API Reference

@matrix(ids...)

Create one or more matrices. Example:

@matrix A X

@vector(ids...)

Create one or more vectors. Example:

@vector x y

@scalar(ids...)

Create one or more scalars. Example:

@scalar a β

derivative(expr, wrt::Tensor)

Compute the derivative of expr with respect to wrt. Example:

@matrix A
@vector x

derivative(x' * x, x)

# output

2x₄

gradient(expr, wrt::Tensor)

Compute the gradient of expr with respect to wrt. expr must be a scalar and wrt a vector. Example:

@matrix A
@vector x

gradient(x' * A * x, x)

# output

x⁴A₄⁶ + A⁶⁵x₅

jacobian(expr, wrt::Tensor)

Compute the jacobian of expr with respect to wrt. expr must be a column vector and wrt a vector. Example:

@matrix A
@vector x

jacobian(A * x, x)

# output

A¹₅

hessian(expr, wrt::Tensor)

Compute the hessian of expr with respect to wrt. expr must be a scalar and wrt a vector. Example:

@matrix A
@vector x

hessian(x' * A * x, x)

# output

A₇⁶ + A⁶₇

JuliaFunc([args=AbstractVector{Variable},])

Julia function that evaluates an expression in standard form. The optional argument args can be used for specifying order of the arguments in the function signature. If args is given, then each variable must occur exactly once.

StdStr()

String format of an expression in standard form.

to_std(expr; format = StdStr())

Convert the expression expr to standard notation.

• format: Output format. Can be one of:
  • StdStr: String format.
  • JuliaFunc: Julia function.

Examples:

@matrix A
@vector x

to_std(gradient(x' * A * x, x))

# output

"Aᵀx + Ax"

to_std(gradient(x' * A * x, x); format = JuliaFunc())

# output

quote
    #= ... =#
    function generated_function(A, x)
        #= ... =#
        #= ... =#
        return transpose(A) * x + A * x
    end
end