numerical_differentiation_module Module

unique ID for the method

the name of the method

2=backward diffs, 3=central diffs, etc...

multiplicative factors for dx perturbation

multiplicative factors for accumulating function evaluations

denominator factor for finite difference equation (times dx)

Constructor for a finite_diff_method.

has the sparsity pattern already been computed?

number of nonzero elements in the jacobian (will be the dimension of irow and icol)

sparsity pattern - rows of non-zero elements

sparsity pattern - columns of non-zero elements

if the linear pattern has been populated

number of constant elements in the jacobian

linear sparsity pattern - rows of non-zero elements

linear sparsity pattern - columns of non-zero elements

linear elements of the jacobian

index vector [1,2,...,num_nonzero_elements] for putting df into jac

the number of groups in the partition of the columns of a.

specifies the partition of the columns of a. column jcol belongs to group ngrp(jcol). size(n)

if true, an exception has been raised

a non-zero value will cause all routine to exit. this can be set to -1 by calling terminate.

error message (if istat/=0)

number of x variables

number of f functions

lower bounds on x

upper bounds on x

if true, warning messages are printed to the error_unit for any errors.

chuck size for allocating the arrays (>0)

perturbation mode:

perturbation vector for x

to partition the sparsity pattern using dsm

the sparsity pattern

lower bounds on x for computing sparsity (optional)

upper bounds on x for computing sparsity (optional)

perturbation vector for x when computing sparsity for sparsity_mode=4

for sparsity_mode=4, the number of jacobian evaluations used to estimate the sparsity pattern. See compute_sparsity_random_2

perturbation mode (if sparsity_mode=4):

to also compute the linear sparsity pattern

the equality tolerance for derivatives to indicate a constant jacobian element (linear sparsity)

the function precision. two functions values that are the within this tolerance are considered the same value. This is used when estimating the sparsity pattern when sparsity_mode=2 in compute_sparsity_random

1 = use meth (specified methods), 2 = use class (specified class, method is selected on-the-fly).

the finite difference method to use compute the nth column of the Jacobian size(n). Either this or class is used

the class of method to use to compute the nth column of the Jacobian size(n). Either this or meth is used

array of methods for the specified classes. used with class when mode=2

tolerance parameter for diff

tolerance parameter for diff

if using the function cache

if we are using the Neville's process method, rather than finite differences

the user-defined function

compute the user-defined function this can point to the problem_func or, if using the cache, it points to compute_function_with_cache.

for computing the sparsity pattern

an optional function the user can define which is called when each column of the jacobian is computed. It can be used to perform any setup operations.

the low-level function called by compute_jacobian that actually computes the jacobian.

initialize the class

initialize the class

main routine to compute the Jacobian using the selected options. It returns the sparse (vector) form.

return the dense size(m,n) matrix form of the Jacobian.

returns the product of the Jacobian matrix and an input vector

destroy the class

print the sparsity pattern in vector form to a file

print the sparsity pattern in matrix form to a file

manually set the sparsity pattern

select a method in a specified class so that the variable bounds are not violated when by the perturbations.

version of select_finite_diff_method for partitioned sparsity pattern.

can be called to change the variable bounds.

if the user needs to compute the sparsity pattern manually. (otherwise it will be done the first time the Jacobian is computed)

returns the sparsity pattern (if it is allocated)

can be called by user to stop the computation

to check if an exception was raised.

the status of error condition

change the dpert values

destroy the sparsity pattern

computes the variable perturbation factor

unique ID for the method

the name of the method

2=backward diffs, 3=central diffs, etc...

multiplicative factors for dx perturbation

multiplicative factors for accumulating function evaluations

denominator factor for finite difference equation (times dx)

the class is the number of points in the finite different computation

the integer

also include the sign (default is False)

file unit for printing (assumed to be opened)

array of variables (size n)

array of functions (size m)

the elements of the function vector that need to be computed (the other are ignored)

the id code for the method

the formula string

the id code for the method

this method (can be used in compute_jacobian)

true if it was found

the variable value

the variable lower bound

the variable upper bound

the perturbation value (>0)

list of available methods to choose from

this method can be used

true if it really doesn't violate the bounds (say, the bounds are very close to each other) if status_ok=False, then the first method in the given class is returned in fd.

the variable values

the variable lower bounds

the variable upper bounds

the perturbation values (>0)

list of available methods to choose from

this method can be used

true if it really doesn't violate the bounds (say, the bounds are very close to each other) if status_ok=False, then the first method in the given class is returned in fd.

number of x variables

number of f functions

lower bounds on x

upper bounds on x

the user function that defines the problem (returns m functions)

the sparsity computation method:

a function the user can define which is called when each column of the jacobian is computed. It can be used to perform any setup operations.

chunk size for allocating the arrays (must be >0) [default is 100]

tolerance parameter for diff if not present, default is 1.0e-9_wp

tolerance parameter for diff if not present, default is 0.0_wp

if present, this is the cache size for the function cache (default is not to enable cache)

lower bounds on x used for sparsity computation (when sparsity_mode is 2). If not present, then xlow is used.

upper bounds on x used for sparsity computation (when sparsity_mode is 2). If not present, then xhigh is used.

required if sparsity_mode=4

perturbation mode (required if sparsity_mode=4):

the equality tolerance for derivatives to indicate a constant jacobian element (linear sparsity)

the function precision. two functions values that are the within this tolerance are considered the same value. This is used when estimating the sparsity pattern when sparsity_mode=2 in compute_sparsity_random

for sparsity_mode=4, the number of jacobian evaluations used to estimate the sparsity pattern.

if true, print error messages to error_unit. default is True.

lower bounds on x

upper bounds on x

the sparsity computation method: 1 - assume dense, 2 - three-point simple method, 3 - will be specified by the user in a subsequent call to set_sparsity_pattern. 4 - computes a two-point jacobian at num_sparsity_points points.

lower bounds on x used for sparsity computation (when sparsity_mode is 2). If not present, then xlow is used.

upper bounds on x used for sparsity computation (when sparsity_mode is 2). If not present, then xhigh is used.

lower bounds on x to be used for sparsity computation. If not present, then then xlow values in the class are used.

upper bounds on x to be used for sparsity computation. If not present, then then xhigh values in the class are used.

perturbation vector for x

number of x variables

number of f functions

lower bounds on x

upper bounds on x

perturbation mode: 1 - perturbation is dx=dpert, 2 - perturbation is dx=dpert*x, 3 - perturbation is dx=dpert*(1+x)

perturbation vector for x

the user function that defines the problem (returns m functions)

the sparsity computation method: 1 - assume dense, 2 - three-point simple method, 3 - will be specified by the user in a subsequent call to set_sparsity_pattern. 4 - computes a two-point jacobian at num_sparsity_points points.

id code for the finite difference method to use for all n variables. see get_finite_difference_method

id codes for the finite difference method to use for each variable. see get_finite_difference_method

method class for the finite difference method to use for all n variables. see get_finite_difference_method

method class for the finite difference methods to use for each variable. see get_finite_difference_method

a function the user can define which is called when each column of the jacobian is computed. It can be used to perform any setup operations.

chunk size for allocating the arrays (must be >0) [default is 100]

if the sparisty pattern is to be partitioned using DSM [default is False]

if present, this is the cache size for the function cache (default is not to enable cache)

lower bounds on x used for sparsity computation (when sparsity_mode is 2). If not present, then xlow is used.

upper bounds on x used for sparsity computation (when sparsity_mode is 2). If not present, then xhigh is used.

for sparsity_mode=4, the perturbation

perturbation mode (required if sparsity_mode=4): 1 - perturbation is dx=dpert, 2 - perturbation is dx=dpert*x, 3 - perturbation is dx=dpert*(1+x)

the equality tolerance for derivatives to indicate a constant jacobian element (linear sparsity)

the function precision. two functions values that are the within this tolerance are considered the same value. This is used when estimating the sparsity pattern when sparsity_mode=2 in compute_sparsity_random

for sparsity_mode=4, the number of jacobian evaluations used to estimate the sparsity pattern.

number of columns of jacobian matrix

number of rows of jacobian matrix

status output from dsm

group number. Should be >0 and <=me%mxgrp

number of columns in the igroup group.

the column numbers in the igroup group. (if none, then it is not allocated)

the row numbers of all the nonzero Jacobian elements in this group

nonzero indices in jac for a group

true if the partition is valid

sparsity pattern nonzero elements row indices

sparsity pattern nonzero elements column indices

linear sparsity pattern nonzero elements row indices

linear sparsity pattern nonzero elements column indices

linear sparsity values (constant elements of the Jacobian)

DSM sparsity partition [only used if me%partition_sparsity_pattern=True]

DSM sparsity partition (size n) [only used if me%partition_sparsity_pattern=True]

vector of variables (size n)

vector of variables (size n) (not used here)

vector of variables (size n) (not used here)

vector of variables (size n)

sparsity pattern nonzero elements row indices

sparsity pattern nonzero elements column indices

linear sparsity pattern nonzero elements row indices

linear sparsity pattern nonzero elements column indices

linear sparsity values (constant elements of the Jacobian)

sparsity pattern nonzero elements row indices

sparsity pattern nonzero elements column indices

linear sparsity pattern nonzero elements row indices

linear sparsity pattern nonzero elements column indices

linear sparsity values (constant elements of the Jacobian)

DSM sparsity partition

DSM sparsity partition

vector of variables (size n)

the jacobian matrix

nominal variable vector

factor to multiply dx

the perturbation value for this column

factor to multiply function value

the variable to perturb

the elements in this column of the Jacobian to compute (passed to function)

the accumulated function value note: for the first call, this should be set to zero

vector of variables (size n)

vector (size n)

The product J*v (size m)

vector of variables (size n)

sparse jacobian vector

the column being computed

set of finite diff methods to use

vector of variables (size n)

sparse jacobian vector

vector of variables (size n)

absolute perturbation (>0) for each variable

sparse jacobian vector (size num_nonzero_elements)

vector of variables (size n)

absolute perturbation (>0) for each variable

sparse jacobian vector (size num_nonzero_elements)

vector of variables (size n)

absolute perturbation (>0) for each variable

sparse jacobian vector

nominal variable vector

factor to multiply dx

the perturbation value for this column

factor to multiply function value

the variables to perturb

the elements in this column of the Jacobian to compute (passed to function)

the accumulated function value note: for the first call, this should be set to zero

vector of variables (size n)

absolute perturbation (>0) for each variable

vector of variables (size n)

absolute perturbation (>0) for each variable

vector of variables (size n)

absolute perturbation (>0) for each variable

number of variables (columns of jacobian)

number of functions (rows of jacobian)

file unit to write to. (assumed to be already opened)

if present and true, the matrix form of the sparsity pattern is printed (default is vector form)

file unit to write to. (assumed to be already opened)

file unit to write to. (assumed to be already opened)

error code.

the routine where the error was raised.

error message string.

error code (istat=0 means no errors).

error message string.