Page 372 - Process Modelling and Simulation With Finite Element Methods

A MATLAB/FEMLAB Primer for Vector Calculus 359

>> help rand
RAND Uniformly distributed random numbers.
RAND(N) is an N-by-N matrix with random entries, chosen from
a uniform distribution on the interval (0.0,l.O).
RAND(M,N) and RAND( [M,NI) are M-by-N matrices with random entries.
RAND (M,N, P, . . . ) or RAND ( [M,N, P, . . .I ) generate random arrays.
RAND with no arguments is a scalar whose value changes each time it
is referenced. RAND(SIZE(A)) is the same size as A.
>> help eye
EYE Identity matrix.
EYE(N) is the N-by-N identity matrix.
EYE(M,N) or EYE( [M,N]) is an M-by-N matrix with 1's on
the diagonal and zeros elsewhere.

EYE(SIZE(A)) is the same size as A.
Scalar - Array Math

Arithmetic of scalars acting on arrays threads across the array. For instance,
>> 3*a
ans =
Columns 1 through 8
0 0.9425 1.8850 2.8274 3.7699 4.7124 5.6549 6.5973
Columns 9 through 11
7.5398 8.4823 9.4248
>> 5+a
ans =
Columns 1 through 8
5.0000 5.3142 5.6283 5.9425 6.2566 6.5708 6.8850 7.1991
Columns 9 through 11
7.5133 7.8274 8.1416
Array - Array Element- Wise Math

Arithmetic of arrays on arrays is a tricky area. If the arrays are compatible sizes,
then dot-operators are applied element-wise:
>> b=linspace (1,11,11)
b=
1 2 3 4 5 6 7 8 9 10 11
>> size(a)
ans =
1 11
>> size(b)
ans =
1 11
>> a.*b
ans =
Columns 1 through 8
0 0.6283 1.8850 3.7699 6.2832 9.4248 13.1947 17.5929
columns 9 through 11
22.6195 28.2743 34.5575