = @(x) sqrt(t)
get(h1)
h1.ZFunction = @(t) sqrt(t)
doc dsolve
which dsolve
syms y(t)
eq = diff(y(t),t)== y(t)+t
format compact
dsolve(eq)
euler01_demo(0.1)
euler01_demo(0.0.2)
euler01_demo(0.02)
h_vect = []; err_vect = []; h = 0.2;
euler02_demo
h
euler02_demo
loglog(h_vect, err_vect); xlabel('Step size'); ylabel('Maximum error'); grid
loglog(h_vect, err_vect. '*-'); xlabel('Step size'); ylabel('Maximum error'); grid
loglog(h_vect, err_vect, '*-'); xlabel('Step size'); ylabel('Maximum error'); grid
h = 0.2; h_vect = []; eul_vect = []; rk2_vect = []; rk4_vect = [];
rk01_demo
rk01_demo
loglog(h_vect, eul_vect, h_vect, rk2_vect, h_vect, rk4_vect);  grid;
%-- 3/14/2025 1:06 PM --%
A = [6,12,4;7,-2,3;2,8,-9]
format compact
pwd
m02
a=1:9, b=9-a
a=4
a=1:9
a==4
whos
tf = a>4
tf = a==b
a,b
(a>2)
b-(a>2)
b-(a>2)*3
x=(-3:3)/3
sin(x)/x
a,b
b./a
x
sin(x)./x
0/0
x==0
(x==0)*10^-10
eps
1+eps > 1
1+eps/2 > 1
(x==0)*eps
x=x+(x==0)*eps
format
help format
format long
x
format compact
format short
x
x(4)
x(4)==0
x(4)>0
sin(x)./x
x=(-3:3)/3
sx = sin(x)./x
isnan(sx)
finite(sx)
isfinite(sx)
any(sx)
any(x)
doc any
edit discont
discont
whos
plot(x,y)
discont
hold on
plot(x,y)
plot(x,y, 'LineWidth',3)
plot(x,y, 'LineWidth',3, Color, [0.8 0 0.8])
plot(x,y, 'LineWidth',3, 'Color', [0.8 0 0.8])
plot(x, cos(x))
figure(2)
plot(x, cos(x))
plot(x,y, 'LineWidth',3, 'Color', [0.8 0 0.8])
hold on
plot(x, cos(x))
grid
hold off
plot(x,y+1, 'LineWidth',3, 'Color', [0.8 0 0.8])
rand
rand(3)
rand(1,2)
x = rand(1,2)
x(1)^2+x(2)^2 <1
f01(2)
f01(1:4)
edit Pi1
which pi1
Pi1(10^4)
Pi1(10^4)*4
Pi1(10^8)
Pi1(10^6)
abs(Pi1(10^6)/pi-1)
abs(Pi1(10^7)/pi-1)
tic. abs(Pi1(10^6)/pi-1), toc
tic, abs(Pi1(10^6)/pi-1), toc
tic, abs(Pi1(10^7)/pi-1), toc
x=1:4
y = 5:8
x,x.^2
y, y.^2
x,y, x.^2 + y.^2
x
sum(x)
tic, abs(Pi2(10^7)/pi-1), toc
tic, abs(Pi2(10^8)/pi-1), toc
A = [1, 2, 3; 4 5 6; 7 8 0]
size(A)
det(A)
b=[366; 804; 351)
b=[366; 804; 351]
x1 = inv(A)*b
A*x1
A*x1-b
x2=A\b
A*x2-b
det(A)
[L, U] = lu(A)
[L, U] =qr(A)
eig(A)
[V,D] = eig(A)
zeros(4)
ones(4)
rand(3)
M = magic(5)
sum(M)
M = magic(3)
sum(M)
M'
sum(M')
%-- 3/17/2025 5:07 PM --%
fplot(@cos)
fplot(@cos, [0 3*pi])
fplot(@(x) cos*x)^2, [0 3*pi])
fplot(@(x) cos(x), [0 3*pi])
fplot(@(x) cos(x)^2, [0 3*pi])
fplot(@(x) cos(x).^2, [0 3*pi])
fplot(@(x) cos(x)*sin(x), [0 3*pi])
fplot(@(x) cos(x).*sin(x), [0 3*pi])
fplot(@(x) [cos(x), sin(x)], [0 3*pi])
fplot(@(x) [cos(x), sin(x)], [0 3*pi], 'Color', [red blue])
fplot(@(x) [cos(x), sin(x)], [0 3*pi], 'Color', [[1 0 0], [0 0 1]])
h1 = fplot(@(x) [cos(x), sin(x)], [0 3*pi])
x = (0:1/2000:1)';
plot(x,cos(tan(pi*x)))
plot(x,cos(tan(pi*x)), '*-')
fplot( @(x) cos(tan(pi.*x)) )
fplot( @(x) cos(tan(pi.*x)), [0 1] )
fplot( @(x) cos(x), [0 3*pi]);
[x,y] = fplot( @(x) cos(x), [0 3*pi]);
clear
[x,y] = fplot( @(x) cos(x), [0 3*pi]);
plot(x,y, '-*')
plot(y,x, '-*')
x = 0:0.1:4*pi;
z = [cos(x)' sin(x)' sin(x).^2'];
plot(z)
plot(x.z)
plot(x,z)
peaks
edit peaks
plot(peaks)
plot(peaks(20))
plot(peaks, rot90(peaks'))
X = peaks(7)
plot(X)
subplot(2,2,1)
fplot(@sin)
subplot(2,2,3)
fplot(@tan)
subplot(1,2,2)
fplot(@cos)
subplot(2,1,1)
fplot(@cos)
doc subplot
fplot(@cos)
figure
peaks
subplot(2,1,1)
subplot(2,1,2)
pe
peaks
which peaks
figure(20)
peaks
figure(20)
doc axis
doc axes
pwd
path
subplot_demo
ginput_demo
messgrid([-2:1:2])
mesgrid([-2:1:2])
meshgrid([-2:1:2])
[X,Y] = meshgrid([-2:1:2])
format compact
clc
format compact
[X,Y] = meshgrid([-2:1:2])
X, flipud(Y)
X.^2
Y, Y.^2
Z = exp(X.^2+ Y.^2)
plot3(Z)
surf(Z)
Z = exp(-X.^2 - Y.^2)
surf(Z)
clear
[X,Y] = meshgrid([-2:0.1:2]);
Z = exp(-X.^2 - Y.^2);
surf(X,Y,Z)
colorbar
colormap(hsv)
colormap(hsv(10))
shading interp
shading faceted
colormap(jet)
colormap(winter(32))
doc jet
surf(X,Y,Z)
colormap(jet)
pcolor(X,Y,Z)
colorb
colorbar
plot3(X,Y,Z)
t=0:pi/50:10*pi;
plot3(sin(t),cos(t),t)
plot3(sin(t),cos(t),t.^2)
x = -8:0.5:8;
y = x;
[X, Y] = meshgrid(x,y);
R = sqrt(X.^2 + Y.^2) + eps;   % distance from the origin (0,0)
Z = sin(R)./R;                 % calculate sin(r)/r
mesh(X,Y,Z)
reshape(1:9,3,3)
M = reshape(1:9,3,3)
M(2,3)
M(:)
M'
M2 = M'
M2(:)
M2(8)
M2(5:8)
M2, max(M2)
M2, max(max(M2))
M2(:)
max(M2(:))
axis([-8 8 -8 8 min(Z(:)) max(Z(:))])
view
[az el] = view
view(2)
view(3)
view(30, 20)
view(30, 70)
contour(peaks)
contour(peaks,30)
contour3(peaks,30)
mesh(peaks(30)+7)
hold on
pcolor(peaks(30))
colorbar
colomap(jet)
colormap(jet)
hold off
pcolor(peaks(30))
surfl(peaks)
colormap(grey)
colormap(gray)
shading interp
surfc(peaks)
colormap(jet)
surfz(peaks)
meshz(peaks)
[X, Y] = meshgrid([-2:.2:2]);
Z = X.* exp(-X.^2 - Y.^2);
surfz(X,Y,Z)
surf(X,Y,Z)
Z = exp(-X.^2 - Y.^2);
surf(X,Y,Z)
Z = X.*exp(-X.^2 - Y.^2);
surf(X,Y,Z)
surf(Z)
surf(X,Y,Z)
surf(X,Y,Z, gradient(Z))
colorba
colorbar
surf(Z, gradient(Z))
P = peaks(40);
C - del2(P)
C = del2(P)
surf(P,C)
colormap(jet)
colorb
colorbar
QUIT
quitquit
%-- 3/19/2025 5:09 PM --%
ode45('0', [0 10], 1)
ode45(@(x,y) 0, [0 10], 1)
F1 = @(x,y) 0
format compact
ode45(F1, [0 10], 1)
[x,y] = ode45(F1, [0 10], 1);
plot(x,y)
ode45(@(x,y) t, [0 10], 1)
ode23(@(t,y) t, [0 10], 1)
ode23(@(t,y) y, [0 10], 1)
ode23(@(t,y) -y, [0 10], 1)
ode23(@(t,y) 1/(1-3*t), [0 10], 1)
ode23(@(t,y) 1/(1-3.*t), [0 10], 1)
ode23(@(t,y) 1./(1-3.*t), [0 10], 1)
ode23s(@(t,y) 1./(1-3.*t), [0 10], 1)
ode23s(@(t,y) 1./(1-3.*t), [1/3 10], 1)
ode23s(@(t,y) 1./(1-3.*t), [1.01/3 10], 1)
sin(sym(pi)), sin(pi)
doc dsolve
which subs
doc subs
ode23(@(t,y) [y(2); -y(1)], [0 3*pi], [0;1]), grid
ode23(@(t,y) [y(2); -y(1)], [0 3*pi], [0;2]), grid
ode23(@(t,y) [y(2); -y(1)], [0 3*pi], [0.5;2]), grid
[t,y] = ode23(@(t,y) [y(2); -y(1)], [0 3*pi], [0;1]), grid
[t,y] = ode23(@(t,y) [y(2); -y(1)], [0 3*pi], [0;1]); grid
plot(t,y(:,1), t,y(:,2))
plot(t,y(:,1), t,y(:,2), '*-')
plot(y(:,1), y(:,2), '*-')
plot(y(:,1), y(:,2), '*-'), grid
axis equal
[t,y] = ode23(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1]); grid
plot(y(:,1), y(:,2), '*-'), grid, axis equal
odeset
[t y] = ode23(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1], odeset('Refine', 2));
plot(y(:,1), y(:,2), '*-'), grid, axis equal
[t y] = ode23(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1]);
[t y] = ode45(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1]);
plot(y(:,1), y(:,2), '*-'), grid, axis equal
[t y] = ode23(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1], odeset('Refine', 1));
plot(y(:,1), y(:,2), '*-'), grid, axis equal
[t y] = ode23(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1], odeset('Refine', 4));
[t y] = ode45(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1], odeset('Refine', 4));
plot(y(:,1), y(:,2), '*-'), grid, axis equal
[t y] = ode45(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1]);
[t y] = ode45(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1], odeset('Refine', 1));
plot(y(:,1), y(:,2), '*-'), grid, axis equal
[t y] = ode45(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1]);
plot(y(:,1), y(:,2), '*-'), grid, axis equal
[t y] = ode45(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1], odeset('Refine', 10));
plot(y(:,1), y(:,2), '*-'), grid, axis equal
ode45(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1]);
sol = ode45(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1]);
sol = ode45(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1])
sol = ode45(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1]);
plot(sol.x, sol.y(1,:)
plot(sol.x, sol.y(1,:))
plot(sol.x, sol.y(1,:), '*-')
sol = ode45(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1], odeset('Refine',5);
sol = ode45(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1], odeset('Refine',5));
plot(sol.x, sol.y(1,:), '*-')
sol
sol = ode45(@(t,y) [y(2); -y(1)], [0 2*pi], [0;1], odeset('Refine',10));
sol
doc odes3et
doc odeset
F = @(t,y) -100*y + 100*t +1
ode45(F, [0 1], 1)
[t y] = ode45(F, [0 1], 1)
[t y] = ode45(F, [0 1], 1);
plot(t,y, '*-')
figure(2)
figure(3)
ode15s(F, [0 1], 1);
tic, ode15s(F, [0 1], 1); toc
tic, ode45(F, [0 1], 1); toc
[t,y] = ode15s(F, [0 1], 1);
sol = ode15s(F, [0 1], 1);
sol
sol.stats
ode01_demo
ode02_demo_sym
ode02_demo
ode03_demo
ode04_demo
ode05_demo
100
10
ode05_demo
10
ode05_demo
5
stiff_demo
stiff_demo02
%-- 3/21/2025 12:59 PM --%
x=(0:0.1:1)*2*pi;
x
format compact
x
y = sin(x); z=cos(x);
plot(x,y, '*-')
plot(x,y, '*-r')
grid
plot(x,y, x,z)
plot(x,y, x,z, 'r--x')
xlabel( 'Independent Variable X')       % x-axis label
ylabel( 'Dependent Variables Y and Z')  % y-axis label
title(`Sine nad Cosine Curves')         % title the plot
title('Sine nad Cosine Curves')         % title the plot
grid
text(2.5, 0.7, 'sin(x)')
text(1.8, 0.4, 'cos(x)')
gtext('cos(x)')
axis off
axis on
x=(0:0.05:1)*2*pi;
x=(0:0.02:1)*2*pi;
plot(x,sin(x), x,cos(x), 'r--x')
x = linspace(0, 2*pi, 30);
y = sin(x); z=cos(x);
plot(x,y)
plot(x,z)
hold on
plot(x,y)
grid
plot(x, tan(x))
plot(x, tan(x), '*-')
hold off
plot(x,y)
figure(2)
plot(x,z, 'LineWidth', 3)
plot(y,z)
plot(y,z, '*-')
axis equal; grid
doc axis
ezplot('sin(x)/(1+x^2)')
fplot('sin(x)/(1+x^2)')
doc ezplot
fplot(@sin)
edit num_dif
f401(2)
f401([1 2 4])
num_dif
grid
h
h=10^-10
format long
f401(1+h), f401(1)
f401(1+h/10), f401(1)
f401(1+h/10000), f401(1)
f401(1+h/1000000), f401(1)
f401(1+h*1000), f401(1)
@(x) x.^2
ans(3)
f1 = @(x) x.^2
f1(1:4)
fplot(@f1)
f1
fplot(f1)
fplot(f1, [-2 3])
hold on
fplot(@sin, [-2 3])
hold off
fplot(@sin, [0 3*pi])
fplot(@(x) x^2, [-3 4])
x=1:3
x=1:4
x^2
x*x
x, x.*x
x, x.^x
x, x.^2
fplot(@(x) x.^2, [-3 4])
fplot( @(x) sin(x)./(1+x.^2)), grid
doc fplot
fimplicit(@(x,y) x.^2+y.^2-4)
axis equal, grid
axis([-2.2 2.4 -2.1 1.8])
ezpolar('sin(t)/t', [-6*pi,6*pi])
fplot(@(t) (sin(t)./t).*cos(t), @(t) (sin(t)./t).*sin(t), ...
[-6*pi,6*pi], 'LineWidth', 2), grid
axis equal, grid
fplot([@sin @cos])
fplot([@sin' @cos'])
fplot([@(x) sin(x) @(x) cos(x)])
fplot([@(x) sin(x)' @(x) cos(x)'])
fplot([@(x) [sin(x) cos(x)])
fplot(@(x) [sin(x) cos(x)])
fplot(@cos. [0 38pi])
fplot(@cos, [0 3*pi])
[x y] = fplot(@cos, [0 3*pi]);
clear
[x y] = fplot(@cos, [0 3*pi]);
plot(x,y, '*-')
figure(2)
plot(x)
plot(x, '*')
x = (0:1/2000:1)';
plot(x, cos(tan(pi*x))
plot(x, cos(tan(pi*x)))
plot(x, tan(pi*x))
plot(x*pi, tan(pi*x))
plot(x*pi, tan(pi*x), '*')
fplot(@tan, [0 pi])
view([0 pi 0 10])
axis([0 pi 0 10])
axis([0 pi -100 10])
axis([0 pi -10 10])
grid
fplot(@tan, [0 pi], '*')
axis([0 pi -10 10]), grid
fplot(@tan, [0 pi], '*-')
axis([0 pi -10 10]), grid
plot(x,cos(tan(pi*x)))
fplot( @(x) cos(tan(pi.*x)) )
fplot( @(x) cos(tan(pi.*x)), [0 1] )
peaks
colorbar off
colorbar
colormap jet
doc colormap
colormap hsv
doc fsurf
fsurf(@(x,y) sin(x).*cos(y))
fsurf(@(x,y) sin(x).*sin(y), [0 3*pi])
fsurf(@(x,y) sin(x).*abs(sin(y)), [0 3*pi])
fplot(exp(-x.^2)
fplot(exp(-x.^2))
fplot(exp(-x.^2), [-3 3])
fplot(@(x) exp(-x.^2), [-3 3])
fsurf(@(x,y) exp(-(x.^2+y.^2)), [-3 3])
fsurf(@(x,y) exp(-(x.^2+y.^2)), [-2 2])
%-- 3/24/2025 5:06 PM --%
peaks
p = peaks;
pcolor(p)
p(35:40,25:30)
p(35:40,25:30) = 0.1;
surf(p)
p(35:40,25:30) = NaN;
surf(p)
p(4,4) = NaN
surf(p)
doc quiver
imag(Z) == 0
~imag(Z) == 0
peaks
colorbar
colomaphot(8))
colomap(hot(8))
colormap(hot(8))
hot(8)
edit hot
edit mapa1
mapa1(3)
edit mapa1
mapa1(3)
doc linspace
mapa1(3)
mapa1(5)
colormap(mapa1(8))
colormap(mapa1(20))
colormap(mapa1(32))
rgbplot(mapa1(32))
colormap(mapa1(32))
mapa1(5)
colormap(mapa1(32))
peaks
colormap(mapa1(32))
colorbar
mapa1(5)
plot(mapa1(32))
doc rgbplot
edit rgbplot
rgbplot(mapa1(32))
rgbplot(mapa1(32), '*')
rgbplot(mapa1(64)), '*')
rgbplot(mapa1(64))
peaks
colormap(mapa1(32))
colorbar
colormap(gray)
figure(2)
rgbplot(gray)
new_gray = brighten(gray,0.5);
rgbplot(newgray)
rgbplot(new_gray)
colormap(new_gray)
edit brighten
[1:17;1:17]'
pcolor([1:17;1:17]')
colormap(hsv(8))
colorbar
caxis([-3 23])
caxis auto
caxis([5 12])
hadamard_demo
edit hadamard_demo
hadamard(4)
hadamard(8)
hadamard(6)
hadamard(4)
which count.dat
type count.dat
pwd
save
clear
cd ..
load
load('matlab.mat')
clear
load
doc save
clear
load count.dat
plot(count)
plot(count, '*-')
max(count)
[mx, idx] = max(count)
[mx, idx] = max(max(count))
M = reshape(1:9. 3,3)
M = reshape(1:9, 3,3)
M(:)'
[mx, idx] = max(M(:)))
[mx, idx] = max(M(:))
[mx, idx] = max(count(:))
size(count)
doc std
%-- 3/28/2025 1:09 PM --%
x = (0:1:30:1**2*pi;
x = (0:1:30:1)*2*pi;
x = (0:1/30:1)*2*pi;
y = sin(x); z=cos(x);
plot(x,y)
plot(x,y, x,z), grid
plot(x,y, x,z, '*--m' ), grid
axis off
axis on
axis tight
axis([0 3/2*pi -1.2 0.8])
fplot('sin')
fplot(f1)
fplot(f01)
fplot(@f01)
fplot(@f01, [-3 3])
fplot(@sin, [-3 3])
fplot(@sin, [-3 3]), grid
[x y] = fplot(@sin, [-3 3]), grid
[x y] = fplot(@sin, [-3 3])
plot(x,y, '*')
h1 = fplot(@sin, [-3 3])
h1.Color = [1 0 1]
h1.LineWidtH = 3
h1.LineWidth = 3
h1.Marker = '*'
doc marker
h1.Function = @cos
h1
fimplicit(@(x,y) x.^2 + y.^2 -4)
axis equal
grid
fimplicit(@(x,y) x.^2 + y.^2 -3)
hold('on')
fimplicit(@(x,y) x.^2 + y.^2 -4)
axis equal
grid
figure(3)
hold off
fplot(@(t) 2*cos(t), @(t) 2*sin(t)), grid
axis equal
fplot(@(t) 2*cos(t), @(t) 2*sin(t), [0 3/2*pi])
fplot(@(t) 2*cos(t), @(t) 2*sin(t), [0.2 3/2*pi])
axis equal
fplot([@(t) 2*cos(t), @(t) 2*sin(t)], [0.2 3/2*pi])
fplot([@(t) cos(t'), @(t) sin(t')], [0.2 3/2*pi])
fplot({@(t) cos(t), @(t) sin(t)}, [0.2 3/2*pi])
fplot({@(t) cos(t), @(t) sin(t), @tan}}, [0.2 2*pi])
fplot({@(t) cos(t), @(t) sin(t), @tan}, [0.2 2*pi])
ylim([-3 3])
@(x) x^2
ans(4)
format compact
f2 = @(x) x^2
f2(3)
f2([3 4 5])
x=[3 4 5]
x^2
x*x
x.*x
x.2
x.^2
f2 = @(x) x.^2
f2([3 4 5])
fplot(f2)
rand(5)
A = rand(5)
fplot(@(x) exp(-x^2))
fplot(@(x) exp(-x^2), -3 3])
fplot(@(x) exp(-x.^2), [-3 3])
fsurf(@(x,y) exp(-x.^2-y^.2), [-3 3])
fsurf(@(x,y) exp(-x.^2-y^.2), [-3 3 -3 3])
fsurf(@(x,y) exp(-x.^2-y^.2))
fsurf(@(x,y) exp(-x.^2-y.^2))
fsurf(@(x,y) exp(-x.^2-y.^2), [-3 3])
fsurf(@(x,y) x.*exp(-x.^2-y.^2), [-3 3])
colorbar off
colorbar
colormap(hsv)
colormap(hsv(10))
hsv(10)
doc hsv
fmesh(@(x,y) x.*exp(-x.^2-y.^2), [-3 3])
fsurf(@(x,y) x.*exp(-x.^2-y.^2), [-3 3])
shading flat
shading faceted
shading interp
peaks
peaks(20)
edit peaks
x=-2:1:2
meshgrid(x)
meshgrid(x,x)
[X,Y] = meshgrid(x,x)
exp(-X.2-Y.^2)
exp(-X.^2-Y.^2)
Z = exp(-X.^2-Y.^2)
surf(Z)
surf(X,Y,Z)
[X,Y] = meshgrid(-2:0.1:2);
Z = exp(-X.^2-Y.^2)
surf(X,Y,Z)
plot3X,Y,Z)
plot3(X,Y,Z)
x = 0:0.1:4*pi;
plot(x, cos(x))
plot(x, [cos(x)' sin(x)'])
1:5
(1:5)'
plot(x, [cos(x)' sin(x)' tan(x')])
axis([0 4*pi -2 2])
t=0:pi/50:10*pi;
plot3(sin(t), cos(x), t)
plot3(sin(t), cos(t), t)
plot3(sin(t), cos(t), sqrt(t))
dcc plo3
dcc plot3
doc plot3
h1 = plot3(sin(t), cos(t), sqrt(t))
h1.LineWidth = 3
surf(X,Y,Z)
view
[az el] = view
pcolor(X,Y,Z)
colorbar
colormap(hsv(10)
colormap(jet)
pcolor(surf(150)
pcolor(surf(15))
pcolor(surf(20))
pcolor(surf(20,20))
pcolor(peaks(20)
pcolor(peaks(20))
shading flat
shading faceted
shading interp
[X, Y] = meshgrid([-2:.2:2]);
Z = X.* exp(-X.^2 - Y.^2);
surf(X, Y, Z)
colorbar
surf(X, Y, Z, gradient(Z))
colorbar
[X, Y] = meshgrid([-3:.2:3]);
Z = X.* exp(-X.^2 - Y.^2);
surf(X, Y, Z, gradient(Z))
colorbar
surf(X, Y, Z, del2(Z))
colorbar
QUIT
%-- 3/31/2025 4:11 PM --%
pwd
cd uvp
edit kostka1
kostka1(600)
k = kostka1(600)
bar(k)
bar(k), grid
k = kostka1(6000)
bar(k), grid
tic, k = kostka1(6000); toc
tic, k = kostka1(6*10^5); toc
tic, k = kostka1(6*10^6); toc
k
format compact
k
doc randi
tic, k = kostka1(6*10^3); toc
k
bar(k), grid
tic, k = kostka1(6*10^6); toc
tic, k = kostka2(6*10^3); toc
k
tic, k = kostka2(6*10^6); toc
rnd = randi(10)
rnd = randi(10,1,10)
rnd = randi(6,1,10)
rnd == 1
sum(rnd == 1)
tic, k = kostka3(6*10^3); toc
k
tic, k = kostka3(6*10^6); toc
bar(k), grid
ylim([10^5 5*10^6])
ylim([10^5 1.2*10^6])
k
ylim([min(k)-100 max(k)+100])
clc
clear
x = (0:0.1:1)*2*pi;
y = sin(x);
plot(x,y, '*--'
plot(x,y, '*--')
plot(x,y, '*--'), grid
xi = (0:0.02:1)*2*pi;
yi = interp1(x,y, xi);
plot(x,y, '*--', xi,yi,'o'), fplot(@sin, [0 2*pi]);grid
plot(x,y, '*--', xi,yi,'o'), hold on, fplot(@sin, [0 2*pi]);grid
yi = interp1(x,y, xi, 'cubic');
plot(x,y, '*--', xi,yi,'o'), hold on, fplot(@sin, [0 2*pi]);grid
plot(x,y, '*--', xi,yi,'o'), hold on, fplot(@sin, [0 2*pi]);grid, hold off
plot(x,y, '*--', xi,yi,'o'), hold on, fplot(@sin, [0 2*pi]);grid
doc interp1
[x, y] = meshgrid(-3:1:3);
z = peaks(x,y);
surf(x,y,z)
hold off
surf(x,y,z)
[xi, yi] = meshgrid(-3:0.25:3);
zi1 = interp2(x,y,z,xi,yi, 'nearest');
surf(xi,yi,zi)
surf(xi,yi,zi1)
zi2 = interp2(x,y,z,xi,yi, 'bilinear');
surf(xi,yi,zi2)
zi3 = interp2(x,y,z,xi,yi, 'bicubic');
surf(xi,yi,zi3)
peaks
humps
plot(humps)
doc humps
edit humps
h1 = fplot(@humps, [-2 3]), grid, h1.LineWidth=2
fzero(@humps, -0.2)
humps(ans)
fzero(@humps, -2)
fzero(@humps, 9)
fzero(@humps, 2)
fzero(@humps, 0.5)
fzero(@sin, 1)
fzero(@sin, 2)
plot(@sin, [0 4*pi])
fplot(@sin, [0 4*pi])
grid
fzero(@sin, 5)
fzero(@sin, 5) - 2*pi
fzero(@sin, 4.5) - 2*pi
fzero(@sin, 4.5)
h1 = fplot(@humps, [-2 3]), grid, h1.LineWidth=2
x = fminbnd(@humps, 0.3, 1)
x = fminbnd(@humps, 1, 3)
doc fminbnd
fminbnd(@(x) -humps(x), -1, 2)
x = fminbnd(@(x) -humps(x), -1, 2)
humps(x)
x = fminbnd(@(x) -humps(x), 0.5, 1.5)
humps(x)
integral(@sin, 0,2*pi)
integral(@(x) sin(x)^2, 0,2*pi)
integral(@(x) sin(x).^2, 0, 2*pi)
doc inegral
doc integral
x=(0:0.05:1)*2*pi
x=(0:0.05:1)*2*pi;
plot(x,sin(x), '*-')
y = sin(x)
doc quad
trapz(x,y)
int(@sin, [0 2*pi])
int(@sin, 0,2*pi)
doc int
which int
syms x
sin(pi)
sin(sym(pi))
syms x
clear
syms x
int(sin(x),0,pi)
int(sin(x),0,2*pi)
%-- 4/2/2025 4:22 PM --%
edit cube1
rand(600)
cube1(600)
su,(ans)
c1 = cube1(600)
sum(c1)
bar(c1)
tic. c1 = cube1(6*10^6), toc
format compact
ba
tic, c1 = cube1(6*10^6), toc
clear
tic, c1 = cube1(6*10^6), toc
bar(c1), grid
ylim([min(c1)-10, max(c1)+10)])
ylim([min(c1)-10, max(c1)+10])
ylim([min(c1)-50, max(c1)+50])
tic, c1 = cube2(6*10^6), toc
tic, c2 = cube2(6*10^6), toc
sum(c2)
r1 = randi(10)
r1 = randi(6,1,10)
r1=1
r1 = randi(6,1,10)
r1==1
sum(r1==1)
sum(r1==2)
tic, c3 = cube3(6*10^6), toc
sum(c3)
bar(c3), grid
ylim([min(c3)-50, max(c3)+50])
min(c3), max(c3
min(c3), max(c3)
min(c3)/max(c3)
x=(0:0.1:1)*2*pi
y = sin(x);
plot(x,y, '*-')
h1 = plot(x,y, '*-')
h1.LineWidth = 2
hold on, fplot(@sin, [0 2*pi])
grid, axis([0 2*pi -1.1 1.1] )
x1 =(0:0.025:1)*2*pi;
y1 = interp1(x,y, x1);
hold off
plot(x,y, '*-', x1,y1, 'o')
y1 = interp1(x,y, x1, 'cubic');
plot(x,y, '*-', x1,y1, 'o')
hold on, fplot(@sin, [0 2*pi])
doc interp1
y1 = interp1(x,y, x1, 'spline');
hold off
plot(x,y, '*-', x1,y1, 'o')
hold on, fplot(@sin, [0 2*pi])
peaks
[x, y] = meshgrid(-3:1:3)
z = peaks(x.y);
z = peaks(x,y);
surf(x,y,z)
[xi, yi] = meshgrid(-3:0.25:3);
zi1 = interp2(x,y,z,xi,yi, 'nearest');
surf(xi,yi,zi1)
zi2 = interp2(x,y,z,xi,yi, 'bilinear');
surf(xi,yi,zi2)
zi3 = interp2(x,y,z,xi,yi, 'bicubic');
surf(xi,yi,zi3)
doc interp2
zi3 = interp2(x,y,z,xi,yi, 'spline');
surf(xi,yi,zi3)
figure(2)
surf(x,y,z)
x=(0:0.1:1)*2*pi
y=sin(x);
h1 = plot(x,y, '*-')
grid
which spline
p1 = [2 2]
y1 = polyval(p1, x);
plot(x,y1, '*-')
y1 = polyval([1 0 2], x);
plot(x,y1, '*-')
edit polyval
p = [1 0 -2 -5];
polyder(p)
g = [1 1 1 1 1]
polyder(g)
roots(p)
r =
r = roots(p)
polyval(r)
polyval(p. r)
polyval(p, r)
poly(r)
which data1
which data1.asc
x = [0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1];
y = [-.447 1.978 3.28 6.16 7.08 7.34 7.66 9.56 9.48 9.30 11.2];
plot(x,y, '*-')
p2 = polyfit(x,y,2)
xi = linspace(0,1,100);
yi = polyval(p,xi);
plot(x,y,'o',x,y,xi,yi,'--');
yi = polyval(p2,xi);
plot(x,y,'o',x,y,xi,yi,'--');
plot(x,y,'o-', xi,yi,'--');
size(x)
p10 = polyfit(x,y,10)
yi = polyval(p10,xi);
plot(x,y,'o-', xi,yi,'--');
xi = linspace(-0.1,1.1,100);
yi = polyval(p10,xi);
plot(x,y,'o-', xi,yi,'--');
ver
%-- 4/4/2025 12:14 PM --%
rand(3)
rand(1,5)
format compact
doc rand
rand(6,1,10)
randi(6,1,10)
edit kostka1
zeros(2,3)
zeros(1,6)
kostka1(5)
k1 = kostka1(600)
sum(k1)
doc bar
bar(k1)
[imin, mn] = min(k1)
max(k1)
tic, k1 = kostka1(6*10^6), toc
tic, k1 = kostka1(6*10^6); toc
bar(k1), grid
fplot(@sin, [0 2*pi])
axis([-0.2 2*pi-1 -1.1 0.8]
axis([-0.2 2*pi-1 -1.1 0.8])
bar(k1), grid
ylim([min(k1) max(k1)])
ylim([min(k1)-50 max(k1)+50])
k2 = kostka2(600)
sum(k2)
tic, k2 = kostka1(6*10^6); toc
tic, k2 = kostka2(6*10^6); toc
tic, k2 = kostka1(6*10^6); toc
randi(6,1,16)
r = randi(6,1,16)
r = randi(6,1,8)
r == 1
sum(ans)
r
r == 3
sum(ans)
kostka3(600)
sum(ans)
k3 = kostka3(600)
bar(k3), grid
tic, k3 = kostka3(6*10^6); toc
bar(k3), grid
ylim([min(k3)-50 max(k3)+50])
pwd
save
whos
clear
whos
load
whos
save k1, k2, r
clear
load k1
doc save
save(d1, k1,k3,r)
save("d1", k1,k3,r)
save('d1', k1,k3,r)
save('d1', 'k1','k3','r')
clear
load d1
which count.dat
path
which count.dat
edit count.dat
clear
load count.dat
whos
size(count)
[n, p] = size(count)
plot(count)
grid
legend
count(2,:)
plot(count(:,1))
plot(count(:,1), '*--')
plot(count(1:2,1))
plot(count(:,1:2))
plot(count(:,:))
grid
max(count)
men(count)
mean(count)
max(count)
max(max(count))
[idx mx] = max(count)
[mx idx] = max(count)
randi(3)
randi(10,3)
r = randi(10,3)
max(r)
r(:)
max(r(:))
[mx idx] = max(r(:))
x = (0:0.1:1)*2*Pi
x = (0:0.1:1)*2*pi
y = sin(y);
y = sin(x);
plot(x,y, '*--'), grid, hold on, fplot(@sin, [0 2*pi])
doc interp1
interp1(x,y, 4.75)
interp1(x,y, [4.75, 4.25])
xi = (0:0.02:1)*2*pi;
yi = interp1(x,y, xi);
plot(xi,yi, 'o')
plot(xi,yi, 'ok')
yic = interp1(x,y, xi, 'cubic');
plot(xi,yic, 'mx')
yis = interp1(x,y, xi, 'spline');
plot(xi,yic, '^c')
%-- 4/7/2025 4:07 PM --%
x = 1:3
y = sin(x)
save
clear
load
doc load
clear
a = -5:0.25:6;
b = a.^2.5;
save('pokus.data')
whos
a1 = a;
b1=b1
whos
b1=b
whos
clear a b
load "pokus.data"
load 'pokus.data'
load('pokus.data')
load pokus.data
load(pokus.data)
save('pokus.data','a','b','-ascii','-double')
save('pokus.data','a1','b1','-ascii','-double')
save('pokus.data','a1','b1','-ascii','-single')
load(pokus.data)
load('pokus.data')
cd ..
clear
imread('slon.pgm')
I = imread('slon.pgm');
imshow(I)
imshow(flipud(I))
imshow(fliplr(I))
imshow(rot90(I))
imshow(rot90(I,2))
imshow(I(end:-1:1,:))
imshow(I(1:2:end,:))
imshow(I(1:2:end,1:2:end))
I = imread('slon.jpg');
imshow(I(:,:,1))
imshow(I(:,:,2))
imshow(I(:,:,3))
imshow(I(:,:,:))
imshow(I)
I2 = I(1:2:end,1:2:end,:);
imshow(I2)
I3(:,:,3) = I(:,:,,3)./2;
I3 = I;
I3(:,:,3) = I(:,:,,3)./2;
I3(:,:,3) = I(:,:,3)./2;
imshow(I3)
I3(:,:,3) = 0
imshow(I3)
I3(:,:,3) = 200;
imshow(I3)
I3(:,:,3) = 100;
imshow(I3)
I3(:,:,3) = 250;
imshow(I3)
doc imshow
which mri.mat
ver
which imagesc
doc imagesc
I = imread('slon.pgm');
imshow(I)
Is - size(I)
Is = size(I)
I2 = zeros(2*Is);
size(I2)
A = resize(1:9,3,3)
doc resize
A = reshape(1:9,3,3)
A2 = zeros(6,6)
A2(1:2:end,1:2:end) = A
I2(1:2:end,1:2:end) = I;
imshow(I2)
shading flat
I2(2:2:end,1:2:end) = I;
I2(:,2:2:end) = I2(I,1:2:end);
I2(:,2:2:end) = I2(:,1:2:end);
imshow(I2)
I3 = cast(I2,'uint8');
imshow(I2)
imshow(I3)
doc imagesc
doc imresizer
I4 = imresize(I,2);
figure(2), imshow(I4)
a = [1 0 -2 -5]
format compact
polyval(a, 1)
fplot(@(x) polyval(a,x), [-3 3])
a2 = [1 0 0];
fplot(@(x) polyval(a2,x), [-3 3])
xi = linspace(-2,2,50);
y = polyval(s2,xi);
y = polyval(a2,xi);
plot(xi,y, '*-')
a
polyder(a)
roots(a)
r = roots(a)
p2 = poly(r)
p-p2
a-p2
doc polyval
edit polyval
QUIT
%-- 4/10/2025 2:46 PM --%