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The colon, :, is one of the most important
Matlab operators. It occurs in several different forms. The
expression
>> 1:10
ans =
1 2 3 4 5 6 7 8 9 10
is a row vector containing the integers from 1
to 10. To obtain nonunit spacing, specify an increment. For
example,
>> 20:2:0
ans =
20 18 16 14 12 10 8 6 4 2 0
Subscript expressions involving colons refer
to portions of a matrix.
>> P(1,3:4)
ans =
6 1
or
>> P(1,:)
ans =
3 5 6 1
The colon by itself refers to all the elements
in a row or column of a matrix and the keyword end refers to the last row or column. As index also
other matrices could be used, e.g.
>> P(:,[1 3 4])
ans =
3 6 1
2 4 9
or
>> P(:,randperm(4))
ans =
1 6 3 5
9 4 2 5
The logical vectors created from logical and
relational operations can be used to reference subarrays. For
example
>> P(:,y)
ans =
5 6 1
5 4 9
specifies the elements of P where the elements
of y are nonzero and
>> P(P>1)'
ans =
3 5 5 4 9
displays all positive elements of P as a row vector.
Concatenation is the process of joining small
matrices to make bigger ones. In fact, you made your first matrix
by concatenating its individual elements. The pair of square
brackets, [], is the concatenation operator.
>> P1 = [3 5 1 0.1; 8 4 2.2 0];
>> [P1 P; P P1]
To delete for instance a column of a matrix,
use
>> X = P;
>> X(:,2) = []
X =
3 6 1
2 4 9
and the remaining elements are shaped into a
smaler matrix.
Arithmetic operations on arrays are done
elementbyelement. Matlab uses a decimal point as part of the
notation for multiplicative array operations. The list of operators
includes multiplication
>> P.*P1
ans =
9.0000 25.0000 6.0000 0.1000
16.0000 20.0000 8.8000 0
division
>> P./P1
ans =
1.0000 1.0000 6.0000 10.0000
0.2500 1.2500 1.8182 Inf
or array power
>> P.^P1
ans =
1.0e+03 *
0.0270 3.1250 0.0060 0.0010
0.2560 0.6250 0.0211 0.0010
as well as left division .
and unconjugated array transpose .'.
Matlab provides five functions that generate
basic matrices.
zeros All zeros
ones All ones
rand Uniformly distributed random elements
randn Normally distributed random elements
eye Identity matrix
The commands, who and
whos, show the current contents of the
workspace. The who command gives a short list,
while whos also gives size and storage
information.
To delete all the existing variables form the workspace,
enter
>> clear all
The save command preserve
the contents of the workspace in a MATfile that can be read withe
the load command in a later Matlab session. For
example
>> save August17th
save the entire workspace contents in the file
August17th.mat. If desired, you can save only certain variables by
specifying the variable names after the filename.
