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Collaboration diagram for Formula Processing: f(x), df/dx:
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Modules | |
| AST Manipulations | |
| Diverse Functions to manipulate libSBML Abstract Syntax Trees. | |
Functions | |
| SBML_ODESOLVER_API void | setUserDefinedFunction (double(*udf)(char *, int, double *)) |
| Sets function pointer for user defined function to udf. | |
| ASTNode_t * | copyAST (const ASTNode_t *f) |
| Copies the passed AST, including potential SOSlib ASTNodeIndex, and returns the copy. | |
| SBML_ODESOLVER_API double | evaluateAST (ASTNode_t *n, cvodeData_t *data) |
| Evaluates the passed formula n by a simple recursion and returns the result as a double value. | |
| SBML_ODESOLVER_API ASTNode_t * | differentiateAST (ASTNode_t *f, char *x) |
| Returns the derivative f' of the passed formula f with respect to the passed variable x, using basic differentiation rules. | |
| ASTNode_t * | determinantNAST (ASTNode_t ***A, int N) |
| !! experimental function determinantNAST !! NOT TESTED !! !! WILL RUN OUT OF MEMORY FOR BIG SYSTEMS !! calculates the determinant of the jacobian matrix, is not used and can only be activated with hidden commandline option -d. | |
These functions are used both for numerical and symbolic analysis
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Sets function pointer for user defined function to udf. Takes a function pointer as an argument. This function udf is called in evaluateAST to interface external data that can be supplied by a calling applications. It must return a double value for the current time of an integration run. ARGUMENTS TO THE PASSED FUNCTION: char *: must be the name of a function used in any formula in the SBML file, but not defined via an SBML Function Definition in the same SBML model int: is the number of arguments the SBML function takes, which is also the size of the following double array double *: is an array that is filled by evaluateAST to supply the external function with current values of the arguments of the respective function the SBML model POSSIBLE APPLICATIONS: Setting a set of udfs could later also be used to enhance integration performance by using SBML sboTerms in kinetic laws, i.e. for hard-coded kinetic law evaluation! The function might also be useful for introducing stochastic effects to the ODE system. An external function could call a random number generator. Sorry, if above description is confusing, because of two different types of `function'. Basically, it allows a hard-coded definition of an otherwise undefined function in the SBML file. While this would be invalid SBML (!), it allows a model to access external data. We will in one of the next releases provide an example of a simple interpolation function, that takes only the current time as argument and interpolates a value for the current time from an external time series data set. |
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Copies the passed AST, including potential SOSlib ASTNodeIndex, and returns the copy.
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Evaluates the passed formula n by a simple recursion and returns the result as a double value. Variable names are searched in passed cvodeData, which is an SBML_odeSolver specific data structure, containing current values of indexed AST. See files cvodedata.c/h and odeConstruct.c to learn how this structure is built. Not implemented:
The node type AST_DELAY defaults to 0. The SBML DELAY function and unknown functions (SBML user-defined functions) use the value of the left child (first argument to function) or 0 if the node has no children and produce an errorMessage via SOSlibs Error Management System. VARIABLES: find the value of the variable in the data->value array. SOSlib's extension to libSBML's AST allows to add the index of the variable in this array to AST_NAME (ASTIndexName). If the ASTNode is not indexed, its array index is searched via the data->model->names array, which corresponds to the data->value array. For nodes with name `Time' or `time' the data->currenttime is returned. If no value is found a fatal error is produced. exp(1) is used to adjust exponentiale to machine precision pi = 4 * atan 1 is used to adjust Pi to machine precision FUNCTIONS: Evaluate external functions, if it was set with setUserDefinedFunction arccot x = arctan (1 / x) arccoth x = 1/2 * ln((x+1)/(x-1)) arccsc(x) = Arctan(1 / sqrt((x - 1)(x + 1))) arccsch(x) = ln((1 + sqrt(1 + x^2)) / x) arcsec(x) = arctan(sqrt((x - 1)(x + 1))) arcsech(x) = ln((1 + sqrt(1 - x^2)) / x) cot x = 1 / tan x coth x = cosh x / sinh x csc x = 1 / sin x csch x = 1 / sinh x log(x,y) = log10(y)/log10(x) (where x is the base) sec x = 1 / cos x sech x = 1 / cosh x |
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Returns the derivative f' of the passed formula f with respect to the passed variable x, using basic differentiation rules. VARIABLES check if variable x is part of f(x): if not f' = 0 f(x) = x => f' = 1 OPERATORS f(x)=a(x)+b(x) => f'(x) = a' + b' f(x)=a(x)-b(x) => f'(x) = a' - b' catch n-ary operators with operand number != 2, and decompose in simplifyAST f(x)=a(x)*b(x) => f'(x) = a'*b + a*b' f(x)=a(x)/b(x) => f'(x) = a'/b - a/b^2*b' f(x)=a(x)^b => f'(x) = b * a^(b-1)*a' f(x)=a^b(x) => f'(x) = f * ln(a)*b' f(x)=a(x)^b(x) => f'(x)= f * ( b/a*a' + ln(a)*b' ) FUNCTIONS: f(x)=abs(a(x)) => f' = sig(a)*a' WRONG: CAN RESULT IN A DISCONTINUOUS FUNCTION! TRIGONOMETRIC FUNCTION DERIVATIVES mostly taken from http://www.rism.com/Trig/circular.htm and http://www.rism.com/Trig/hyperbol.htm f(x)=arccos(a(x)) => f' = - a' / sqrt(1 - a^2) f(x)=arccosh(a(x)) => f' = a' / sqrt(a^2 - 1) f(x)=arccot(a(x)) => f' = - a' / (1 + a^2) f(x)=arccoth(a(x)) => f' = - a' / (-1 + a^2) f(x)=arccsc(a(x)) => f' = - a' * a * sqrt(a^2 - 1) f(x)=arccos(a(x)) => f' = - a' * a * sqrt(a^2 + 1) f(x)=arcsec(a(x)) => f' = a' * a * sqrt(a^2 - 1) f(x)=arcsech(a(x)) => f' = - a' * a * sqrt(1 - a^2) f(x)=arcsin(a(x)) => f' = a' / sqrt(1 - a^2) f(x)=arcsinh(a(x)) => f' = a' / sqrt(1 + a^2) f(x)=atan(a(x)) => f' = a' / (1 + a^2) f(x)=atan(a(x)) => f' = a' / (1 - a^2) f(x) = ceil(a(x)) f(x)=cos(a(x)) => f' = a' * -sin(a) f(x)=cosh(a(x)) => f' = a' * -sinh(a) f(x)=cot(a(x)) => f' = - a' / (sin(a))^2 f(x)=cot(a(x)) => f' = - a' / (sinh(a))^2 f(x)=csc(a(x)) => f' = - a' * csc(a) * cot(a) f(x)=csch(a(x)) => f' = - a' * csch(a) * coth(a) f(x)=e^a(x) => f' = e^a * a' f(x) = floor(a(x)) WRONG: CAN RESULT IN A DISCONTINUOUS FUNCTION! f(x)=ln(a(x)) => f' = 1 / a * a' f(x)=log(b,x) = 1/ln(b)*ln(x) differentiate ln(x)! f(x)=root(a(x),b(x)) = a(x)^(1/b(x)) differentiate this! f(x)=sec(a(x)) => f' = a' * sec(a) * tan(x) f(x)=sech(a(x)) f' = - a' * sech(a) * tanh(a) f(x)=sin(a(x)) => f' = a' * cos(a) f(x)=sinh(a(x)) => f' = a' * cosh(a) f(x)= tan(a(x)) => f' = a' / (cos(a))^2 f(x)= tanh(a(x)) => f' = a' / (cosh(a))^2 |
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!! experimental function determinantNAST !! NOT TESTED !! !! WILL RUN OUT OF MEMORY FOR BIG SYSTEMS !! calculates the determinant of the jacobian matrix, is not used and can only be activated with hidden commandline option -d. Doesn't work if expressions get too big for yet unknown reasons!?? |
1.4.4