AD Model Builder/Cheat sheet

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ADMB Handy operations and functions (aka ADMB cheat sheet)

Adapted from a Word document written by Carolina Minte-Vera.

Let V, X, Y be vectors and v_i, x_i, y_i be the elements of the vectors. Let M, N, A be matrices and m_ij, n_ij, a_ij be the elements of the matrices. Let α be a scalar.

Contents 1 Matrix and vector operations 2 Element–wise (e-w) operations in a matrix or vector object 3 Other matrix or vector operations 4 Still more matrix or vector operations 5 Useful functions

Matrix and vector operations

Operation	Math notation	ADMB slow code	ADMB fast code
Sum of two vectors	vi = xi + yi	V = X + Y	X+=Y
Sum of scalar to a vector	vi = xi + α	V = X + nu	X+=nu
Sum of two matrices	aij = mij + nij	A = M + N
Sum of a scalar to a matrix	aij = mij + α	A = M +alpha	M+=alpha
Subtract two vectors	vi = xi − yi	V = X - Y	X-=Y
Subtract a scalar from a vector	vi = xi − α	V=X-alpha	X-=alpha
Subtract a scalar from a matrix	vi = xi − α	A=M-alpha	M-=alpha
Subtract two matrices	aij = mij − nij	A=M-N	M-=N
Vector dot product	α = ∑ xiyi i	alpha=X*Y
Outer product of two vectors	mij = xiyj	M=outer_prod(X,Y)
Multiply a scalar by a vector	xi = αyi	X=alpha*Y	Y*=alpha
Multiply a vector by a scalar	xi = yiα	X=Y*alpha
Multiply a scalar by a matrix	mij = αaij	A=alpha*M	M*=alpha
Multiply a vector by a matrix	xj = ∑ yimij i	X=Y*M
Multiply a matrix by a vector	xi = ∑ mijyi j	X=M*Y
Multiply two matrices	aij = ∑ miknkj k	A=M*N
Division of vector by scalar	yi = xi / α	Y=X/alpha	X/=alpha
Division of scalar by a vector	yi = α / xi	Y=alpha/X
Division of a matrix by a scalar	mij = aij / α	M=N/alpha

Element–wise (e-w) operations in a matrix or vector object

Operation [need objects of the same dimension]	Math notation	ADMB code
Vectors e-w multiplication	vi = xiyi	V=elem_prod(X,Y)
Vectors e-w division	vi = xi / yi	V=elem_div(X,Y)
Matrices e-w multiplication	mij = aijnij	M=elem_prod(A,N)
Matrices e-w division	mij = aij / nij	M=elem_div(A,N)
Vectors e-w multiplication	vi = xiyi	V=elem_prod (X,Y)

Other matrix or vector operations

Operation	Math notation	ADMB code
Norm of a vector		alpha=norm(V)
Norm square of a vector		alpha=norm2(V)
Norm of a matrix		alpha=norm(M)
Norm square of a matrix		alpha=norm2(M)
Sum over elements of a vector	α = ∑ vi i	alpha=sum(V)
Row sums of a matrix object	xi = ∑ mij j	X=rowsum(M)
Column sum of a matrix object	yj = ∑ mij i	Y=colsum(M)
Concatenation	X = (x1,x2,x3),Y = (y1,y2),V = (x1,x2,x3,y1,y2)	V=X&Y

Still more matrix or vector operations

Operation	ADMB code
Determinant (must be a square matrix cols=rows)	alpha=det(M)
Logarithm of the determinant? (must be a square matrix cols=rows), sgn is an integer. Not explained in the manual, but used in the codes.	alpha=ln_det(M,sgn)
Inverse (must be a square matrix cols=rows)	N=inv(M)
Minimum value of a vector object	alpha=min(V)
Maximum value of a vector object	alpha=max(V)
Eigenvalues of a symmetric matrix	V=Eigenvalues(M)
Eigenvectors of a symmetric matrix	N=eigenvectors(M)
Identity matrix function	M=identity_matrix(int min, int max)

Useful functions

Function	Action
current_phase()	return an integer that is the value of the current phase
last_phase()	return a binary: "true" if the current phase is the last phase and "false" (=0) otherwise
Active(Par)	return a binary: "true" if the parameter Par is active in the current phase and "false" (=0) otherwise
mceval_phase()	return a binary: "true" if the current phase is the mceval phase and "false" (=0) otherwise
bolinha.initialize()	Initializes (sets all elements equal to zero) the object bolinha