List of Operators

The following shows all of the operators supported in SIMO.

Arithmetic Operators

Unary Minus

-A

• Element-wise operation that negates values in A.

Unary Plus

+A

• Element-wise operation that gives A as it is.

Addition

A + B

• Element-wise operation that adds A(i) to B(i) for all i.
• A and B should have compatible sizes.

Subtraction

A - B

• An element-wise operation that subtracts B(i) from A(i) for all i.
• A and B should have compatible sizes.

Multiplication

A .* B

• Element-wise operation that multiplies A(i) with B(i) for all i.
• A and B should have compatible sizes.

Right Division

A ./ B

• Element-wise operation that divides A(i) by B(i) for all i.
• A and B should have compatible sizes.

Left Division

A .\ B

• Element-wise operation that divides B(i) by A(i) for all i.
• A and B should have compatible sizes.

Power

A .^ B

• Element-wise operation that computes A(i) raised to the power of B(i) for all i.
• A and B should have compatible sizes.

Comparison Operators

Equal

A == B

• It returns a logical array C.

• It checks if A(i) is equal to B(i) for all i.

  • C(i) is logical 1 if they are equal.
  • C(i) is logical 0 if they are not equal.

• A and B should have compatible sizes.

Not Equal

A != B or A ~= B

• It returns a logical array C.

• It checks if A(i) is equal to B(i) for all i.

  • C(i) is logical 0 if they are equal.
  • C(i) is logical 1 if they are not equal.

• A and B should have compatible sizes.

Greater Than

A > B

• It returns a logical array C.

• It checks if A(i) is greater than B(i) for all i.

  • C(i) is logical 1 if A(i) is greater.
  • C(i) is logical 0 if A(i) is less than or equal to B(i).

• A and B should have compatible sizes.

Not Greater Than

A <= B

• It returns a logical array C.

• It checks if A(i) is smaller than or equal to B(i) for all i.

  • C(i) is logical 1 if A(i) is smaller than or equal to B(i).
  • C(i) is logical 0 if A(i) is greater.

• A and B should have compatible sizes.

Smaller Than

A < B

• It returns a logical array C.

• It checks if A(i) is smaller than B(i) for all i.

  • C(i) is logical 1 if A(i) is smaller.
  • C(i) is logical 0 if A(i) is greater than or equal to B(i).

• A and B should have compatible sizes.

Not Smaller Than

A >= B

• It returns a logical array C.

• It checks if A(i) is greater than or equal to B(i) for all i.

  • C(i) is logical 1 if A(i) is greater than or equal to the B(i).
  • C(i) is logical 0 if A(i) is smaller.

• A and B should have compatible sizes.

Logical Operators

NOT

!A or ~A

• It returns a logical array C, in which for each i,

  • C(i) is 0 if A(i) is not 0.
  • C(i) is 1 if A(i) is 0.

• Both !A and ~A return exactly the same result.

OR

A | B or A || B

• It returns a logical array C.

• It performs logical OR of A(i) and B(i) for all i.

  • C(i) is logical 1 if either A(i) or B(i) is non-zero.
  • C(i) is logical 0 if both A(i) and B(i) are 0.

• A and B should have compatible sizes.

• Both | and || operate in a non-short-circuiting fashion.

AND

A & B or A && B

• It returns a logical array C.

• It performs logical AND of A(i) and B(i) for all i.

  • C(i) is logical 1 if both A(i) and B(i) are non-zero.
  • C(i) is logical 0 if either A(i) or B(i) is 0.

• A and B should have compatible sizes.

• Both & and && operate in a non-short-circuiting fashion.

Exclusive OR

• It returns a logical array C.

• It performs exclusive OR of A(i) and B(i) for all i.

  • C(i) is logical 1 if one of A(i) and B(i) is zero and the other non-zero.
  • C(i) is logical 0 if both of A(i) and B(i) are zero or both of them non-zero.

• A and B should have compatible sizes.

• XOR is obtained by the built-in function xor().

Matrix Operators

Conjugate Transpose

A'

• Matrix operation that gives the conjugate transpose of the matrix A.
• A should be a matrix (two dimensional array).
• When A is complex, it gives the transpose of the conjugates of A.
• When A is real or non-numerical (e.g., structure array), it is the same as A.'.
• It gives the same result as ctranspose(A).

Non-conjugate Transpose

A.'

• Matrix operation that gives the transpose of the matrix A.
• A should be a matrix (two dimensional array).
• It gives the same result as transpose(A).

Matrix Power

A ^ B

• It returns A raised to the power B.
• A should be either a square matrix or scalar.
• B should always be a scalar.
• When A is a square matrix, B should be a real integer scalar.
• Matrix to non-integer power (e.g., [1 2;3 4]^2.33) is not supported yet.
• A ^ B gives the same result as mpower(A, B).

Matrix Multiplication

A * B

• Both A and B should be $m\times k$ and $k\times n$ matrices.
• It performs matrix multiplication of A and B.
• If either A or B is a scalar, element-wise multiplication, i.e., A.* B is performed instead.

Right Division (Matrix Equation Solving)

b / A

• It solves the matrix equation $xA=b$ for the unknown vector $x$.
• See the document page of mrdivide() for details.

Left Division (Matrix Equation Solving)

A \ b

• It solves the matrix equation $Ax=b$ for the unknown vector $x$.
• See the document page of mldivide() for details.