Multiplies two numerical arrays (elementwise). There are two forms for its use, both with the same general syntax:
y = a .* b
where a and b are n-dimensional arrays of numerical type. In the
first case, the two arguments are the same size, in which case, the
output y is the same size as the inputs, and is the element-wise
product of a and b. In the second case, either a or b is a scalar,
in which case y is the same size as the larger argument,
and is the product of the scalar with each element of the other argument.
The type of y depends on the types of a and b using type
promotion rules. All of the types are preserved under multiplication except
for integer types, which are promoted to int32 prior to
multiplication (same as C).
There are three formulae for the dot-times operator, depending on the sizes of the three arguments. In the most general case, in which the two arguments are the same size, the output is computed via:
If
a is a scalar, then the output is computed via
On the other hand, if
b is a scalar, then the output is computed via
Here are some examples of using the dottimes operator. First, a
straight-forward usage of the .* operator. The first example
is straightforward:
--> 3 .* 8
ans =
<int32> - size: [1 1]
24
Note, however, that because of the way that input is parsed, eliminating
the spaces 3.*8 results in the input being parsed as 3. * 8,
which yields a double result:
--> 3.*8 ans = <double> - size: [1 1] 24.0000000000000
This is really an invokation of the times operator.
Next, we use the floating point syntax to force one of the arguments
to be a double, which results in the output being double:
--> 3.1 .* 2
ans =
<double> - size: [1 1]
6.200000000000000
Note that if one of the arguments is complex-valued, the output will be complex also.
--> a = 3 + 4*i
a =
<complex> - size: [1 1]
3.0000000 4.0000000 i
--> b = a .* 2.0f
b =
<complex> - size: [1 1]
6.0000000 8.0000000 i
If a complex value is multiplied by a double, the result is
promoted to dcomplex.
--> b = a .* 2.0
b =
<dcomplex> - size: [1 1]
6.000000000000000 8.000000000000000 i
We can also demonstrate the three forms of the dottimes operator. First the element-wise version:
--> a = [1,2;3,4]
a =
<int32> - size: [2 2]
Columns 1 to 2
1 2
3 4
--> b = [2,3;6,7]
b =
<int32> - size: [2 2]
Columns 1 to 2
2 3
6 7
--> c = a .* b
c =
<int32> - size: [2 2]
Columns 1 to 2
2 6
18 28
Then the scalar versions
--> c = a .* 3
c =
<int32> - size: [2 2]
Columns 1 to 2
3 6
9 12
--> c = 3 .* a
c =
<int32> - size: [2 2]
Columns 1 to 2
3 6
9 12