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/* |
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* Function module |
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* by Tom Epperly |
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* Version: $Revision: 1.16 $ |
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* Version control file: $RCSfile: func.h,v $ |
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* Date last modified: $Date: 2001/01/31 22:23:57 $ |
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* Last modified by: $Author: ballan $ |
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* |
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* This file is part of the Ascend Language Interpreter. |
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* |
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* Copyright (C) 1990, 1993, 1994 Thomas Guthrie Epperly |
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* |
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* The Ascend Language Interpreter is free software; you can redistribute |
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* it and/or modify it under the terms of the GNU General Public License as |
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* published by the Free Software Foundation; either version 2 of the |
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* License, or (at your option) any later version. |
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* |
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* The Ascend Language Interpreter is distributed in hope that it will be |
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* useful, but WITHOUT ANY WARRANTY; without even the implied warranty of |
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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* General Public License for more details. |
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* |
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* You should have received a copy of the GNU General Public License |
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* along with the program; if not, write to the Free Software Foundation, |
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* Inc., 675 Mass Ave, Cambridge, MA 02139 USA. Check the file named |
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* COPYING. |
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* |
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* Revision notes: |
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* If CHRIS_FUNC defined, auxillary quantities to func structure. |
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* 2/96 baa Probably somebody should properly set these evaluation |
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* defined below based on math.h when possible. |
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* |
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*/ |
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|
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/** @file |
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* Function module. |
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* <pre> |
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* When #including func.h, make sure these files are #included first: |
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* #include "utilities/ascConfig.h" |
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* #include "fractions.h" |
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* #include "compiler.h" |
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* #include "dimen.h" |
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* #include "functype.h" |
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* </pre> |
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* @todo Complete documentation of func.h. |
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*/ |
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|
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#ifndef __FUNC_H_SEEN__ |
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#define __FUNC_H_SEEN__ |
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|
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/* |
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* the following should be ifdefed to deal with math.h values |
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*/ |
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#define F_ERF_COEF 1.1283791670955130 /**< = 2 / sqrt(PI) */ |
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#define F_LOG10_COEF 0.4342944819032518 /**< = log10(e) = 1/ln(10) */ |
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#define F_PI 3.1415926535897932385E0 |
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#define F_PI_HALF 1.5707963267948966192E0 |
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#define F_LIM_EXP 709.78 /**< approximately ln(maxdouble) */ |
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#define F_LIM_CUBE 5.6438030941223618e101 /**< cbrt(maxdouble)*/ |
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#define F_LIM_SQR 1.0e154 /**< sqrt(maxdouble) */ |
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|
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#ifdef __STDC__ |
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#if __STDC__ |
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/** |
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* stdc==1 --> erf, cbrt not defined in headers. user should link |
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* against a library that does provide them. ASCEND is research |
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* code: we aren't going to waste time reimplementing these basic |
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* functions. |
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*/ |
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extern double DLEXPORT cbrt(double); |
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#ifdef HAVE_ERF |
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extern double erf(double); |
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#endif /* HAVE_ERF */ |
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#endif /* __STDC__ == 1*/ |
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/**< |
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* in the case where __STDC__ is defined but == 0, system headers |
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* should provide cbrt, erf. |
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*/ |
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#endif /* stdc defined */ |
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|
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extern CONST struct Func *LookupFunc(CONST char *name); |
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/**< |
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* <!-- const struct Func *LookupFunc(name) --> |
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* <!-- const char *name; (ascend name, not C) --> |
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* Lookup the function with the given name. If no match is found, it |
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* returns NULL. name is the ASCEND name, not C name. |
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* <pre> |
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* Currently defined: |
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* "exp" e^x |
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* "ln" natural logarithm of x |
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* "log" logarithm of x base 10 |
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* "sin" sine of x |
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* "cos" cosine of x |
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* "tan" tangent of x |
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* "sqr" x*x |
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* "sqrt" the square root of x |
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* "arcsin" the inverse sine of x |
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* "arccos" the inverse cosine of x |
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* "arctan" the inverse tangent of x |
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* |
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* "erf" the error function |
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* "lnm" modified natural log: |
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* x>epsilon? ln(x): x/epsilon +ln(epsilon) -1 |
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* "sinh" hyperbolic sine |
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* "cosh" hyperbolic cosine |
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* "tanh" hyperbolic tangent |
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* "arcsinh" inv hyperbolic sine |
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* "arccosh" inv hyperbolic cosine |
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* "arctanh" inv hyperbolic tangent |
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* |
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* "cube" the cube of x |
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* "cbrt" the cube root of x |
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* "abs" absolute value of x |
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* |
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* "hold" returns the current value of x. |
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* </pre> |
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* The last 10 are not fully supported for chris.[ch] |
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* All functions return principal (postive) values if there is a choice. |
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* None of them perform range checking. ln(-1) -> float error. |
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*/ |
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|
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extern CONST struct Func *LookupFuncById(enum Func_enum id); |
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/**< |
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* <!-- const struct Func *LookupFuncById(id) --> |
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* <!-- enum Func_emum id; --> |
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* Lookups a function by its enumerated type rather than by a string as |
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* in the above function. |
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*/ |
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|
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extern double FuncGetLnmEpsilon(void); |
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/**< |
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* Return the current epsilon for the modified log function lnm. |
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*/ |
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#define FuncGetLnmEpsilon() (g_lnm_epsilon) |
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|
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extern void FuncSetLnmEpsilon(double e); |
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/**< |
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* Change the current epsilon for the modified log function lnm. |
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* epsilon > 0.0. |
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*/ |
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extern double g_lnm_epsilon; |
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#define FuncSetLnmEpsilon(e) \ |
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(e>(double)0.0 ? g_lnm_epsilon=e : FPRINTF(ASCERR,"bad lnm eps")) |
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|
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/**< |
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* declare cbrt() and erf() since some vendors put |
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* these functions in odd headers |
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*/ |
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extern double DLEXPORT cbrt(double); |
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#ifdef HAVE_ERF |
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extern double erf(double); |
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#endif /* HAVE_ERF */ |
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|
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#ifdef NDEBUG |
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#define ascnint(d) (((int) (d)>=0.0 ? floor((d) + 0.5) : -floor(0.5 - (d)))) |
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/**< |
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* Converts a double to the nearest integer (release version). |
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* @param d double, the real number to convert. |
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* @return The nearest integer as an int. |
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*/ |
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#else |
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#define ascnint(a) ascnintF(a) |
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/**< |
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* Converts a double to the nearest integer (debug version). |
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* @param d double, the real number to convert. |
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* @return The nearest integer as an int. |
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*/ |
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extern int DLEXPORT ascnintF(double); |
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/**< |
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* Implementation function for debug version of ascnint(). |
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* Do not call this function directly - use ascnint() instead. |
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*/ |
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|
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#endif |
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|
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extern double DLEXPORT dln(double x); |
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extern double DLEXPORT dln2(double x); |
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extern double DLEXPORT dlog(double x); |
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extern double DLEXPORT dlog2(double x); |
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extern double DLEXPORT lnm(double x); |
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extern double DLEXPORT dlnm(double x); |
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extern double DLEXPORT dlnm2(double x); |
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/**< |
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* Modified natural log function and derivatives. |
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* <pre> |
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* |
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* ( ln(x) if x.ge.epsilon |
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* lnm(x)= ( |
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* ( x/epsilon + ln(epsilon) - 1 otherwise |
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* |
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* |
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* ( 1/x if x.ge.epsilon |
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* d( lnm(x) )/dx = ( |
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* ( 1/epsilon otherwise |
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* |
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* |
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* ( -1/x^2 if x.ge.epsilon |
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* d^2( lnm(x) )/dx^2 = ( |
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* ( 0 otherwise |
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* |
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* epsilon determined by FuncGet/SetLnmEpsilon. |
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* </pre> |
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*/ |
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|
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extern double DLEXPORT dtanh(double x); |
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extern double DLEXPORT dtanh2(double x); |
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extern double DLEXPORT arcsinh(double x); |
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extern double DLEXPORT arccosh(double x); |
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extern double DLEXPORT arctanh(double x); |
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extern double DLEXPORT darcsinh(double x); |
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extern double DLEXPORT darcsinh2(double x); |
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extern double DLEXPORT darccosh(double x); |
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extern double DLEXPORT darccosh2(double x); |
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extern double DLEXPORT darctanh(double x); |
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extern double DLEXPORT darctanh2(double x); |
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/**< |
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* Zero, first and second partials of (inverse) hyperbolic functions. |
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*/ |
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|
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extern double DLEXPORT sqr(double x); |
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extern double DLEXPORT dsqr(double x); |
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extern double DLEXPORT dsqr2(double x); |
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extern double DLEXPORT cube(double x); |
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extern double DLEXPORT dcube(double x); |
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extern double DLEXPORT dcube2(double x); |
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/**< |
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* Zero, first and second partials of x for sqr, cube. |
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*/ |
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|
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extern double DLEXPORT asc_ipow(double a, int n); |
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extern double DLEXPORT asc_d1ipow(double a, int n); |
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extern double DLEXPORT asc_d2ipow(double a, int n); |
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/**< |
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* Integer power function, a^n, and its first and second derivatives. |
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* d = asc_ipow(a,n); |
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* d1 = asc_d1ipow(a,n); |
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* d2 = asc_d2ipow(a,n); |
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* |
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* Special cases ipow: |
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* a^0 = 1, 0^n = 0, 0^0=1 -- the last is mathematically undefined, |
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* so this function should not be called with 0.0,0. |
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* |
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* Special cases d1ipow,d2ipow: |
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*/ |
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|
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extern double DLEXPORT hold(double x); |
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/**< |
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* Returns the value it is passed. |
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* The primary purpose is as an operator so we can write |
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* equations of the form x = hold(x) which act essentially |
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* as a fixed flag when a solver is partitioning. |
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* If x is fixed, the equation is singular. |
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* hold(x) is a constant value, so its derivatives are 0. |
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*/ |
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|
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extern double DLEXPORT dsqrt(double x); |
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extern double DLEXPORT dsqrt2(double x); |
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extern double DLEXPORT dcbrt(double x); |
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extern double DLEXPORT dcbrt2(double x); |
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extern double DLEXPORT dfabs(double x); |
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extern double DLEXPORT dfabs2(double x); |
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extern double DLEXPORT dhold(double x); |
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#define dhold2 dhold |
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/**< |
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* first and second partials of sqrt cbrt fabs hold |
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* dfabs is undefined at 0. We take the standard kluge: d(abs(x=0))/dx=0 |
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* dfabs2(x) = 0. It might be thought of as infinite at x=0, but not here. |
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* dhold, dhold2 = 0 for all x. |
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*/ |
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|
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extern double DLEXPORT dasin(double x); |
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extern double DLEXPORT dasin2(double x); |
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extern double DLEXPORT dcos(double x); |
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extern double DLEXPORT dcos2(double x); |
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extern double DLEXPORT dacos(double x); |
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extern double DLEXPORT dacos2(double x); |
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extern double DLEXPORT dtan(double x); |
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extern double DLEXPORT dtan2(double x); |
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extern double DLEXPORT datan(double x); |
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extern double DLEXPORT datan2(double x); |
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/**< |
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* First and second partials of the cosine, tangent, arctangent functions |
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*/ |
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|
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#ifdef HAVE_ERF |
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extern double DLEXPORT derf(double x); |
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extern double DLEXPORT derf2(double x); |
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#endif /* HAVE_ERF */ |
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/**< |
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* First and second derivatives of erf() |
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*/ |
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|
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extern CONST char *FuncName(CONST struct Func *f); |
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/**< |
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* <!-- const char *FuncName(f) --> |
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* <!-- const struct Func *f; --> |
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* Return the ASCEND language name of the function. |
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* Not a symchar. |
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*/ |
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|
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extern CONST char *FuncCName(CONST struct Func *f); |
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/**< |
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* <!-- const char *FuncCName(f) --> |
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* <!-- const struct Func *f; --> |
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* Return the C language name of the function, if any. |
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*/ |
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|
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extern CONST char *FuncDeriv1CName(CONST struct Func *f); |
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/**< |
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* <!-- const char *FuncDerive1CName(f) --> |
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* <!-- const struct Func *f; --> |
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* Return the C language name of the function first derivative, if any. |
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*/ |
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|
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extern CONST char *FuncDeriv2CName(CONST struct Func *f); |
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/**< |
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* <!-- const char *FuncName(f) --> |
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* <!-- const struct Func *f; --> |
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* Return the C language name of the function second derivative, if any. |
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*/ |
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|
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extern enum Func_enum FuncId(CONST struct Func *f); |
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/**< |
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* <!-- enum Func_enum FuncId(f) --> |
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* <!-- const struct Func *f; --> |
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* Return the identification of the function. |
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*/ |
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|
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extern CONST dim_type *FuncDimens(CONST struct Func *f); |
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/**< |
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* <!-- dim_type *FuncDimens(f) --> |
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* <!-- const struct Func *f; --> |
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* Return the dimensionality required for the arg of the function. |
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* sin, cos, tan -> P. |
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* arc(sin,cos,tan),exp,ln,log,lnm,erf ->dimensionless. |
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* sqrt->wilddimension (user must check for even poweredness of arg) |
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* as this may be the case for an infinite # of different dims. |
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* sqr ->wilddimension (sqr, abs, cube anything you like.) |
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*/ |
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|
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extern double FuncEval(CONST struct Func *f, double u); |
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/**< |
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* <!-- double FuncEval(f,u) --> |
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* <!-- const struct Func *f; --> |
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* <!-- double u; --> |
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* Return f(u). |
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*/ |
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|
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extern double FuncEvalSafe(CONST struct Func *f, |
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double u, |
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enum safe_err *not_safe); |
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/**< |
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* <!-- double FuncEval(f,u,not_safe) --> |
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* <!-- const struct Func *f; --> |
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* <!-- double u; --> |
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* <!-- enum safe_err *not_safe; --> |
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* Return f(u) (safe version). |
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*/ |
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|
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extern double FuncDeriv(CONST struct Func *f, double u); |
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/**< |
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* <!-- double FuncDeriv(f,u) --> |
| 363 |
* <!-- const struct Func *f; --> |
| 364 |
* <!-- double u; --> |
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* Return df/du evaluated at u. |
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*/ |
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|
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extern double FuncDerivSafe(CONST struct Func *f, |
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double u, |
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enum safe_err *not_safe); |
| 371 |
/**< |
| 372 |
* <!-- double FuncDerivSafe(f,u,not_safe) --> |
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* <!-- const struct Func *f; --> |
| 374 |
* <!-- double u; --> |
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* <!-- enum safe_err *not_safe; --> |
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* Return df/du evaluated at u (safe version). |
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*/ |
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|
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extern double FuncDeriv2(CONST struct Func *f, double u); |
| 380 |
/**< |
| 381 |
* <!-- double FuncDeriv2(f,u) --> |
| 382 |
* <!-- const struct Func *f; --> |
| 383 |
* <!-- double u; --> |
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* Return the second derivative (d^2f/du^2) evaluated at u. |
| 385 |
*/ |
| 386 |
|
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extern double FuncDeriv2Safe(CONST struct Func *f, |
| 388 |
double u, |
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enum safe_err *not_safe); |
| 390 |
/**< |
| 391 |
* <!-- double FuncDeriv2(f,u,not_safe) --> |
| 392 |
* <!-- const struct Func *f; --> |
| 393 |
* <!-- double u; --> |
| 394 |
* <!-- enum safe_err *not_safe; --> |
| 395 |
* Return the second derivative (d^2f/du^2) evaluated at u (safe version). |
| 396 |
*/ |
| 397 |
|
| 398 |
#ifdef CHRIS_FUNC |
| 399 |
|
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extern struct Interval FuncRange(CONST struct Func *f, struct Interval i); |
| 401 |
/**< |
| 402 |
* <!-- struct Interval FuncRange(f,i) --> |
| 403 |
* <!-- const struct Func *f; --> |
| 404 |
* <!-- struct Interval i; --> |
| 405 |
* Return a bound on the range of the function over the given interval. |
| 406 |
*/ |
| 407 |
|
| 408 |
extern void FuncSlope(CONST struct Func *f, |
| 409 |
unsigned long nvar, |
| 410 |
struct Interval *center, |
| 411 |
struct Interval *range, |
| 412 |
struct Interval *slope); |
| 413 |
/**< |
| 414 |
* <!-- struct Interval FuncSlope(f,nvar,center,range,slope) --> |
| 415 |
* <!-- const struct Func *f; --> |
| 416 |
* <!-- unsigned long nvar; --> |
| 417 |
* <!-- struct Interval *center,*range; --> |
| 418 |
* <!-- struct Interval slope[]; --> |
| 419 |
* Perform the interval slope calculation. |
| 420 |
*/ |
| 421 |
|
| 422 |
extern struct Interval FuncIDeriv(CONST struct Func *f, struct Interval i); |
| 423 |
/**< |
| 424 |
* <!-- struct Interval FuncIDeriv(f,i) --> |
| 425 |
* <!-- const struct Func *f --> |
| 426 |
* <!-- struct Interval i; --> |
| 427 |
*/ |
| 428 |
|
| 429 |
extern double ArgMin(CONST struct Func *f, double lower, double upper); |
| 430 |
/**< |
| 431 |
* <!-- double ArgMin(f,lower,upper) --> |
| 432 |
* <!-- const struct Func *f; --> |
| 433 |
* <!-- double lower,upper; --> |
| 434 |
* Return the arg min of the function over the range. |
| 435 |
*/ |
| 436 |
|
| 437 |
extern double ArgMax(CONST struct Func *f, double lower, double upper); |
| 438 |
/**< |
| 439 |
* <!-- double ArgMax(f,lower,upper) --> |
| 440 |
* <!-- CONST struct Func *f; --> |
| 441 |
* <!-- double lower,upper; --> |
| 442 |
* Return the arg max of the function over the range. |
| 443 |
*/ |
| 444 |
|
| 445 |
extern double ConvexEnv(CONST struct Func *f, double x, |
| 446 |
double lower, double upper); |
| 447 |
/**< |
| 448 |
* <!-- double ConvexEnv(f,x,lower,upper) --> |
| 449 |
* <!-- CONST struct Func *f; --> |
| 450 |
* <!-- double x,lower,upper; --> |
| 451 |
* Return the value of the convex envelope of the function at the value |
| 452 |
* x which ranges from lower to upper. |
| 453 |
*/ |
| 454 |
|
| 455 |
extern double ConvexEnvDeriv(CONST struct Func *f, double x, |
| 456 |
double lower, double upper); |
| 457 |
/**< |
| 458 |
* <!-- double ConvexEnvDeriv(f,x,lower,upper) --> |
| 459 |
* <!-- CONST struct Func *f; --> |
| 460 |
* <!-- double x,lower,upper; --> |
| 461 |
* Return the derivative of the convex envelope of the function at the |
| 462 |
* value x which ranges from lower to upper. |
| 463 |
*/ |
| 464 |
|
| 465 |
extern double ConcaveEnv(CONST struct Func *f, double x, |
| 466 |
double lower, double upper); |
| 467 |
/**< |
| 468 |
* <!-- double ConcaveEnv(f,x,lower,upper) --> |
| 469 |
* <!-- CONST struct Func *f; --> |
| 470 |
* <!-- double x,lower,upper; --> |
| 471 |
* Return the value of the concave envelope of the function at the value |
| 472 |
* x which ranges from lower to upper. |
| 473 |
*/ |
| 474 |
|
| 475 |
extern double ConcaveEnvDeriv(CONST struct Func *f, double x, |
| 476 |
double lower, double upper); |
| 477 |
/**< |
| 478 |
* <!-- double ConcaveEnvDeriv(f,x,lower,upper) --> |
| 479 |
* <!-- CONST struct Func *f; --> |
| 480 |
* <!-- double x,lower,upper; --> |
| 481 |
* Return the derivative of the concave envelope of the function at the |
| 482 |
* value x which ranges from lower to upper. |
| 483 |
*/ |
| 484 |
|
| 485 |
#endif /* CHRIS_FUNC */ |
| 486 |
|
| 487 |
#endif /* __FUNC_H_SEEN__ */ |
| 488 |
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