Matlab: Difference between revisions
From charlesreid1
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\left[ | \left[ | ||
A + \left( \frac{i}{ | A + \left( \frac{i}{N-1} \right) B | ||
\right] \qquad i=0, \dots, N-1 | \right] \qquad i=0, \dots, N-1 | ||
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\left[ | \left[ | ||
10^{A} + 10^{ \left( \frac{i}{ | 10^{A} + 10^{ \left( \frac{i}{N-1} \right) B } | ||
\right] \qquad i=0, \dots, N-1 | \right] \qquad i=0, \dots, N-1 | ||
</math> | </math> | ||
Revision as of 01:33, 27 November 2010
Matrices
Basics
Special matrices/vectors
| Name (matrix type) | Matlab syntax | Result |
|---|---|---|
| Ones | >> ones(3,2);
|
$ \left[ \begin{array}{cc} 1 & 1 \\ 1 & 1 \\ 1 & 1 \end{array} \right] $ |
| Zeros | >> zeros(3,1);
|
$ \left[ \begin{array}{cc} 0 \\ 0 \\ 0 \end{array} \right] $ |
| Eye (identity) | >> eye(3);
|
$ \left[ \begin{array}{ccc} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right] $ |
| Rand (random numbers) | >> rand(3,2);
|
$ \left[ \begin{array}{cc} 0.21955 & 0.27560\\ 0.42385 & 0.62212\\ 0.53343 & 0.69182 \end{array} \right] $ |
| Meshgrid | >> [x,y] = meshgrid(1:4,1:4);
|
$ x = \left[ \begin{array}{cccc} 1& 2& 3& 4\\ 1& 2& 3& 4\\ 1& 2& 3& 4\\ 1& 2& 3& 4 \end{array} \right] $
$ y = \left[ \begin{array}{cccc} 1& 1& 1& 1\\ 2& 2& 2& 2\\ 3& 3& 3& 3\\ 4& 4& 4& 4 \end{array} \right] $ |
| Magic (magic square matrix)
(The sum of each row and column is equal to the same value) |
>> magic(4);
|
$ \left[ \begin{array}{cccc} 16& 2& 3& 13\\ 5& 11& 10& 8\\ 9& 7& 6& 12\\ 4& 14& 15& 1 \end{array} \right] $ |
| Linspace | >> linspace(A,B,N) |
$ \left[ A + \left( \frac{i}{N-1} \right) B \right] \qquad i=0, \dots, N-1 $ |
| Logspace | >> logspace(A,B,N) |
$ \left[ 10^{A} + 10^{ \left( \frac{i}{N-1} \right) B } \right] \qquad i=0, \dots, N-1 $ |
Functions
| Function name | Matlab syntax/output |
|---|---|
| det | Returns the determinant of a matrix:
>> A=magic(4)
A =
16 2 3 13
5 11 10 8
9 7 6 12
4 14 15 1
>> det(A)
ans = -1.4495e-12
|
| find | |
| flipud | |
| fliplr | |
| length | |
| max | |
| min | |
| repmat | This function creates a new matrix consisting of several copies of an existing matrix.
>> A = magic(3)
A =
8 1 6
3 5 7
4 9 2
>> repmat(A,2,2)
ans =
8 1 6 8 1 6
3 5 7 3 5 7
4 9 2 4 9 2
8 1 6 8 1 6
3 5 7 3 5 7
4 9 2 4 9 2
|
| size | |
| sort |
Operators
Addition, subtraction
Addition/subtraction can be done with vectors or matrices as with numbers:
>> A=ones(2,3)
A =
1 1 1
1 1 1
>> B=ones(2,3)
B =
1 1 1
1 1 1
>> C = A + B
C =
2 2 2
2 2 2
>> C = A - B
C =
0 0 0
0 0 0
Multiplication, division
Multiplication of matrices requires that the inner dimensions must match (i.e. $ M \times N) * (N \times P) $):
>> A
A =
0.85645 0.86793 0.39228
0.22329 0.82611 0.40042
0.79097 0.45921 0.30861
>> B
B =
0.976938 0.200895 0.239939
0.300156 0.205414 0.963250
0.396226 0.425022 0.041877
>> C = A*B
C =
1.25264 0.51707 1.05796
0.62476 0.38474 0.86609
1.03284 0.38440 0.64504
Division of matrices is defined as $ A/B = A B^{-1} $:
>> A = rand(3,3)
A =
0.85645 0.86793 0.39228
0.22329 0.82611 0.40042
0.79097 0.45921 0.30861
>> B = rand(3,3)
B =
0.976938 0.200895 0.239939
0.300156 0.205414 0.963250
0.396226 0.425022 0.041877
>>
>> C = A/B
C =
0.015664 0.321640 1.879233
-0.763591 0.516569 2.054946
0.435077 0.177713 0.788906
>> C = A*inv(B)
C =
0.015664 0.321640 1.879233
-0.763591 0.516569 2.054946
0.435077 0.177713 0.788906
Component-wise multiplication and division can also be done:
>> A
A =
0.85645 0.86793 0.39228
0.22329 0.82611 0.40042
0.79097 0.45921 0.30861
>> B
B =
0.976938 0.200895 0.239939
0.300156 0.205414 0.963250
0.396226 0.425022 0.041877
>> C = A.*B
C =
0.836694 0.174363 0.094122
0.067023 0.169693 0.385709
0.313402 0.195175 0.012924
>> C = A./B
C =
0.87666 4.32032 1.63489
0.74392 4.02167 0.41570
1.99626 1.08044 7.36944
Input/output
Switches
Functions
Graphics
Examples
Fluid mechanics
Heat transfer
Optimization
Statistics
See also
- Introduction to Matlab (lecture)