This chapter extends the interface discussion in Chapter Interfaces and its discussion of generic black-box interfaces to simulations (Section Building a Black-Box Interface to a Simulation Code). It describes specialized, tightly integrated, and advanced interfaces through which Dakota can perform function evaluation mappings. It describes AMPL-based algebraic mappings (Section Algebraic Mappings), tight integration of a simulation code into Dakota (Section Developing a Direct Simulation Interface), and specialized interfaces to Matlab, Python, and Scilab (Sections Existing Direct Interfaces to External Simulators and Scilab Script and Direct Interfaces).

## Algebraic Mappings

If desired, one can define algebraic input-output mappings using the AMPL code [FGK03] and save these mappings in 3 files: stub.nl, stub.col, and stub.row, where stub is a particular root name describing a particular problem. These files names can be communicated to Dakota using the algebraic_mappings input.

Dakota will use stub.col and stub.row to obtain input and output identifier strings, respectively, and will use the AMPL solver library [Gay97] to evaluate expressions conveyed in stub.nl, and, if needed, their first and second derivatives.

As a simple example (from dakota/share/dakota/test/dakota_ampl*), consider algebraic mappings based on Newton’s law $$F = m a$$. The following is an AMPL input file of variable and expression declarations and output commands:

var mass;
var a;
var v;
minimize force: mass*a;
minimize energy: 0.5 * mass * v^2;
option auxfiles rc;	# request stub.row and stub.col
write gfma;		# write stub.nl, stub.row, stub.col


When processed by an AMPL processor, three files are created (as requested by the “option auxfiles” command). The first is the file dakota_ampl_fma.nl containing problem statistics, expression graphs, bounds, etc.:

g3 0 1 0	# problem fma
3 0 2 0 0	# vars, constraints, objectives, ranges, eqns
0 2	# nonlinear constraints, objectives
0 0	# network constraints: nonlinear, linear
0 3 0	# nonlinear vars in constraints, objectives, both
0 0 0 1	# linear network variables; functions; arith, flags
0 0 0 0 0	# discrete variables: binary, integer, nonlinear (b,c,o)
0 4	# nonzeros in Jacobian, gradients
6 4	# max name lengths: constraints, variables
0 0 0 0 0	# common exprs: b,c,o,c1,o1
O0 0
o2
v0
v1
O1 0
o2
o2
n0.5
v0
o5
v2
n2
b
3
3
3
k2
0
0
G0 2
0 0
1 0
G1 2
0 0
2 0


Next, the file dakota_ampl_fma.col contains the set of variable descriptor strings:

mass
a
v


and the file dakota_ampl_fma.row contains the set of response descriptor strings:

force
energy


The variable and objective function names declared within AMPL should be a subset of the variable descriptors and response descriptors used by Dakota. Ordering of the inputs and outputs within the AMPL declaration is not important, as Dakota will reorder data as needed. The following listing shows an excerpt from dakota/share/dakota/test/dakota_ampl_fma.in, which demonstrates a combined algebraic/simulation-based mapping in which algebraic mappings from the fma definition are overlaid with simulation-based mappings from text_book:

variables,
continuous_design = 5
descriptor    'x1' 'mass' 'a' 'x4' 'v'
initial_point  0.0  2.0  1.0  0.0  3.0
lower_bounds  -3.0  0.0 -5.0 -3.0 -5.0
upper_bounds   3.0 10.0  5.0  3.0  5.0

interface,
algebraic_mappings = 'dakota_ampl_fma.nl'
system
analysis_driver = 'text_book'
parameters_file = 'tb.in'
results_file    = 'tb.out'
file_tag

responses,
response_descriptors = 'force' 'ineq1' 'energy'
num_objective_functions = 1
num_nonlinear_inequality_constraints = 1
num_nonlinear_equality_constraints = 1
nonlinear_equality_targets = 20.0
no_hessians


Note that the algebraic inputs and outputs are a subset of the total inputs and outputs and that Dakota will track the algebraic contributions to the total response set using the order of the descriptor strings. In the case where both the algebraic and simulation-based components contribute to the same function, they are added together.

To solve text_book algebraically (refer to Section Textbook for definition), the following AMPL model file could be used

#   Problem : Textbook problem used in DAKOTA testing
#             Constrained quartic, 2 continuous variables
#   Solution: x=(0.5, 0.5), obj = .125, c1 = 0, c2 = 0
#

# continuous variables
var x1 >=  0.5 <= 5.8 := 0.9;
var x2 >= -2.9 <= 2.9 := 1.1;

# objective function
minimize obj: (x1 - 1)^4 + (x2 - 1)^4;

# constraints (current required syntax for DAKOTA/AMPL interface)
minimize c1: x1^2 - 0.5*x2;
minimize c2: x2^2 - 0.5*x1;

# required for output of *.row and *.col files
option auxfiles rc;


Note that the nonlinear constraints should not currently be declared as constraints within AMPL. Since the Dakota variable bounds and constraint bounds/targets currently take precedence over any AMPL specification, the current approach is to declare all AMPL outputs as objective functions and then map them into the appropriate response function type (objectives, least squares terms, nonlinear inequality/equality constraints, or generic response functions) within the Dakota input specification.

## Developing a Direct Simulation Interface

If a more efficient interface to a simulation is desired (e.g., to eliminate process creation and file I/O overhead) or if a targeted computer architecture cannot accommodate separate optimization and simulation processes (e.g., due to lightweight operating systems on compute nodes of large parallel computers), then linking a simulation code directly with Dakota may be desirable. This is an advanced capability of Dakota, and it requires a user to have access to (and knowledge of) the Dakota source code, as well as the source code of the simulation code.

Three approaches are outlined below for developing direct linking between Dakota and a simulation: extension, derivation, and sandwich. For additional information, refer to “Interfacing with Dakota as a Library”.

Once performed, Dakota can bind with the new direct simulation interface using the direct interface specification in combination with an analysis_driver, input_filter or output_filter specification that corresponds to the name of the new subroutine.

### Extension

The first approach to using the direct function capability with a new simulation (or new internal test function) involves extension of the existing DirectFnApplicInterface class to include new simulation member functions. In this case, the following steps are performed:

1. The functions to be invoked (analysis programs, input and output filters, internal testers) must have their main programs changed into callable functions/subroutines.

2. The resulting callable function can then be added directly to the private member functions in DirectFnApplicInterface if this function will directly access the Dakota data structures (variables, active set, and response attributes of the class). It is more common to add a wrapper function to DirectFnApplicInterface which manages the Dakota data structures, but allows the simulator subroutine to retain a level of independence from Dakota (see Salinas, ModelCenter, and Matlab wrappers as examples).

3. The if-else blocks in the derived_map_if(), derived_map_ac(), and derived_map_of() member functions of the DirectFnApplicInterface class must be extended to include the new function names as options. If the new functions are class member functions, then Dakota data access may be performed through the existing class member attributes and data objects do not need to be passed through the function parameter list. In this case, the following function prototype is appropriate:

int function_name();


If, however, the new function names are not members of the DirectFnApplicInterface class, then an extern declaration may additionally be needed and the function prototype should include passing of the Variables, ActiveSet, and Response data members:

int function_name(const Dakota::Variables& vars,
const Dakota::ActiveSet& set, Dakota::Response& response);

1. The Dakota system must be recompiled and linked with the new function object files or libraries.

Various header files may have to be included, particularly within the DirectFnApplicInterface class, in order to recognize new external functions and compile successfully. Refer to Dakota’s source code documentation for additional information on the DirectFnApplicInterface class and the Dakota data types.

### Derivation

As described in “Interfacing with Dakota as a Library”, a derivation approach can be employed to further increase the level of independence between Dakota and the host application. In this case, rather than adding a new function to the existing DirectFnApplicInterface class, a new interface class is derived from DirectFnApplicInterface which redefines the derived_map_if(), derived_map_ac(), and derived_map_of() virtual functions.

In the approach of the sandwich section below, the class derivation approach avoids the need to recompile the Dakota library when the simulation or its direct interface class is modified.

### Sandwich

In a “sandwich” implementation, a simulator provides both the “front end” and “back end” with Dakota sandwiched in the middle. To accomplish this approach, the simulation code is responsible for interacting with the user (the front end), links Dakota in as a library (refer to “Interfacing with Dakota as a Library”), and plugs in a derived direct interface class to provide a closely-coupled mechanism for performing function evaluations (the back end). This approach makes Dakota services available to other codes and frameworks and is currently used by Sandia codes such as Xyce (electrical simulation), Sage (CFD), and SIERRA (multiphysics).

## Existing Direct Interfaces to External Simulators

In addition to built-in polynomial test functions described in Section Direct Simulation Interface, Dakota includes direct interfaces to Sandia’s Salinas code for structural dynamics, Phoenix Integration’s ModelCenter framework, The Mathworks’ Matlab scientific computing environment, Scilab (as described in Section Scilab Script and Direct Interfaces), and Python. While these can be interfaced to with a script-based approach, some usability and efficiency gains may be realized by re-compiling Dakota with these direct interfaces enabled. Some details on Matlab and Python interfaces are provided here. Note that these capabilities permit using Matlab or Python to evaluate a parameter to response mapping; they do not make Dakota algorithms available as a service, i.e., as a Matlab toolbox or Python module.

### Matlab

Dakota’s direct function interface includes the capability to invoke Matlab for function evaluations, using the Matlab engine API. When using this close-coupling, the Matlab engine is started once when Dakota initializes, and then during analysis function evaluations are performed exchanging parameters and results through the Matlab C API. This eliminates the need to use the file system and the expense of initializing the Matlab engine for each function evaluation.

The Dakota/Matlab interface has been built and tested on 32-bit Linux with Matlab 7.0 (R14) and on 64-bit Linux with Matlab 7.1 (R14SP3). Configuration support for other platforms is included, but is untested. Builds on other platforms or with other versions of Matlab may require modifications to Dakota including its build system

To use the Dakota/Matlab interface, Dakota must be configured and compiled with the Matlab feature enabled. The Mathworks only provides shared object libraries for its engine API, so Dakota must be dynamically linked to at least the Matlab libraries. To compile Dakota with the Matlab interface enabled, set the CMake variable DAKOTA_MATLAB:BOOL=ON, possibly with MATLAB_DIR:FILEPATH=/path/to/matlab, where
MATLAB_DIR is the root of your Matlab installation (it should be a directory containing directories bin/YOURPLATFORM and extern/include).

Since the Matlab libraries are linked dynamically, they must be accessible at compile time and at run time. Make sure the path to the appropriate Matlab shared object libraries is on your LD_LIBRARY_PATH. For example to accomplish this in BASH on 32-bit Linux, one might type

export LD_LIBRARY_PATH=/usr/local/matlab/bin/glnx86:$LD_LIBRARY_PATH  or add such a command to the .bashrc file. Then proceed with compiling as usual. Example files corresponding to the following tutorial are available in dakota/share/dakota/examples/users/MATLAB/linked/. #### Dakota/Matlab input file specification The Matlab direct interface is specified with matlab keywords in an interface specification. The Matlab m-file which performs the analysis is specified through the analysis_drivers keyword. Here is a sample Dakota interface specification: interface, matlab analysis_drivers = 'myanalysis.m'  Multiple Matlab analysis drivers are supported. Multiple analysis components are supported as for other interfaces as described in Section Simulation Interface Components. The .m extension in the analysis_drivers specification is optional and will be stripped by the interface before invoking the function. So myanalysis and myanalysis.m will both cause the interface to attempt to execute a Matlab function myanalysis for the evaluation. #### Matlab .m file specification The Matlab analysis file myanalysis.m must define a Matlab function that accepts a Matlab structure as its sole argument and returns the same structure in a variable called Dakota. A manual execution of the call to the analysis in Matlab should therefore look like: >> Dakota = myanalysis(Dakota)  Note that the structure named Dakota will be pushed into the Matlab workspace before the analysis function is called. The structure passed from Dakota to the analysis m-function contains essentially the same information that would be passed to a Dakota direct function included in DirectApplicInterface.C, with fields shown in Figure Listing 65. Listing 65 Dakota/Matlab parameter data structure. Dakota. numFns number of functions (responses, constraints) numVars total number of variables numACV number active continuous variables numADIV number active discrete integer variables numADRV number active discrete real variables numDerivVars number of derivative variables specified in directFnDVV xC continuous variable values ([1 x numACV]) xDI discrete integer variable values ([1 x numADIV]) xDR discrete real variable values ([1 x numADRV]) xCLabels continuous var labels (cell array of numACV strings) xDILabels discrete integer var labels (cell array of numADIV strings) xDRLabels discrete real var labels (cell array of numADIV strings) directFnASV active set vector ([1 x numFns]) directFnDVV derivative variables vector ([1 x numDerivVars]) fnFlag nonzero if function values requested gradFlag nonzero if gradients requested hessFlag nonzero if hessians requested currEvalId current evaluation ID  The structure Dakota returned from the analysis must contain a subset of the fields shown in Figure Listing 66. It may contain additional fields and in fact is permitted to be the structure passed in, augmented with any required outputs. Listing 66 Dakota/Matlab response data structure. Dakota. fnVals ([1 x numFns], required if function values requested) fnGrads ([numFns x numDerivVars], required if gradients requested) fnHessians ([numFns x numDerivVars x numDerivVars], required if hessians requested) fnLabels (cell array of numFns strings, optional) failure (optional: zero indicates success, nonzero failure  An example Matlab analysis driver rosenbrock.m for the Rosenbrock function is shown in Figure Listing 67. Listing 67 Sample Matlab implementation of the Rosenbrock test function for the Dakota/Matlab interface. function Dakota = rosenbrock(Dakota) Dakota.failure = 0; if ( Dakota.numVars ~= 2 | Dakota.numADV | ... ( ~isempty( find(Dakota.directFnASM(2,:)) | ... find(Dakota.directFnASM(3,:)) ) & Dakota.numDerivVars ~= 2 ) ) sprintf('Error: Bad number of variables in rosenbrock.m fn.\n'); Dakota.failure = 1; elseif (Dakota.numFns > 2) % 1 fn -> opt, 2 fns -> least sq sprintf('Error: Bad number of functions in rosenbrock.m fn.\n'); Dakota.failure = 1; else if Dakota.numFns > 1 least_sq_flag = true; else least_sq_flag = false; end f0 = Dakota.xC(2)-Dakota.xC(1)*Dakota.xC(1); f1 = 1.-Dakota.xC(1); % **** f: if (least_sq_flag) if Dakota.directFnASM(1,1) Dakota.fnVals(1) = 10*f0; end if Dakota.directFnASM(1,2) Dakota.fnVals(2) = f1; end else if Dakota.directFnASM(1,1) Dakota.fnVals(1) = 100.*f0*f0+f1*f1; end end % **** df/dx: if (least_sq_flag) if Dakota.directFnASM(2,1) Dakota.fnGrads(1,1) = -20.*Dakota.xC(1); Dakota.fnGrads(1,2) = 10.; end if Dakota.directFnASM(2,2) Dakota.fnGrads(2,1) = -1.; Dakota.fnGrads(2,2) = 0.; end else if Dakota.directFnASM(2,1) Dakota.fnGrads(1,1) = -400.*f0*Dakota.xC(1) - 2.*f1; Dakota.fnGrads(1,2) = 200.*f0; end end % **** d^2f/dx^2: if (least_sq_flag) if Dakota.directFnASM(3,1) Dakota.fnHessians(1,1,1) = -20.; Dakota.fnHessians(1,1,2) = 0.; Dakota.fnHessians(1,2,1) = 0.; Dakota.fnHessians(1,2,2) = 0.; end if Dakota.directFnASM(3,2) Dakota.fnHessians(2,1:2,1:2) = 0.; end else if Dakota.directFnASM(3,1) fx = Dakota.xC(2) - 3.*Dakota.xC(1)*Dakota.xC(1); Dakota.fnHessians(1,1,1) = -400.*fx + 2.0; Dakota.fnHessians(1,1,2) = -400.*Dakota.xC(1); Dakota.fnHessians(1,2,1) = -400.*Dakota.xC(1); Dakota.fnHessians(1,2,2) = 200.; end end Dakota.fnLabels = {'f1'}; end  ### Python Dakota’s Python direct interface has been tested on Linux with Python 2 and 3. When enabled, it allows Dakota to make function evaluation calls directly to an analysis function in a user-provided Python module. Data may flow between Dakota and Python either in multiply-subscripted lists or NumPy arrays. The Python direct interface must be enabled when compiling Dakota. Set the CMake variable DAKOTA_PYTHON:BOOL=ON, and optionally DAKOTA_PYTHON_NUMPY:BOOL=ON (default is ON) to use Dakota’s NumPy array interface (requires NumPy installation providing arrayobject.h). If NumPy is not enabled, Dakota will use multiply-subscripted lists for data flow. An example of using the Python direct interface with both lists and arrays is included in dakota/share/dakota/examples/official/drivers/Python/linked/. The Python direct driver is selected with, for example, interface, python # numpy analysis_drivers = 'python_module:analysis_function'  where python_module denotes the module (file python_module.py) Dakota will attempt to import into the Python environment and analysis_function denotes the function to call when evaluating a parameter set. If the Python module is not in the directory from which Dakota is started, setting the PYTHONPATH environment variable to include its location can help the Python engine find it. The optional numpy keyword indicates Dakota will communicate with the Python analysis function using numarray data structures instead of the default lists. Whether using the list or array interface, data from Dakota is passed (via kwargs) into the user function in a dictionary containing the entries shown in Table Table 13. The analysis_function must return a dictionary containing the data specified by the active set vector with fields “fns”, “fnGrads”, and “fnHessians”, corresponding to function values, gradients, and Hessians, respectively. The function may optionally include a failure code in “failure” (zero indicates success, nonzero failure) and function labels in “fnLabels”. When metadata are active, they must be returned as an array of floats in the dictionary field “metadata”. See the linked interfaces example referenced above for more details. Table 13 Data dictionary passed to Python direct interface. Entry Name Description variables total number of variables functions number of functions (responses, constraints) metadata number of metadata fields variable_labels variable labels in input specification order function_labels function (response, constraint) labels metadata_labels metadata field labels cv list/array of continuous variable values cv_labels continuous variable labels div list/array of discrete integer variable values div_labels discrete integer variable labels dsv list of discrete string variable values (NumPy not supported) dsv_labels discrete string variable labels drv list/array of discrete real variable values drv_labels discrete real variable labels asv active set vector dvv derivative variables vector (list of one-based variable IDs) analysis_components list of analysis components strings eval_id one-based evaluation ID number ## Scilab Script and Direct Interfaces Scilab is open source computation software which can be used to perform function evaluations during Dakota studies, for example to calculate the objective function in optimization. Dakota includes three Scilab interface variants: scripted, linked, and compiled. In each mode, Dakota calls Scilab to perform a function evaluation and then retrieves the Scilab results. Dakota’s Scilab interface was contributed in 2011 by Yann Collette and Yann Chapalain. The Dakota/Scilab interface variants are described next. ### Scilab Script Interface Dakota distributions include a directory dakota/share/dakota/examples/users/Scilab/script/ which demonstrates script-based interfacing to Scilab. The Rosenbrock subdirectory contains four notable files: • dakota_scilab_rosenbrock.in (the Dakota input file), • rosenbrock.sci (the Scilab computation code), • scilab_rosen_bb_simulator.sh (the analysis driver), and • scilab_rosen_wrapper.sci (Scilab script). The dakota_scilab_rosenbrock.in file specifies the Dakota study to perform. The interface type is external (fork) and the shell script scilab_rosen_bb_simulator.sh is the analysis driver used to perform function evaluations. The Scilab file rosenbrock.sci accepts variable values and computes the objective, gradient, and Hessian values of the Rosenbrock function as requested by Dakota. The scilab_rosen_bb_simulator.sh is a short shell driver script, like that described in Section Building a Black-Box Interface to a Simulation Code, that Dakota executes to perform each function evaluation. Dakota passes the names of the parameters and results files to this script as $argv[1] and $argv[2], respectively. The scilab_rosen_bb_simulator.sh is divided into three parts: pre-processing, analysis, and post-processing. In the analysis portion, the scilab_rosen_bb_simulator.sh uses scilab_rosen_wrapper.sci to extract the current variable values from the input parameters file ($argv[1]) and communicate them to the computation code in rosenbrock.sci. The resulting objective function is transmitted to Dakota via the output result file ($argv[1]), and the driver script cleans up any temporary files. The directory also includes PID and FemTRUSS examples, which are run in a similar way. ### Scilab Linked Interface The Dakota/Scilab linked interface allows Dakota to communicate directly with Scilab through in-memory data structures, typically resulting in faster communication, as it does not rely on files or pipes. In this mode, Dakota publishes a data structure into the Scilab workspace, and then invokes the specified Scilab analysis_driver directly. In Scilab, this structure is an mlist (http://help.scilab.org/docs/5.3.2/en_US/mlist.html), with the same fields as in the Matlab interface Listing 65, with the addition of a field dakota_type, which is used to validate the names of fields in the data structure. The linked interface is implemented in source files src/ScilabInterface.[CH] directory, and must be enabled at compile time when building Dakota from source by setting DAKOTA_SCILAB:BOOL=ON, and setting appropriate environment variables at compile and run time as described in README.Scilab in dakota/share/dakota/examples/users/Scilab/linked/. This directory also contains examples for the Rosenbrock and PID problems. A few things to note about these examples: 1. There is no shell driver script 2. The Dakota input file specifies the interface as ’scilab’, indicating a direct, internal interface to Scilab using the Dakota data structure described above: interface, scilab analysis_driver = 'rosenbrock.sci'  ### Scilab Compiled Interface In “compiled interface” mode, the Dakota analysis driver is a lightweight shim, which communicates with the running application code such as Scilab via named pipes. It is similar to that for Matlab in dakota/share/dakota/examples/users/MATLAB/compiled/, whose README is likely instructive. An example of a Scilab compiled interface is included in dakota/share/dakota/examples/users/Scilab/compiled/Rosenbrock/. As with the other Scilab examples, there are computation code and Dakota input files. Note the difference in the Dakota input file rosenbrock.in, where the analysis driver starts the dakscilab shim program and always evaluates functions, gradients, and Hessians. interface, fork analysis_driver = '../dakscilab -d -fp "exec fp.sci" -fpp "exec fpp.sci"' parameters_file = 'r.in' results_file = 'r.out' deactivate active_set_vector  The dakscilab executable results from compiling dakscilab.c and has the following behavior and options. The driver dakscilab launches a server. This server then facilitates communication between Dakota and Scilab via named pipes communication. The user can also use the first named pipe (${DAKSCILAB_PIPE}1) to communicate with the server:

echo dbg scilab_script.sce > ${DAKSCILAB_PIPE}1 echo quit >${DAKSCILAB_PIPE}1


The first command, with the keyword ’dbg’, launches the script scilab_script.sci for evaluation in Scilab. It permits to give instructions to Scilab. The second command ’quit’ stops the server.

The dakscilab shim supports the following options for the driver call:

1. -s to start the server

2. -si to run an init script

3. -sf to run a final script

4. -f -fp -fpp to specify names of objective function, gradient and hessian, then load them.

For the included PID example, the driver call is

analysis_driver = '../dakscilab -d -si "exec init_test_automatic.sce;"
-sf "exec visualize_solution.sce;" -f "exec f_pid.sci"'


Here there is an initialization script (init_test_automatic.sce) which is launched before the main computation. It initializes a specific Scilab module called xcos. A finalization script to visualize the xcos solution is also specified (visualize_solution.sce). Finally, the objective function is given with the computation code called f_pid.sci.