Functions
dmatrix	trans (const dmatrix &m1)
	Transpose of a matrix; constant objects.
double	norm (const dmatrix &m1)
	Norm of a matrix; constant object.
double	norm2 (const dmatrix &m1)
	Norm squared of a matrix; constant object.
dmatrix	inv (const dmatrix &m1)
	Inverse of a constant matrix by LU decomposition.
double	det (const dmatrix &m1)
	Compute determinant of a constant matrix.
dvector	elem_prod (const dvector &t1, const dvector &t2)
	Element-wise multiplication of two vectors; constant objects.
dvector	elem_div (const dvector &t1, const dvector &t2)
	Element-wise division of two vectors; constant objects.
double	norm (const dvector &t1)
	Norm of a vector; constant objects.
double	norm2 (const dvector &t1)
	Squared norm of a vector; constant objects.
double	operator* (const dvector &t1, const dvector &t2)
	Compute the dot product of two vectors.
dvector	operator+ (const dvector &t1, const dvector &t2)
	Add two dvectors.
dvector	operator- (const dvector &t1, const dvector &t2)
	Subtract two dvectors.
dvector	operator* (double x, const dvector &t1)
	Multiply a dvector by a constant.
dmatrix	expm (const dmatrix &A)
	Matrix exponential.
dvar_matrix	expm (const dvar_matrix &A)
	Matrix exponential.
dvariable	operator* (const dvar_vector &v1, const dvar_vector &v2)
	Compute the dot product of two variable type vectors.
dvariable	sum (const dvar_vector &v1)
	Compute the sum of a variable type vector.
dvariable	sum (const dvar_matrix &m)
	Compute the sum of a variable type matrix.
df1b2matrix	expm (const df1b2matrix &A)
	Matrix exponential.
dvector &	dvector::shift (int min)
	Shift valid range of subscripts.
dvector &	dvector::operator= (double x)
	Assignment operator for double argument.
dvector &	dvector::operator= (const dvector &t)
	Assignment operator for dvector argument.
independent_variables &	independent_variables::operator= (const dvector &t)
	Assignment operator for dvector argument.

Detailed Description

The syntax of ADMB Matrix and vector operations follows normal mathematical conventions as much as possible. If u and v are vectors and M is a matrix,

u*M

is a normal matrix multiplication and

u*v

is a dot product. Element-wise multiplications and divisions are accomplished by elem_prod and elem_div respectively. If the arguments to these operations are not conformable for the appropriate type and operation, the application will exit with an error message.

These operations have been overloaded for appropriate combinations of constant and variable objects. The overloaded versions with variable types are optimized for efficient derivative computation. Only the constant types are currently documented here.

Function Documentation

dmatrix trans ( const dmatrix & m1 )

Transpose of a matrix; constant objects.

Parameters:

m1	The matrix, , to be transposed.

Returns:

Definition at line 18 of file dmat2.cpp.

Referenced by calculate_laplace_approximation(), laplace_approximation_calculator::check_hessian_type(), laplace_approximation_calculator::default_calculations(), laplace_approximation_calculator::default_calculations_check_derivatives(), derch(), laplace_approximation_calculator::do_newton_raphson_banded(), function_minimizer::get_bigS(), function_minimizer::hess_inv(), function_minimizer::normalize_posterior_distribution(), orthpoly(), orthpoly_constant_begin(), orthpoly_constant_begin_end(), positive_definite_matrix(), print_is_diagnostics(), read_hessian_matrix_and_scale1(), seldif_basis(), solve(), and tensor_prod().

double norm ( const dmatrix & m1 )

Norm of a matrix; constant object.

Parameters:

m1 a matrix,

Returns:

Definition at line 38 of file dmat2.cpp.

double norm2 ( const dmatrix & m1 )

Norm squared of a matrix; constant object.

Parameters:

m1 a matrix,

Returns:

Definition at line 54 of file dmat2.cpp.

dmatrix inv ( const dmatrix & m1 )

Inverse of a constant matrix by LU decomposition.

Parameters:

m1	A dmatrix, , for which the inverse is to be computed.

Returns:: A dmatrix containing $M^{-1}$ .

The implementation of this algorithm was inspired by "Numerical Recipes in C", 2nd edition, Press, Teukolsky, Vetterling, Flannery, chapter 2

Definition at line 30 of file dmat3.cpp.

double det ( const dmatrix & m1 )

Compute determinant of a constant matrix.

\param m1 A dmatrix, \form#28, for which the determinant is computed.
\return A double containing \form#36.
\n\n The implementation of this algorithm was inspired by
"Numerical Recipes in C", 2nd edition,
Press, Teukolsky, Vetterling, Flannery, chapter 2

Deprecated:: Scheduled for replacement by 2010.

Definition at line 431 of file dmat3.cpp.

Referenced by det().

dvector elem_prod	(	const dvector &	t1,
		const dvector &	t2
	)

Element-wise multiplication of two vectors; constant objects.

Exits with error if bounds of the two arguments differ.

Parameters:

t1	A vector, with valid subscripts in
t2	A vector, with valid subscripts in

Returns:: A vector containing $z_i = u_i\times v_i; [i_1,i_n]$ .

Definition at line 20 of file dvect2.cpp.

dvector elem_div	(	const dvector &	t1,
		const dvector &	t2
	)

Element-wise division of two vectors; constant objects.

Exits with error if bounds of the two arguments differ.

Parameters:

t1	A vector, with valid subscripts in
t2	A vector, with valid subscripts in

Returns:: A vector containing $z_i = u_i\div v_i; [i_1,i_n]$ .

Definition at line 51 of file dvect2.cpp.

double norm ( const dvector & t1 )

Norm of a vector; constant objects.

Parameters:

t1	A vector, .

Returns:: $||v|| = (v\times v)^{1/2} = (\sum_i v_i^2)^{1/2}$

Definition at line 18 of file dvect3.cpp.

double norm2 ( const dvector & t1 )

Squared norm of a vector; constant objects.

Computes the sum of squares of its vector argument.

Parameters:

t1	A vector, .

Returns:: $||v||^2 = v\times v = \sum_i v_i^2$

Definition at line 35 of file dvect3.cpp.

double operator*	(	const dvector &	t1,
		const dvector &	t2
	)

Compute the dot product of two vectors.

The minimum and maxium legal subscripts of the arguments must agree; otherwize an error message is printed and execution terminates.

Parameters:

t1	A dvector, .
t2	A dvector, .

Returns:: A double, $z = a\cdot b = \sum_i a_i\cdot b_i$ containing the value of the dot product of the two arguments.

Definition at line 534 of file dvector.cpp.

dvector operator+	(	const dvector &	t1,
		const dvector &	t2
	)

Add two dvectors.

Exits with error if bounds of the two arguments differ.

Parameters:

t1	dvector reference, .
t2	dvector reference, .

Returns:: A dvector, containing the value of the sum of the two arguments.

Definition at line 580 of file dvector.cpp.

dvector operator-	(	const dvector &	t1,
		const dvector &	t2
	)

Subtract two dvectors.

Exits with error if bounds of the two arguments differ.

Parameters:

t1	dvector reference, .
t2	dvector reference, .

Returns:: A dvector, containing the value of the difference of the two arguments.

Definition at line 618 of file dvector.cpp.

dvector operator*	(	double	x,
		const dvector &	t1
	)

Multiply a dvector by a constant.

Parameters:

x	Double constant, .
t1	dvector reference, .

Returns:: A dvector .

Definition at line 654 of file dvector.cpp.

dmatrix expm ( const dmatrix & A )

Matrix exponential.

The matrix exponential is calculated using the Pade approximation adapted from Moler, Cleve; Van Loan, Charles F. (2003), "Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later"

The main use of the matrix exponential is to solve linear ordinary differential equation (ODE) systems:

$\frac{d}{dt}y(t) = Ay(t)\ , \ \mbox{with } y(0) = y_0$

then the solution becomes

$y(t) = e^{At}y_0$

Parameters:

A	square dmatrix

Returns:: The matrix exponential of A

Definition at line 60 of file linad99/expm.cpp.

dvar_matrix expm ( const dvar_matrix & A )

Matrix exponential.

The matrix exponential is calculated using the Pade approximation adapted from Moler, Cleve; Van Loan, Charles F. (2003), "Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later"

The main use of the matrix exponential is to solve linear ordinary differential equation (ODE) systems:

$\frac{d}{dt}y(t) = Ay(t)\ , \ \mbox{with } y(0) = y_0$

then the solution becomes

$y(t) = e^{At}y_0$

Parameters:

A	square dvar_matrix

Returns:: The matrix exponential of A

Definition at line 122 of file linad99/expm.cpp.

dvariable operator*	(	const dvar_vector &	v1,
		const dvar_vector &	v2
	)

Compute the dot product of two variable type vectors.

The minimum and maxium legal subscripts of the arguments must agree; otherwize an error message is printed and execution terminates.

Parameters:

v1	A dvar_vector, .
v2	A dvar_vector, .

Returns:: A dvariable, $z = a\cdot b = \sum_i a_i\cdot b_i$ containing the value of the dot product of the two arguments.

Definition at line 35 of file fvar_a14.cpp.

dvariable sum ( const dvar_vector & v1 )

Compute the sum of a variable type vector.

Parameters:

v1	A dvar_vector, .

Returns:: A dvariable, $s = \sum a$ containing the sum of the vector.

Definition at line 133 of file fvar_a14.cpp.

dvariable sum ( const dvar_matrix & m )

Compute the sum of a variable type matrix.

Parameters:

v1	A dvar_matrix, .

Returns:: A dvariable, $s = \sum A$ containing the sum of the matrix.

Definition at line 187 of file fvar_a14.cpp.

df1b2matrix expm ( const df1b2matrix & A )

Matrix exponential.

The matrix exponential is calculated using the Pade approximation adapted from Moler, Cleve; Van Loan, Charles F. (2003), "Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later"

The main use of the matrix exponential is to solve linear ordinary differential equation (ODE) systems:

$\frac{d}{dt}y(t) = Ay(t)\ , \ \mbox{with } y(0) = y_0$

then the solution becomes

$y(t) = e^{At}y_0$

Parameters:

A	square df1b2matrix

Returns:: The matrix exponential of A

Definition at line 215 of file df1b2-separable/expm.cpp.

dvector & dvector::shift ( int min )

Shift valid range of subscripts.

Parameters:

min	Ingeger value subtracted from the subscripts

Returns:: A devector containing shifted vector.

Definition at line 42 of file dvector.cpp.

Referenced by calculate_importance_sample_shess(), dmatrix::colshift(), evaluate_function_gradient(), dvar_matrix::fill(), dmatrix::fill(), gauss_legendre(), get_inverse_sparse_hessian(), function_minimizer::hess_routine_noparallel_random_effects(), imtqlx(), function_minimizer::neldmead(), return_choleski_decomp_solve(), return_choleski_factor_solve(), function_minimizer::sd_routine(), solve(), safe_choleski_solver::solve(), spline(), spline_cubic_val(), spline_cubic_val2(), and VEC().

dvector & dvector::operator= ( double x )

Assignment operator for double argument.

Assigns a the same value to all members of the vector object.

Parameters:

x	A double constant.

Returns:: Reference to a dvector object.

Reimplemented in data_vector, data_vector, data_vector, named_dvector, named_dvector, named_dvector, and SPnamed_dvector.

Definition at line 247 of file dvector.cpp.

dvector & dvector::operator= ( const dvector & t )

Assignment operator for dvector argument.

Assigns the values of the argument to a target dvector in the LHS of the assignment operator. The range of valid subscripts in the argument and the target must be identical.

Parameters:

t	A dvector constant

Returns:: Reference to a dvector object.

Reimplemented in independent_variables, dll_data_vector, data_vector, dll_data_vector, data_vector, data_vector, named_dvector, named_dvector, named_dvector, and SPnamed_dvector.

Definition at line 275 of file dvector.cpp.

independent_variables & independent_variables::operator= ( const dvector & t )

Assignment operator for dvector argument.

Assigns the values of the argument to a independent_variables target in the LHS of the assignment operator. The range of valid subscripts in the argument and the target must be identical.

Parameters:

t	A dvector constant

Returns:: Reference to a independent_variables object.

Reimplemented from dvector.

Definition at line 315 of file dvector.cpp.

Functions

Detailed Description

Function Documentation