# AIMMS Function Reference - Arithmetic Functions

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1 AIMMS Function Reference - Arithmetic Functions This file contains only one chapter of the book. For a free download of the complete book in pdf format, please visit Aimms 3.13

2 Part I Function Reference

3 Arithmetic Functions Aimms supports the following arithmetic functions: Abs ArcCosh ArcCos ArcSin ArcSinh ArcTanh ArcTan Ceil Cos Cosh Cube Degrees Div ErrorF Ep Floor Log Log10 MapVal Ma Min Mod Power Precision Radians Round ScalarValue Sign Sin Sinh Sqr Sqrt Tan Tanh Trunc

4 Val Arithmetic Functions 3

5 Arithmetic Functions 4 Abs Abs(! (input numerical epression A scalar numerical epression. The function Abs returns the absolute value of. The function Abs can be used in constraints of nonlinear mathematical programs. However, nonlinear solvers may eperience convergence problems if the argument assumes values around 0. Arithmetic functions are discussed in full detail in Section of the Language Reference.

6 Arithmetic Functions 5 ArcCos ArcCos(! (input numerical epression A scalar numerical epression in the range[ 1, 1]. The ArcCos function returns the arccosine of in the range 0 toπ radians. A run-time error results if is outside the range[ 1, 1]. The functionarccos can be used in constraints of nonlinear mathematical programs. The functions ArcSin, ArcTan, Cos. Arithmetic functions are discussed in full detail in Section of the Language Reference.

7 Arithmetic Functions 6 ArcCosh ArcCosh(! (input numerical epression A scalar numerical epression in the range[1,. The ArcCosh function returns the inverse hyperbolic cosine of in the range from 0 to. A run-time error results if is outside the range[1, ]. The function ArcCosh can be used in constraints of nonlinear mathematical programs. The functions ArcSinh, ArcTanh, Cosh. Arithmetic functions are discussed in full detail in Section of the Language Reference.

8 Arithmetic Functions 7 ArcSin ArcSin(! (input numerical epression A scalar numerical epression in the range[ 1, 1]. The ArcSin function returns the arcsine of in the range π/2 to π/2 radians. A run-time error results if is outside the range[ 1, 1]. The functionarcsin can be used in constraints of nonlinear mathematical programs. The functions ArcCos, ArcTan, Sin. Arithmetic functions are discussed in full detail in Section of the Language Reference.

9 Arithmetic Functions 8 ArcSinh ArcSinh(! (input numerical epression A scalar numerical epression. The ArcSinh function returns the inverse hyperbolic sine of in the range from to. The function ArcSinh can be used in constraints of nonlinear mathematical programs. The functions ArcCosh, ArcTanh, Sinh. Arithmetic functions are discussed in full detail in Section of the Language Reference.

10 Arithmetic Functions 9 ArcTan ArcTan(! (input numerical epression A scalar numerical epression. The ArcTan function returns the arctangent of in the range π/2 toπ/2 radians. The function ArcTan can be used in constraints of nonlinear mathematical programs. The functions ArcSin, ArcCos, Tan. Arithmetic functions are discussed in full detail in Section of the Language Reference.

11 Arithmetic Functions 10 ArcTanh ArcTanh(! (input numerical epression A scalar numerical epression in the range( 1, 1. The ArcTanh function returns the inverse hyperbolic tangent of. A run-time error results if is outside the range( 1, 1. The function ArcTanh can be used in constraints of nonlinear mathematical programs. The functions ArcCosh, ArcSinh, Tanh. Arithmetic functions are discussed in full detail in Section of the Language Reference.

12 Arithmetic Functions 11 Ceil Ceil(! (input numerical epression A scalar numerical epression. The function Ceil returns the smallest integer value. The function Ceil will round to the nearest integer, if it lies within the equality tolerances equality absolute tolerance and equality relative tolerance. The function Ceil can be used in the constraints of nonlinear mathematical programs. However, nonlinear solvers may eperience convergence problems around integer values. When the numerical epression contains a unit, the function Ceil will first convert the epression to the corresponding base unit, before evaluating the function itself. The functions Floor, Round, Precision, Trunc. Arithmetic functions are discussed in full detail in Section of the Language Reference. Numeric tolerances are discussed in Section of the Language Reference.

13 Arithmetic Functions 12 Cos Cos(! (input numerical epression A scalar numerical epression in radians. The Cos function returns the cosine of in the range 1 to 1. The function Cos can be used in constraints of nonlinear mathematical programs. The functions Sin, Tan, ArcCos. Arithmetic functions are discussed in full detail in Section of the Language Reference.

14 Arithmetic Functions 13 Cosh Cosh(! (input numerical epression A scalar numerical epression. The Cosh function returns the hyperbolic cosine of in the range 1 to. The function Cosh can be used in constraints of nonlinear mathematical programs. The functions Sinh, Tanh, ArcCosh. Arithmetic functions are discussed in full detail in Section of the Language Reference.

15 Arithmetic Functions 14 Cube Cube(! (input numerical epression A scalar numerical epression. The function Cube returns 3. The function Cube can be used in constraints of nonlinear mathematical programs. The functions Power, Sqr, and Sqrt. Arithmetic functions are discussed in full detail in Section of the Language Reference.

16 Arithmetic Functions 15 Degrees Degrees(! (input numerical epression A scalar numerical epression. The function Degrees returns the value of converted from radians to degrees. The function Degrees can be used in constraints of linear and nonlinear mathematical programs. The function Radians. Arithmetic functions are discussed in full detail in Section of the Language Reference.

17 Arithmetic Functions 16 Div Div(,! (input numerical epression y! (input numerical epression y A scalar numerical epression. A scalar numerical epression unequal to 0. The function Div returns divided byy rounded down to an integer. A run-time error results if y equals 0. Arithmetic functions are discussed in full detail in Section of the Language Reference.

18 Arithmetic Functions 17 ErrorF ErrorF(! (input numerical epression A scalar numerical epression. The function ErrorF returns the error function value 1 2π e t2 2 The function ErrorF can be used in constraints of nonlinear mathematical programs. Arithmetic functions are discussed in full detail in Section of the Language Reference. dt.

19 Arithmetic Functions 18 Ep Ep(! (input numerical epression A scalar numerical epression. The function Ep returns the eponential valuee. The function Ep can be used in constraints of nonlinear mathematical programs. The functions Log, Log10. Arithmetic functions are discussed in full detail in Section of the Language Reference.

20 Arithmetic Functions 19 Floor Floor(! (input numerical epression A scalar numerical epression. The function Floor returns the largest integer value. The function Floor will round to the nearest integer, if it lies within the equality tolerances equality absolute tolerance and equality relative tolerance. The function Floor can be used in the constraints of nonlinear mathematical programs. However, nonlinear solvers may eperience convergence problems around integer values. When the numerical epression contains a unit, the function Floor will first convert the epression to the corresponding base unit, before evaluating the function itself. The functions Ceil, Round, Precision, Trunc. Arithmetic functions are discussed in full detail in Section of the Language Reference. Numeric tolerances are discussed in Section of the Language Reference.

21 Arithmetic Functions 20 Log Log(! (input numerical epression A scalar numerical epression in the range(0,. The function Log returns the natural logarithm ln(. A run-time error results if is outside the range(0,. The function Log can be used in constraints of nonlinear mathematical programs. The functions Ep, Log10. Arithmetic functions are discussed in full detail in Section of the Language Reference.

22 Arithmetic Functions 21 Log10 Log10(! (input numerical epression A scalar numerical epression in the range(0,. The function Log10 returns the base-10 logarithm of. A run-time error results if is outside the range(0,. The function Log10 can be used in constraints of nonlinear mathematical programs. The functions Ep, Log. Arithmetic functions are discussed in full detail in Section of the Language Reference.

23 Arithmetic Functions 22 MapVal MapVal(! (input numerical epression A scalar numerical epression. The function MapVal returns the (integer mapping value of any real or special number, according to the following table. Value Description MapVal value number any valid real number 0 UNDF undefined (result of an arithmetic error 4 NA not available 5 INF + 6 -INF 7 ZERO numerically indistinguishable from zero, but has the logical value of one. 8 Special numbers in Aimms and the MapVal function are discussed in full detail in Section of the Language Reference.

24 Arithmetic Functions 23 Ma Ma( 1,! (input numerical epression 2,! (input numerical epression.. 1,2,... Multiple numerical epressions. The function Ma returns the largest number among1,2,.... The function Ma can be used in constraints of nonlinear mathematical programs. However, nonlinear solvers may eperience convergence problems if the first order derivatives of two arguments between which the Ma function switches are discontinous. The function Min. Arithmetic functions are discussed in full detail in Section of the Language Reference.

25 Arithmetic Functions 24 Min Min( 1,! (input numerical epression 2,! (input numerical epression.. 1,2,... Multiple numerical epressions. The function Min returns the smallest number among1,2,.... The function Min can be used in constraints of nonlinear mathematical programs. However, nonlinear solvers may eperience convergence problems if the first order derivatives of two arguments between which the Min function switches are discontinous. The function Ma. Arithmetic functions are discussed in full detail in Section of the Language Reference.

26 Arithmetic Functions 25 Mod Mod(,! (input numerical epression y! (input numerical epression y A scalar numerical epression. A scalar numerical epression unequal to 0. The function Mod returns the remainder of after division by y. For y > 0, the result is an integer in the range 0,...,y 1 if both and y are integers, or in the interval[0,y otherwise. For y < 0, the result is an integer in the rangey 1,...,0 if both andy are integers, or in the interval(y, 0] otherwise. A run-time error results if y equals 0. The function Mod can be used in constraints of mathematical programs. However, nonlinear solver may eperience convergence problems if assumes values around multiples ofy. Arithmetic functions are discussed in full detail in Section of the Language Reference.

27 Arithmetic Functions 26 Power Power(,! (input numerical epression y! (input numerical epression y A scalar numerical epression. A scalar numerical epression. The function Power returnsraised to the powery. The following combination of arguments is allowed: > 0 = 0 andy> 0 < 0 andy integer In all other cases a run-time error will result. The function can be used in constraints of nonlinear mathematical programs. The functions Cube, Sqr, and Sqrt. Arithmetic functions are discussed in full detail in Section of the Language Reference.

28 Arithmetic Functions 27 Precision Precision(,! (input numerical epression y! (input integer epression y A scalar numerical epression. An integer epression. The function Precision returns rounded to y significant digits. The function Precision can be used in constraints of nonlinear mathematical programs. However, nonlinear solvers may eperience convergence problems around the discontinuities of the Precision function. When the numerical epression contains a unit, the function Precision will first convert the epression to the corresponding base unit, before evaluating the function itself. The functions Round, Ceil, Floor, Trunc. Arithmetic functions are discussed in full detail in Section of the Language Reference.

29 Arithmetic Functions 28 Radians Radians(! (input numerical epression A scalar numerical epression. The function Radians returns the value of converted from degrees to radians. The function Radians can be used in constraints of linear and nonlinear mathematical programs. The function Degrees. Arithmetic functions are discussed in full detail in Section of the Language Reference.

30 Arithmetic Functions 29 Round Round(,! (input numerical epression decimals! (optional integer epression A scalar numerical epression. decimals (optional An integer epression. The function Round returns the integer value nearest to. In the presence of the optional argument n the function Round returns the value of rounded to n decimal places left (decimals < 0 or right (decimals > 0 of the decimal point. The function Round can be used in constraints of nonlinear mathematical programs. However, nonlinear solvers may eperience convergence problems around the discontinuities of the Round function. When the numerical epression contains a unit, the function Round will first convert the epression to that unit, before evaluating the function itself. See also the option rounding compatibility in the option category backward compatibility. The functions Precision, Ceil, Floor, Trunc. Arithmetic functions are discussed in full detail in Section of the Language Reference.

31 Arithmetic Functions 30 ScalarValue ScalarValue( identifier,! (input element epression into AllIdentifiers suffi! (optional element epression into AllSuffiNames identifier A scalar element epression into AllIdentifiers suffi A scalar element epression into AllSuffiNames The function ScalarValue returns the value contained in the scalar identifier identifier or scalar reference identifier.suffi. When identifier or identifier.suffi is not a scalar numerical valued reference, the function ScalarValue returns 0.0. The function Val. The ScalarValue function is a function that operates on subsets of AllIdentifiers. Other functions that operate on subsets of AllIdentifiers are referenced in Section 24.4 of the Language Reference.

32 Arithmetic Functions 31 Sign Sign(! (input numerical epression A scalar numerical epression. The function Sign returns+1 if> 0, 1 if< 0 and 0 if= 0. The function Sign can be used in constraints of nonlinear mathematical programs. However, nonlinear solver may eperience convergence problems round 0. The function Abs. Arithmetic functions are discussed in full detail in Section of the Language Reference.

33 Arithmetic Functions 32 Sin Sin(! (input numerical epression A scalar numerical epression in radians. The Sin function returns the sine of in the range 1 to 1. The function Sin can be used in constraints of nonlinear mathematical programs. The functions Cos, Tan, ArcSin. Arithmetic functions are discussed in full detail in Section of the Language Reference.

34 Arithmetic Functions 33 Sinh Sinh(! (input numerical epression A scalar numerical epression. The Sinh function returns the hyperbolic sine of in the range to. The function Sinh can be used in the constraints of nonlinear mathematical programs. The functions Cosh, Tanh, ArcSinh. Arithmetic functions are discussed in full detail in Section of the Language Reference.

35 Arithmetic Functions 34 Sqr Sqr(! (input numerical epression A scalar numerical epression. The function Sqr returns 2. The function Sqr can be used in constraints of nonlinear mathematical programs. The functions Power, Cube, and Sqrt. Arithmetic functions are discussed in full detail in Section of the Language Reference.

36 Arithmetic Functions 35 Sqrt Sqrt(! (input numerical epression A scalar numerical epression in the range[0,. The function Sqrt returns the. A run-time error results if is outside the range[0,. The function Sqrt can be used in the constraints of nonlinear mathematical programs. The functions Power, Cube, and Sqr. Arithmetic functions are discussed in full detail in Section of the Language Reference.

37 Arithmetic Functions 36 Tan Tan(! (input numerical epression A scalar numerical epression in radians. The Tan function returns the tangent of in the range to. The function Tan can be used in constraints of nonlinear mathematical programs. The functions Cos, Sin, ArcTan. Arithmetic functions are discussed in full detail in Section of the Language Reference.

38 Arithmetic Functions 37 Tanh Tanh(! (input numerical epression A scalar numerical epression. The Tanh function returns the hyperbolic tangent of in the range 1 to 1. The function Tanh can be used in constraints of nonlinear mathematical programs. The functions Cosh, Sinh, ArcTanh. Arithmetic functions are discussed in full detail in Section of the Language Reference.

39 Arithmetic Functions 38 Trunc Trunc(! (input numerical epression A scalar numerical epression. The function Trunc returns the truncated value of : Sign( Floor(Abs(. The function Trunc will round to the nearest integer, if it lies within the equality tolerances equality absolute tolerance and equality relative tolerance. The function Trunc can be used in the constraints of nonlinear mathematical programs. However, nonlinear solver may eperience convergence problems around integer argument values. When the numerical epression contains a unit, the function Trunc will first convert the epression to the corresponding base unit, before evaluating the function itself. The functions Ceil, Floor, Round, Precision. Arithmetic functions are discussed in full detail in Section of the Language Reference. Numeric tolerances are discussed in Section of the Language Reference.

40 Arithmetic Functions 39 Val Val( str! (input string or element epression str A scalar string or element epression. The function Val returns the numerical value represented by the string or element str. If str cannot be interpreted as a numerical value, a runtime error may occur, see option suppress error messages of val function. The Val function is discussed in full detail in Section of the Language Reference.

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