HELP topics:
matlab/general - General purpose
commands.
matlab/ops
- Operators and special characters.
matlab/lang -
Programming language constructs.
matlab/elmat -
Elementary matrices and matrix manipulation.
matlab/elfun -
Elementary math functions.
matlab/specfun - Specialized
math functions.
matlab/matfun - Matrix
functions - numerical linear algebra.
matlab/datafun - Data analysis
and Fourier transforms.
matlab/polyfun - Interpolation
and polynomials.
matlab/funfun - Function
functions and ODE solvers.
matlab/sparfun - Sparse matrices.
matlab/graph2d - Two dimensional
graphs.
matlab/graph3d - Three dimensional
graphs.
matlab/specgraph - Specialized graphs.
matlab/graphics - Handle Graphics.
matlab/uitools - Graphical
user interface tools.
matlab/strfun - Character
strings.
matlab/iofun -
File input/output.
matlab/timefun - Time and
dates.
matlab/datatypes - Data types and structures.
matlab/demos -
Examples and demonstrations.
simulink/simulink - Simulink
simulink/blocks - Simulink block
library.
simulink/simdemos - Simulink 3 demonstrations
and samples.
simulink/dee -
Differential Equation Editor
toolbox/control - Control System
Toolbox.
control/ctrlguis - Control System Toolbox
-- GUI support functions.
control/obsolete - Control System Toolbox
-- obsolete commands.
fuzzy/fuzzy -
Fuzzy Logic Toolbox.
fuzzy/fuzdemos - Fuzzy Logic
Toolbox Demos.
toolbox/ident - System
Identification Toolbox.
images/images - Image
Processing Toolbox.
images/imdemos - Image Processing
Toolbox --- demos and sample images
lmi/lmictrl -
LMI Control Toolbox: Control Applications
lmi/lmilab
- LMI Control Toolbox
toolbox/local - Preferences.
nnet/nnet
- Neural Network Toolbox.
nnet/nndemos -
Neural Network Demonstrations.
nnet/nnutils -
(No table of contents file)
nnet/nnobsolete - (No table of
contents file)
toolbox/optim - Optimization
Toolbox.
toolbox/pde -
Partial Differential Equation Toolbox.
toolbox/robust - Robust Control
Toolbox.
toolbox/sb2sl - SystemBuild
to Simulink Translator
signal/signal - Signal
Processing Toolbox.
signal/siggui - Signal
Processing Toolbox GUI
signal/sigdemos - Signal Processing
Toolbox Demonstrations
stateflow/stateflow - Stateflow
stateflow/sfdemos - Stateflow demonstrations
and samples.
toolbox/symbolic - Symbolic Math Toolbox.
toolbox/tour -
MATLAB Tour
wavelet/wavelet - Wavelet Toolbox.
wavelet/wavedemo - Wavelet Toolbox Demos.
For more help on directory/topic, type "help topic".
>> more on
>> help
HELP topics:
matlab/general - General purpose
commands.
matlab/ops
- Operators and special characters.
matlab/lang -
Programming language constructs.
matlab/elmat -
Elementary matrices and matrix manipulation.
matlab/elfun -
Elementary math functions.
matlab/specfun - Specialized
math functions.
matlab/matfun - Matrix
functions - numerical linear algebra.
matlab/datafun - Data analysis
and Fourier transforms.
matlab/polyfun - Interpolation
and polynomials.
matlab/funfun - Function
functions and ODE solvers.
matlab/sparfun - Sparse matrices.
matlab/graph2d - Two dimensional
graphs.
matlab/graph3d - Three dimensional
graphs.
matlab/specgraph - Specialized graphs.
matlab/graphics - Handle Graphics.
matlab/uitools - Graphical
user interface tools.
matlab/strfun - Character
strings.
matlab/iofun -
File input/output.
matlab/timefun - Time and
dates.
matlab/datatypes - Data types and structures.
matlab/demos -
Examples and demonstrations.
simulink/simulink - Simulink
simulink/blocks - Simulink block
library.
simulink/simdemos - Simulink 3 demonstrations
and samples.
simulink/dee -
Differential Equation Editor
toolbox/control - Control System
Toolbox.
control/ctrlguis - Control System Toolbox
-- GUI support functions.
control/obsolete - Control System Toolbox
-- obsolete commands.
fuzzy/fuzzy -
Fuzzy Logic Toolbox.
fuzzy/fuzdemos - Fuzzy Logic
Toolbox Demos.
toolbox/ident - System
Identification Toolbox.
images/images - Image
Processing Toolbox.
images/imdemos - Image Processing
Toolbox --- demos and sample images
lmi/lmictrl -
LMI Control Toolbox: Control Applications
lmi/lmilab
- LMI Control Toolbox
toolbox/local - Preferences.
nnet/nnet
- Neural Network Toolbox.
nnet/nndemos -
Neural Network Demonstrations.
nnet/nnutils -
(No table of contents file)
nnet/nnobsolete - (No table of
contents file)
toolbox/optim - Optimization
Toolbox.
toolbox/pde -
Partial Differential Equation Toolbox.
toolbox/robust - Robust Control
Toolbox.
toolbox/sb2sl - SystemBuild
to Simulink Translator
signal/signal - Signal
Processing Toolbox.
signal/siggui - Signal
Processing Toolbox GUI
signal/sigdemos - Signal Processing
Toolbox Demonstrations
stateflow/stateflow - Stateflow
stateflow/sfdemos - Stateflow demonstrations
and samples.
toolbox/symbolic - Symbolic Math Toolbox.
toolbox/tour -
MATLAB Tour
wavelet/wavelet - Wavelet Toolbox.
wavelet/wavedemo - Wavelet Toolbox Demos.
For more help on directory/topic, type "help topic".
>> diary off
>> help
HELP topics:
matlab/general - General purpose
commands.
matlab/ops
- Operators and special characters.
matlab/lang -
Programming language constructs.
matlab/elmat -
Elementary matrices and matrix manipulation.
matlab/elfun -
Elementary math functions.
matlab/specfun - Specialized
math functions.
matlab/matfun - Matrix
functions - numerical linear algebra.
matlab/datafun - Data analysis
and Fourier transforms.
matlab/polyfun - Interpolation
and polynomials.
matlab/funfun - Function
functions and ODE solvers.
matlab/sparfun - Sparse matrices.
matlab/graph2d - Two dimensional
graphs.
matlab/graph3d - Three dimensional
graphs.
matlab/specgraph - Specialized graphs.
matlab/graphics - Handle Graphics.
matlab/uitools - Graphical
user interface tools.
matlab/strfun - Character
strings.
matlab/iofun -
File input/output.
matlab/timefun - Time and
dates.
matlab/datatypes - Data types and structures.
matlab/demos -
Examples and demonstrations.
simulink/simulink - Simulink
simulink/blocks - Simulink block
library.
simulink/simdemos - Simulink 3 demonstrations
and samples.
simulink/dee -
Differential Equation Editor
toolbox/control - Control System
Toolbox.
control/ctrlguis - Control System Toolbox
-- GUI support functions.
control/obsolete - Control System Toolbox
-- obsolete commands.
fuzzy/fuzzy -
Fuzzy Logic Toolbox.
fuzzy/fuzdemos - Fuzzy Logic
Toolbox Demos.
toolbox/ident - System
Identification Toolbox.
images/images - Image
Processing Toolbox.
images/imdemos - Image Processing
Toolbox --- demos and sample images
lmi/lmictrl -
LMI Control Toolbox: Control Applications
lmi/lmilab
- LMI Control Toolbox
toolbox/local - Preferences.
nnet/nnet
- Neural Network Toolbox.
nnet/nndemos -
Neural Network Demonstrations.
nnet/nnutils -
(No table of contents file)
nnet/nnobsolete - (No table of
contents file)
toolbox/optim - Optimization
Toolbox.
toolbox/pde -
Partial Differential Equation Toolbox.
toolbox/robust - Robust Control
Toolbox.
toolbox/sb2sl - SystemBuild
to Simulink Translator
signal/signal - Signal
Processing Toolbox.
signal/siggui - Signal
Processing Toolbox GUI
signal/sigdemos - Signal Processing
Toolbox Demonstrations
stateflow/stateflow - Stateflow
stateflow/sfdemos - Stateflow demonstrations
and samples.
toolbox/symbolic - Symbolic Math Toolbox.
toolbox/tour -
MATLAB Tour
wavelet/wavelet - Wavelet Toolbox.
wavelet/wavedemo - Wavelet Toolbox Demos.
For more help on directory/topic, type "help topic".
>> more on
>> help
HELP topics:
matlab/general - General purpose
commands.
matlab/ops
- Operators and special characters.
matlab/lang -
Programming language constructs.
matlab/elmat -
Elementary matrices and matrix manipulation.
matlab/elfun -
Elementary math functions.
matlab/specfun - Specialized
math functions.
matlab/matfun - Matrix
functions - numerical linear algebra.
matlab/datafun - Data analysis
and Fourier transforms.
matlab/polyfun - Interpolation
and polynomials.
matlab/funfun - Function
functions and ODE solvers.
matlab/sparfun - Sparse matrices.
matlab/graph2d - Two dimensional
graphs.
matlab/graph3d - Three dimensional
graphs.
matlab/specgraph - Specialized graphs.
matlab/graphics - Handle Graphics.
matlab/uitools - Graphical
user interface tools.
matlab/strfun - Character
strings.
matlab/iofun -
File input/output.
matlab/timefun - Time and
dates.
>> help elmat
Elementary matrices and matrix manipulation.
Elementary matrices.
zeros - Zeros
array.
ones -
Ones array.
eye
- Identity matrix.
repmat - Replicate
and tile array.
rand -
Uniformly distributed random numbers.
randn - Normally
distributed random numbers.
linspace - Linearly spaced vector.
logspace - Logarithmically spaced
vector.
meshgrid - X and Y arrays for
3-D plots.
:
- Regularly spaced vector and index into matrix.
Basic array information.
size -
Size of matrix.
length - Length of
vector.
ndims - Number
of dimensions.
disp -
Display matrix or text.
isempty - True for empty
matrix.
isequal - True if arrays
are identical.
isnumeric - True for numeric arrays.
islogical - True for logical array.
logical - Convert numeric values to logical.
Matrix manipulation.
reshape - Change size.
diag - Diagonal matrices and
diagonals of matrix.
blkdiag - Block diagonal concatenation.
tril - Extract lower triangular
part.
triu - Extract upper triangular
part.
fliplr - Flip matrix in left/right direction.
flipud - Flip matrix in up/down direction.
flipdim - Flip matrix along specified dimension.
rot90 - Rotate matrix 90 degrees.
: - Regularly
spaced vector and index into matrix.
find - Find indices of nonzero
elements.
end - Last index.
sub2ind - Linear index from multiple subscripts.
ind2sub - Multiple subscripts from linear index.
Special variables and constants.
ans - Most recent answer.
eps - Floating point
relative accuracy.
realmax - Largest positive floating point number.
realmin - Smallest positive floating point
number.
pi - 3.1415926535897....
i, j - Imaginary unit.
inf - Infinity.
NaN - Not-a-Number.
isnan - True for Not-a-Number.
isinf - True for infinite elements.
isfinite - True for finite elements.
flops - Floating point operation
count.
why - Succinct answer.
Specialized matrices.
compan - Companion matrix.
gallery - Higham test matrices.
hadamard - Hadamard matrix.
hankel - Hankel matrix.
hilb - Hilbert matrix.
invhilb - Inverse Hilbert matrix.
magic - Magic square.
pascal - Pascal matrix.
rosser - Classic symmetric eigenvalue
test
toeplitz - Toeplitz matrix.
vander - Vandermonde matrix.
wilkinson - Wilkinson's eigenvalue test matrix.
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>> help ones
ONES Ones array.
ONES(N) is an N-by-N matrix of ones.
ONES(M,N) or ONES([M,N]) is an M-by-N matrix of
ones.
ONES(M,N,P,...) or ONES([M N P ...]) is an M-by-N-by-P-by-...
array of ones.
ONES(SIZE(A)) is the same size as A and all ones.
See also ZEROS.
>> a = 1
a =
1
>> a = 1;
>> who
Your variables are:
a
>> B = [ 1 2 3 ; 4 5 6]
B =
1 2
3
4 5
6
>> B2 = [ 1,2,3
4 5 6]
B2 =
1 2
3
4 5
6
>> c = [1,2,3,4,5]
c =
1 2 3 4 5
>> d = 0:0.5:100;
>> B
B =
1 2
3
4 5
6
>> B2
B2 =
1 2
3
4 5
6
>> E = B*B2
Error using ==> *
Inner matrix dimensions must agree.
>> B3 = B2'
B3 =
1 4
2 5
3 6
>> E = B*B3
E =
14 32
32 77
>> F = B.*B2
F =
1 4
9
16 25 36
>> help arith
Arithmetic operators.
+ Plus.
X + Y adds matrices X and Y. X
and Y must have the same
dimensions unless one is a scalar (a
1-by-1 matrix).
A scalar can be added to anything.
- Minus.
X - Y subtracts matrix X from Y.
X and Y must have the same
dimensions unless one is a scalar.
A scalar can be subtracted
from anything.
* Matrix multiplication.
X*Y is the matrix product of X and Y.
Any scalar (a 1-by-1 matrix)
may multiply anything. Otherwise,
the number of columns of X must
equal the number of rows of Y.
.* Array multiplication
X.*Y denotes element-by-element multiplication.
X and Y
must have the same dimensions unless
one is a scalar.
A scalar can be multiplied into anything.
^ Matrix power.
Z = X^y is X to the y power if y is a scalar and
X is square. If y is an
integer greater than one, the power is computed by repeated
multiplication. For other values of y the calculation
involves eigenvalues and eigenvectors.
Z = x^Y is x to the Y power, if Y is a square matrix and x is a scalar,
computed using eigenvalues and eigenvectors.
Z = X^Y, where both X and Y are matrices, is an error.
.^ Array power.
Z = X.^Y denotes element-by-element powers.
X and Y
must have the same dimensions unless one is a scalar.
A scalar can operate into anything.
>>
>>
>> help arith
Arithmetic operators.
+ Plus.
X + Y adds matrices X and Y. X
and Y must have the same
dimensions unless one is a scalar (a
1-by-1 matrix).
A scalar can be added to anything.
- Minus.
X - Y subtracts matrix X from Y.
X and Y must have the same
dimensions unless one is a scalar.
A scalar can be subtracted
from anything.
* Matrix multiplication.
X*Y is the matrix product of X and Y.
Any scalar (a 1-by-1 matrix)
may multiply anything. Otherwise,
the number of columns of X must
equal the number of rows of Y.
.* Array multiplication
X.*Y denotes element-by-element multiplication.
X and Y
must have the same dimensions unless
one is a scalar.
A scalar can be multiplied into anything.
^ Matrix power.
>> help *
Operators and special characters.
Arithmetic operators.
plus - Plus
+
uplus - Unary plus
+
minus - Minus
-
uminus - Unary minus
-
mtimes - Matrix multiply
*
times - Array multiply
.*
mpower - Matrix power
^
power - Array power
.^
mldivide - Backslash or left matrix
divide \
mrdivide - Slash or right matrix divide
/
ldivide - Left array divide
.\
rdivide - Right array divide
./
kron - Kronecker
tensor product kron
Relational operators.
eq
- Equal ==
ne
- Not equal
~=
lt
- Less than
<
gt
- Greater than
>
le
- Less than or equal
<=
ge
- Greater than or equal
>=
Logical operators.
and - Logical AND
&
or - Logical
OR
|
not - Logical NOT
~
xor - Logical EXCLUSIVE
OR
any - True if any
element of vector is nonzero
all - True if all
elements of vector are nonzero
Special characters.
colon - Colon :
paren - Parentheses and subscripting
( )
paren - Brackets
[ ]
paren - Braces and subscripting
{ }
punct - Decimal point
.
punct - Structure field access
.
punct - Parent directory
..
punct - Continuation
...
punct - Separator
,
punct - Semicolon
;
punct - Comment%
punct - Invoke operating system
command !
punct - Assignment
=
punct - Quote '
transpose - Transpose
.'
ctranspose - Complex conjugate transpose
'
horzcat - Horizontal concatenation
[,]
vertcat - Vertical concatenation
[;]
subsasgn - Subscripted assignment
( ),{
subsref - Subscripted reference
( ),{
subsindex - Subscript index
Bitwise operators.
bitand - Bit-wise AND.
bitcmp - Complement bits.
bitor - Bit-wise OR.
bitmax - Maximum floating
point integer.
bitxor - Bit-wise XOR.
bitset - Set bit.
bitget - Get bit.
bitshift - Bit-wise shift.
Set operators.
union - Set union.
unique - Set unique.
intersect - Set intersection.
setdiff - Set difference.
setxor - Set exclusive-or.
ismember - True for set member.
See also ARITH, RELOP, SLASH.
>> % Hello World
>> ones(1,2)
ans =
1 1
>> zeros(3,4)
ans =
0 0
0 0
0 0
0 0
0 0
0 0
>> eye(3,3)
ans =
1 0
0
0 1
0
0 0
1
>> who
Your variables are:
B B3
F ans
d
B2 E
a c
>> size(B2)
ans =
2 3
>> B = [1,2,3
2,3,5
2,4,6]
B =
1 2
3
2 3
5
2 4
6
>> size(B)
ans =
3 3
>> rank(B)
ans =
2
>> % Polynome ax^2+bx+c
>> a = 3
a =
3
>> b = 4
b =
4
>> c = 5
c =
5
>> x = 0:.01:10;
>> y = a*x.^2+b*x+c*ones(size(x));
>> plot(x,y)
>> xlabel('x')
>> ylabel('y')
>> title('poly2')
>> Poly
>> x = 0:.1:3
x =
Columns 1 through 7
0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000
Columns 8 through 14
0.7000 0.8000 0.9000 1.0000 1.1000 1.2000 1.3000
Columns 15 through 21
1.4000 1.5000 1.6000 1.7000 1.8000 1.9000 2.0000
Columns 22 through 28
2.1000 2.2000 2.3000 2.4000 2.5000 2.6000 2.7000
Columns 29 through 31
2.8000 2.9000 3.0000
>> y = sin(x)
y =
Columns 1 through 7
0 0.0998 0.1987 0.2955 0.3894 0.4794 0.5646
Columns 8 through 14
0.6442 0.7174 0.7833 0.8415 0.8912 0.9320 0.9636
Columns 15 through 21
0.9854 0.9975 0.9996 0.9917 0.9738 0.9463 0.9093
Columns 22 through 28
0.8632 0.8085 0.7457 0.6755 0.5985 0.5155 0.4274
Columns 29 through 31
0.3350 0.2392 0.1411
>> Integ = trapz(y)
Integ =
19.8833
>> Integ = trapz(y)*0.1
Integ =
1.9883
>> z = Square(3)
y =
9
z =
9
>> t = [ 0 1 2
3 4 5]
t =
0 1
2
3 4
5
>> z = Square(t)
y =
0 1
4
9 16 25
z =
0 1
4
9 16 25
>> % c' = -c IC c0 = 1 for t = 0
>> help ode45
ODE45 Solve non-stiff differential equations, medium order
method.
[T,Y] = ODE45('F',TSPAN,Y0) with TSPAN = [T0 TFINAL]
integrates the
system of differential equations y' = F(t,y) from
time T0 to TFINAL with
initial conditions Y0. 'F' is a string containing
the name of an ODE
file. Function F(T,Y) must return a column
vector. Each row in
solution array Y corresponds to a time returned
in column vector T. To
obtain solutions at specific times T0, T1, ...,
TFINAL (all increasing
or all decreasing), use TSPAN = [T0 T1 ... TFINAL].
[T,Y] = ODE45('F',TSPAN,Y0,OPTIONS) solves as above
with default
integration parameters replaced by values in OPTIONS,
an argument
created with the ODESET function. See ODESET
for details. Commonly
used options are scalar relative error tolerance
'RelTol' (1e-3 by
default) and vector of absolute error tolerances
'AbsTol' (all
components 1e-6 by default).
[T,Y] = ODE45('F',TSPAN,Y0,OPTIONS,P1,P2,...) passes
the additional
parameters P1,P2,... to the ODE file as F(T,Y,FLAG,P1,P2,...)
(see
ODEFILE). Use OPTIONS = [] as a place holder
if no options are set.
It is possible to specify TSPAN, Y0 and OPTIONS
in the ODE file (see
ODEFILE). If TSPAN or Y0 is empty, then ODE45
calls the ODE file
>> t = [ 0 10]
t =
0 10
>> c0 = 1
c0 =
1
>> [t,y] = ode45('F',t,c0)
t =
0
0.0502
0.1005
0.1507
0.2010
0.4063
0.6117
0.8171
1.0225
1.2186
1.4147
1.6108
1.8069
2.0036
2.2002
2.3968
2.5934
2.7900
2.9866
3.1832
3.3798
3.5764
3.7730
3.9696
4.1662
4.3628
4.5594
4.7560
4.9526
5.1492
5.3457
5.5423
5.7389
5.9355
6.1321
6.3287
6.5253
6.7219
6.9185
7.1151
7.3117
7.5083
7.7049
7.9015
8.0981
8.3111
8.5242
8.7372
8.9503
9.2127
9.4751
9.7376
10.0000
y =
1.0000
0.9510
0.9044
0.8601
0.8180
0.6659
0.5421
0.4416
0.3598
0.2957
0.2430
0.1997
0.1642
0.1349
0.1108
0.0910
0.0748
0.0615
0.0505
0.0415
0.0341
0.0280
0.0230
0.0189
0.0155
0.0128
0.0105
0.0086
0.0071
0.0058
0.0048
0.0039
0.0032
0.0026
0.0022
0.0018
0.0015
0.0012
0.0010
0.0008
0.0007
0.0005
0.0005
0.0004
0.0003
0.0002
0.0002
0.0002
0.0001
0.0001
0.0001
0.0001
0.0000
>> plot(t,y)
>> exit
::::::::::::::
F.m
::::::::::::::
function cprime = F(t,c)
k = 1.0;
cprime = -k*c;
::::::::::::::
Poly.m
::::::::::::::
x = 0:.01:10;
y = sin(x);
plot(x,y)
xlabel('x')
ylabel('y')
title('sin')
::::::::::::::
Poly2.m
::::::::::::::
echo on;
% Polynomial ax^2+bx+c
a = 1;
b = 2;
c = 3;
x = 0:.01:1;
y = a*x.^2+b*x+c*ones(size(x));
plot(x,y,'.');
echo off;
::::::::::::::
Square.m
::::::::::::::
function y = Square(x)
y=x.^2
::::::::::::::
Statistic.m
::::::::::::::
function [m,s,v,sze] = Statistic(x);
m = mean(x)
s = std(x)
v = sqrt(s)
sze = size(x)