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Functions
Vector and Matrix Operations.

Functions

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

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

double det ( const dmatrix &  m1)

Compute determinant of a constant matrix.

Parameters:
m1A dmatrix, $M$, for which the determinant is computed.
Returns:
A double containing $|M|$.

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

Definition at line 434 of file dmat3.cpp.

Referenced by det().

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:
t1A vector, $u$ with valid subscripts in $[i_1,i_n]$
t2A vector, $v$ with valid subscripts in $[i_1,i_n]$
Returns:
A vector containing $z_i = u_i\div v_i; [i_1,i_n]$.

Definition at line 52 of file dvect2.cpp.

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:
t1A vector, $u$ with valid subscripts in $[i_1,i_n]$
t2A vector, $v$ with valid subscripts in $[i_1,i_n]$
Returns:
A vector containing $z_i = u_i\times v_i; [i_1,i_n]$.

Definition at line 20 of file dvect2.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:
Asquare dmatrix
Returns:
The matrix exponential of A

Definition at line 63 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:
Asquare dvar_matrix
Returns:
The matrix exponential of A

Definition at line 136 of file linad99/expm.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:
Asquare df1b2matrix
Returns:
The matrix exponential of A

Definition at line 213 of file df1b2-separable/expm.cpp.

dmatrix inv ( const dmatrix &  m1)

Inverse of a constant matrix by LU decomposition.

Parameters:
m1A dmatrix, $M$, 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 36 of file dmat3.cpp.

double norm ( const dvector &  t1)

Norm of a vector; constant objects.

Parameters:
t1A vector, $v$.
Returns:
$||v|| = (v\times v)^{1/2} = (\sum_i v_i^2)^{1/2}$

Definition at line 18 of file dvect3.cpp.

double norm ( const dmatrix &  m1)

Norm of a matrix; constant object.

Parameters:
m1a matrix, $M$
Returns:
$||M||$

Definition at line 38 of file dmat2.cpp.

double norm2 ( const dvector &  t1)

Squared norm of a vector; constant objects.

Computes the sum of squares of its vector argument.

Parameters:
t1A vector, $v$.
Returns:
$||v||^2 = v\times v = \sum_i v_i^2$

Definition at line 34 of file dvect3.cpp.

double norm2 ( const dmatrix &  m1)

Norm squared of a matrix; constant object.

Parameters:
m1a matrix, $M$
Returns:
$||M||^2$

Definition at line 54 of file dmat2.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:
v1A dvar_vector, $a$.
v2A dvar_vector, $b$.
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.

int operator* ( const ivector &  t1,
const ivector &  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:
t1A ivector, $a$.
t2A ivector, $b$.
Returns:
A int, $z = a\cdot b = \sum_i a_i\cdot b_i$ containing the value of the dot product of the two arguments.

Definition at line 40 of file imat10.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:
t1A dvector, $a$.
t2A dvector, $b$.
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 523 of file dvector.cpp.

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

Multiply a dvector by a constant.

Parameters:
xDouble constant, $x$.
t1dvector reference, $y$.
Returns:
A dvector $z_i = x*y_i$.

Definition at line 646 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:
t1dvector reference, $a$.
t2dvector reference, $b$.
Returns:
A dvector, $z_i = a_i + b_i$ containing the value of the sum of the two arguments.

Definition at line 570 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:
t1dvector reference, $a$.
t2dvector reference, $b$.
Returns:
A dvector, $z_i = a_i - b_i$ containing the value of the difference of the two arguments.

Definition at line 609 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:
tA dvector constant
Returns:
Reference to a dvector object.

Reimplemented in independent_variables, dll_data_vector, data_vector, and named_dvector.

Definition at line 256 of file dvector.cpp.

dvector & dvector::operator= ( double  x)

Assignment operator for double argument.

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

Parameters:
xA double constant.
Returns:
Reference to a dvector object.

Reimplemented in data_vector, and named_dvector.

Definition at line 229 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:
tA dvector constant
Returns:
Reference to a independent_variables object.

Reimplemented from dvector.

Definition at line 302 of file dvector.cpp.

dvector & dvector::shift ( int  min)

Shift valid range of subscripts.

Parameters:
minIngeger value subtracted from the subscripts
Returns:
A devector containing shifted vector.

Definition at line 52 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(), splint(), and VEC().

dvariable sum ( const dvar_vector &  v1)

Compute the sum of a variable type vector.

Parameters:
v1A dvar_vector, $a$.
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:
v1A dvar_matrix, $A$.
Returns:
A dvariable, $s = \sum A $ containing the sum of the matrix.

Definition at line 187 of file fvar_a14.cpp.

dmatrix trans ( const dmatrix &  m1)

Transpose of a matrix; constant objects.

Parameters:
m1The matrix, $M$, to be transposed.
Returns:
$M^T$

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().

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