operator_expand

Arguments

X, Y

Scalars, vectors, matrices or hypermatrices of numbers (real or complex), encoded integers, polynomials or texts, according to the operator being applied.

Description

Expanding automatically replicates any dimension equal to 1 so that both operands get identical shapes before applying an element-wise binary operator. Missing trailing dimensions are considered to be 1. The resulting size is the per-dimension maximum of both shapes.

A scalar is just a special case where all dimensions are singletons, so scalar expansion is naturally covered by expanding.

Expanding is currently implemented for the following operators: + (addition), - (subtraction), .* (element-wise multiplication), ./ (element-wise right division), and .^ (element-wise power).

Examples

// Addition with expand
a = [1; 2];
b = [10 20 30];
a + b

--> a = [1; 2];
--> b = [10 20 30];
--> a + b
 ans  =
   11.   21.   31.
   12.   22.   32.

// Subtraction with expand
a = [1; 2];
b = [10 20 30];
b - a

--> b - a
 ans  =
   9.    19.   29.
   8.    18.   28.

// Element-wise multiplication with expand
a = [1; 2; 3];
b = [10 20];
a .* b

--> a = [1; 2; 3];
--> b = [10 20];
--> a .* b
 ans  =
   10.   20.
   20.   40.
   30.   60.

// Element-wise division with expand
a = [100; 200];
b = [1 2 4];
a ./ b

--> a = [100; 200];
--> b = [1 2 4];
--> a ./ b
 ans  =
   100.   50.   25.
   200.   100.  50.

// Element-wise power with expand
a = [2; 3];
b = [1 2 3];
a .^ b

--> a = [2; 3];
--> b = [1 2 3];
--> a .^ b
 ans  =
   2.   4.   8.
   3.   9.   27.

// Complex doubles
ca = [1+%i; -2+2*%i];
cb = [%i, 2-%i, -1+3*%i];
ca + cb

--> ca = [1+%i; -2+2*%i];
--> cb = [%i, 2-%i, -1+3*%i];
--> ca + cb
 ans  =
   1. + 2.i   3. + 0.i  0. + 4.i
  -2. + 3.i   0. + i   -3. + 5.i

// Polynomials
pcol = [%s; 1 + %s];
prow = [%s^2, 2 - %s];
pcol + prow

--> pcol = [%s; 1 + %s];
--> prow = [%s^2, 2 - %s];
--> pcol + prow
 ans  =
   s +s^2       2
   1. +s +s^2   3

// Incompatible shapes still fail
[1 2; 3 4] + ones(3, 2)

--> [1 2; 3 4] + ones(3, 2)

Operator +: Wrong dimensions for operation [2x2] + [3x2], same dimensions expected.

See also

• addition — Numerical addition. Text concatenation (gluing)
• subtraction — (-) subtraction operator. Sign change
• multiplication — (*) multiplication operator
• division — (/) right divisions. System's feed back. Comments
• power — (^) exponentiation
• operators — scilab operator names

History