Adds two numerical arrays (elementwise) together. 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 the sum
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 sum of the scalar added to each element of the other argument.
The type of y
depends on the types of a
and b
using the type
promotion rules. The types are ordered as:
uint8
- unsigned, 8-bit integers range [0,255]
int8
- signed, 8-bit integers [-127,128]
uint16
- unsigned, 16-bit integers [0,65535]
int16
- signed, 16-bit integers [-32768,32767]
uint32
- unsigned, 32-bit integers [0,4294967295]
int32
- signed, 32-bit integers [-2147483648,2147483647]
float
- 32-bit floating point
double
- 64-bit floating point
complex
- 32-bit complex floating point
dcomplex
- 64-bit complex floating point
C
. Numerical overflow rules are also the same as C
.
There are three formulae for the addition 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 addition operator. First, a
straight-forward usage of the plus operator. The first example
is straightforward - the int32
is the default type used for
integer constants (same as in C
), hence the output is the
same type:
--> 3 + 8 ans = <int32> - size: [1 1] 11
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] 5.100000000000000
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] 5.0000000 4.0000000 i
If a complex
value is added to a double
, the result is
promoted to dcomplex
.
--> b = a + 2.0 b = <dcomplex> - size: [1 1] 5.000000000000000 4.000000000000000 i
We can also demonstrate the three forms of the addition 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 3 5 9 11
Then the scalar versions
--> c = a + 1 c = <int32> - size: [2 2] Columns 1 to 2 2 3 4 5 --> c = 1 + b c = <int32> - size: [2 2] Columns 1 to 2 3 4 7 8