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()

Julia function that evaluates an expression in standard form.

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