TMath

class TMath

    private:

      static Double_t GamCf(Double_t a, Double_t x)
      static Double_t GamSer(Double_t a, Double_t x)

    public:

                 TMath TMath()
                 TMath TMath(TMath&)
                  void ~TMath()
        static Short_t Abs(Short_t d)
          static Int_t Abs(Int_t d)
         static Long_t Abs(Long_t d)
        static Float_t Abs(Float_t d)
       static Double_t Abs(Double_t d)
       static Double_t ACos(Double_t x)
       static Double_t ACosH(Double_t)
       static Double_t ASin(Double_t x)
       static Double_t ASinH(Double_t)
       static Double_t ATan(Double_t x)
       static Double_t ATan2(Double_t y, Double_t x)
       static Double_t ATanH(Double_t)
       static Double_t BesselI(Int_t n, Double_t x)
       static Double_t BesselI0(Double_t x)
       static Double_t BesselI1(Double_t x)
       static Double_t BesselK(Int_t n, Double_t x)
       static Double_t BesselK0(Double_t x)
       static Double_t BesselK1(Double_t x)
          static Int_t BinarySearch(Int_t n, const Short_t* array, Short_t value)
          static Int_t BinarySearch(Int_t n, const Short_t** array, Short_t value)
          static Int_t BinarySearch(Int_t n, const Int_t* array, Int_t value)
          static Int_t BinarySearch(Int_t n, const Int_t** array, Int_t value)
          static Int_t BinarySearch(Int_t n, const Float_t* array, Float_t value)
          static Int_t BinarySearch(Int_t n, const Float_t** array, Float_t value)
          static Int_t BinarySearch(Int_t n, const Double_t* array, Double_t value)
          static Int_t BinarySearch(Int_t n, const Double_t** array, Double_t value)
          static Int_t BinarySearch(Int_t n, const Long_t* array, Long_t value)
          static Int_t BinarySearch(Int_t n, const Long_t** array, Long_t value)
       static Double_t Ceil(Double_t x)
        static TClass* Class()
       static Double_t Cos(Double_t x)
       static Double_t CosH(Double_t x)
       static Float_t* Cross(Float_t* v1, Float_t* v2, Float_t* out)
      static Double_t* Cross(Double_t* v1, Double_t* v2, Double_t* out)
       static Double_t E()
       static Double_t Erf(Double_t x)
       static Double_t Erfc(Double_t x)
         static Bool_t Even(Long_t a)
       static Double_t Exp(Double_t x)
          static Int_t Finite(Double_t x)
       static Double_t Floor(Double_t x)
       static Double_t Freq(Double_t x)
       static Double_t Gamma(Double_t z)
       static Double_t Gamma(Double_t a, Double_t x)
       static Double_t Gaus(Double_t x, Double_t mean = 0, Double_t sigma = 1)
        static ULong_t Hash(const void* txt, Int_t ntxt)
        static ULong_t Hash(const char* str)
       static Double_t Hypot(Double_t x, Double_t y)
         static Long_t Hypot(Long_t x, Long_t y)
       virtual TClass* IsA() const
          static Int_t IsNaN(Double_t x)
       static Double_t KolmogorovProb(Double_t z)
       static Double_t Landau(Double_t x, Double_t mean = 0, Double_t sigma = 1)
       static Double_t LnGamma(Double_t z)
          static Int_t LocMax(Int_t n, const Short_t* a)
          static Int_t LocMax(Int_t n, const Int_t* a)
          static Int_t LocMax(Int_t n, const Float_t* a)
          static Int_t LocMax(Int_t n, const Double_t* a)
          static Int_t LocMax(Int_t n, const Long_t* a)
          static Int_t LocMin(Int_t n, const Short_t* a)
          static Int_t LocMin(Int_t n, const Int_t* a)
          static Int_t LocMin(Int_t n, const Float_t* a)
          static Int_t LocMin(Int_t n, const Double_t* a)
          static Int_t LocMin(Int_t n, const Long_t* a)
       static Double_t Log(Double_t x)
       static Double_t Log10(Double_t x)
       static Double_t Log2(Double_t x)
        static Short_t Max(Short_t a, Short_t b)
       static UShort_t Max(UShort_t a, UShort_t b)
          static Int_t Max(Int_t a, Int_t b)
         static UInt_t Max(UInt_t a, UInt_t b)
         static Long_t Max(Long_t a, Long_t b)
        static ULong_t Max(ULong_t a, ULong_t b)
        static Float_t Max(Float_t a, Float_t b)
       static Double_t Max(Double_t a, Double_t b)
        static Short_t Min(Short_t a, Short_t b)
       static UShort_t Min(UShort_t a, UShort_t b)
          static Int_t Min(Int_t a, Int_t b)
         static UInt_t Min(UInt_t a, UInt_t b)
         static Long_t Min(Long_t a, Long_t b)
        static ULong_t Min(ULong_t a, ULong_t b)
        static Float_t Min(Float_t a, Float_t b)
       static Double_t Min(Double_t a, Double_t b)
         static Long_t NextPrime(Long_t x)
          static Int_t Nint(Float_t x)
          static Int_t Nint(Double_t x)
       static Float_t* Normal2Plane(Float_t* v1, Float_t* v2, Float_t* v3, Float_t* normal)
      static Double_t* Normal2Plane(Double_t* v1, Double_t* v2, Double_t* v3, Double_t* normal)
        static Float_t Normalize(Float_t* v)
       static Double_t Normalize(Double_t* v)
        static Float_t NormCross(Float_t* v1, Float_t* v2, Float_t* out)
       static Double_t NormCross(Double_t* v1, Double_t* v2, Double_t* out)
         static Bool_t Odd(Long_t a)
       static Double_t Pi()
       static Double_t Power(Double_t x, Double_t y)
       static Double_t Prob(Double_t chi2, Int_t ndf)
        static Short_t Range(Short_t lb, Short_t ub, Short_t x)
          static Int_t Range(Int_t lb, Int_t ub, Int_t x)
         static Long_t Range(Long_t lb, Long_t ub, Long_t x)
        static ULong_t Range(ULong_t lb, ULong_t ub, ULong_t x)
       static Double_t Range(Double_t lb, Double_t ub, Double_t x)
          virtual void ShowMembers(TMemberInspector& insp, char* parent)
        static Short_t Sign(Short_t a, Short_t b)
          static Int_t Sign(Int_t a, Int_t b)
         static Long_t Sign(Long_t a, Long_t b)
        static Float_t Sign(Float_t a, Float_t b)
       static Double_t Sign(Double_t a, Double_t b)
       static Double_t Sin(Double_t x)
       static Double_t SinH(Double_t x)
           static void Sort(Int_t n, const Short_t* a, Int_t* index, Bool_t down = kTRUE)
           static void Sort(Int_t n, const Int_t* a, Int_t* index, Bool_t down = kTRUE)
           static void Sort(Int_t n, const Float_t* a, Int_t* index, Bool_t down = kTRUE)
           static void Sort(Int_t n, const Double_t* a, Int_t* index, Bool_t down = kTRUE)
           static void Sort(Int_t n, const Long_t* a, Int_t* index, Bool_t down = kTRUE)
       static Double_t Sqrt(Double_t x)
         static Long_t Sqrt(Long_t x)
          virtual void Streamer(TBuffer& b)
                  void StreamerNVirtual(TBuffer& b)
       static Double_t Tan(Double_t x)
       static Double_t TanH(Double_t x)

Data Members

    private:


    protected:


    public:

Class Description

                                                                      
 TMath                                                                
                                                                      
 Encapsulate math routines (i.e. provide a kind of namespace).        
 For the time being avoid templates.                                  
                                                                      

 Return next prime number after x, unless x is a prime in which case
 x is returned.

 Round to nearest integer. Rounds half integers to the nearest
 even integer.

 Round to nearest integer. Rounds half integers to the nearest
 even integer.

 Calculate the Cross Product of two vectors
         out = [v1 x v2]

 Calculate the Cross Product of two vectors
         out = [v1 x v2]

 Computation of the error function erf(x).
 Erf(x) = (2/sqrt(pi)) Integral(exp(-t^2))dt between 0 and x

 Computation of the complementary error function erfc(x).
 Erfc(x) = (2/sqrt(pi)) Integral(exp(-t^2))dt between x and infinity

 The algorithm is based on a Chebyshev fit as denoted in
 Numerical Recipes 2nd ed. on p. 214 (W.H.Press et al.).

 The fractional error is always less than 1.2e-7.

--- Nve 14-nov-1998 UU-SAP Utrecht

 Computation of the normal frequency function freq(x).
 Freq(x) = (1/sqrt(2pi)) Integral(exp(-t^2/2))dt between -infinity and x

 translated from CERNLIB C300 by Rene Brun

 Computation of gamma(z) for all z>0.

 The algorithm is based on the article by C.Lanczos [1] as denoted in
 Numerical Recipes 2nd ed. on p. 207 (W.H.Press et al.).

 [1] C.Lanczos, SIAM Journal of Numerical Analysis B1 (1964), 86.

--- Nve 14-nov-1998 UU-SAP Utrecht

 Computation of the incomplete gamma function P(a,x)

 The algorithm is based on the formulas and code as denoted in
 Numerical Recipes 2nd ed. on p. 210-212 (W.H.Press et al.).

--- Nve 14-nov-1998 UU-SAP Utrecht

 Computation of the incomplete gamma function P(a,x)
 via its continued fraction representation.

 The algorithm is based on the formulas and code as denoted in
 Numerical Recipes 2nd ed. on p. 210-212 (W.H.Press et al.).

--- Nve 14-nov-1998 UU-SAP Utrecht

 Computation of the incomplete gamma function P(a,x)
 via its series representation.

 The algorithm is based on the formulas and code as denoted in
 Numerical Recipes 2nd ed. on p. 210-212 (W.H.Press et al.).

--- Nve 14-nov-1998 UU-SAP Utrecht

 Calculate a gaussian function with mean and sigma

 The LANDAU function with mpv(most probable value) and sigma.
 This function has been adapted from the CERNLIB routine G110 denlan.

 Computation of ln[gamma(z)] for all z>0.

 The algorithm is based on the article by C.Lanczos [1] as denoted in
 Numerical Recipes 2nd ed. on p. 207 (W.H.Press et al.).

 [1] C.Lanczos, SIAM Journal of Numerical Analysis B1 (1964), 86.

 The accuracy of the result is better than 2e-10.

--- Nve 14-nov-1998 UU-SAP Utrecht

 Normalize a vector v in place
 Return:
    The norm of the original vector

 Normalize a vector v in place
  Return:
    The norm of the original vector

 Calculate a normal vector of a plane

  Input:
     Float_t *p1,*p2,*p3  -  3 3D points belonged the plane to define it.

  Return:
     Pointer to 3D normal vector (normalized)

 Calculate a normal vector of a plane

  Input:
     Float_t *p1,*p2,*p3  -  3 3D points belonged the plane to define it.

  Return:
     Pointer to 3D normal vector (normalized)

 Computation of the probability for a certain Chi-squared (chi2)
 and number of degrees of freedom (ndf).

 Calculations are based on the incomplete gamma function P(a,x),
 where a=ndf/2 and x=chi2/2.

 P(a,x) represents the probability that the observed Chi-squared
 for a correct model should be less than the value chi2.

 The returned probability corresponds to 1-P(a,x),
 which denotes the probability that an observed Chi-squared exceeds
 the value chi2 by chance, even for a correct model.

--- NvE 14-nov-1998 UU-SAP Utrecht

 Calculates the Kolmogorov distribution function,

   /*
   
   */

 which gives the probability that Kolmogorov's test statistic will exceed
 the value z assuming the null hypothesis. This gives a very powerful
 test for comparing two one-dimensional distributions.
 see, for example, Eadie et al, "statistocal Methods in Experimental
 Physics', pp 269-270).

 This function returns the confidence level for the null hypothesis, where:
   z = dn*sqrt(n), and
   dn  is the maximum deviation between a hypothetical distribution
       function and an experimental distribution with
   n    events

 NOTE: To compare two experimental distributions with m and n events,
       use z = sqrt(m*n/(m+n))*dn

 Accuracy: The function is far too accurate for any imaginable application.
           Probabilities less than 10^-15 are returned as zero.
           However, remember that the formula is only valid for "large" n.
 Theta function inversion formula is used for z <= 1

 This function was translated by Rene Brun from PROBKL in CERNLIB

 Return index of array with the minimum element
 If more than one element is minimum returns first found

 Return index of array with the minimum element
 If more than one element is minimum returns first found

 Return index of array with the minimum element
 If more than one element is minimum returns first found

 Return index of array with the minimum element
 If more than one element is minimum returns first found

 Return index of array with the minimum element
 If more than one element is minimum returns first found

 Return index of array with the maximum element
 If more than one element is maximum returns first found

 Return index of array with the maximum element
 If more than one element is maximum returns first found

 Return index of array with the maximum element
 If more than one element is maximum returns first found

 Return index of array with the maximum element
 If more than one element is maximum returns first found

 Return index of array with the maximum element
 If more than one element is maximum returns first found

 Binary search in an array of n values to locate value

 Array is supposed  to be sorted prior to this call.
 If match is found, function returns position of element.
 If no match found, function gives nearest element smaller than value.

 Binary search in an array of n values to locate value

 Array is supposed  to be sorted prior to this call.
 If match is found, function returns position of element.
 If no match found, function gives nearest element smaller than value.

 Binary search in an array of n values to locate value

 Array is supposed  to be sorted prior to this call.
 If match is found, function returns position of element.
 If no match found, function gives nearest element smaller than value.

 Binary search in an array of n values to locate value

 Array is supposed  to be sorted prior to this call.
 If match is found, function returns position of element.
 If no match found, function gives nearest element smaller than value.

 Binary search in an array of n values to locate value

 Array is supposed  to be sorted prior to this call.
 If match is found, function returns position of element.
 If no match found, function gives nearest element smaller than value.

 Binary search in an array of n values to locate value

 Array is supposed  to be sorted prior to this call.
 If match is found, function returns position of element.
 If no match found, function gives nearest element smaller than value.

 Binary search in an array of n values to locate value

 Array is supposed  to be sorted prior to this call.
 If match is found, function returns position of element.
 If no match found, function gives nearest element smaller than value.

 Binary search in an array of n values to locate value

 Array is supposed  to be sorted prior to this call.
 If match is found, function returns position of element.
 If no match found, function gives nearest element smaller than value.

 Binary search in an array of n values to locate value

 Array is supposed  to be sorted prior to this call.
 If match is found, function returns position of element.
 If no match found, function gives nearest element smaller than value.

 Binary search in an array of n values to locate value

 Array is supposed  to be sorted prior to this call.
 If match is found, function returns position of element.
 If no match found, function gives nearest element smaller than value.

  Sort the n1 elements of the Short_t array a.
  In output the array index contains the indices of the sorted array.
  If down is false sort in increasing order (default is decreasing order).
  This is a translation of the CERNLIB routine sortzv (M101)
  based on the quicksort algorithm.
  NOTE that the array index must be created with a length >= n1
  before calling this function.

  Sort the n1 elements of the Int_t array a.
  In output the array index contains the indices of the sorted array.
  If down is false sort in increasing order (default is decreasing order).
  This is a translation of the CERNLIB routine sortzv (M101)
  based on the quicksort algorithm.
  NOTE that the array index must be created with a length >= n1
  before calling this function.

  Sort the n1 elements of the Float_t array a.
  In output the array index contains the indices of the sorted array.
  If down is false sort in increasing order (default is decreasing order).
  This is a translation of the CERNLIB routine sortzv (M101)
  based on the quicksort algorithm.
  NOTE that the array index must be created with a length >= n1
  before calling this function.

  Sort the n1 elements of the Double_t array a.
  In output the array index contains the indices of the sorted array.
  If down is false sort in increasing order (default is decreasing order).
  This is a translation of the CERNLIB routine sortzv (M101)
  based on the quicksort algorithm.
  NOTE that the array index must be created with a length >= n1
  before calling this function.

  Sort the n1 elements of the Long_t array a.
  In output the array index contains the indices of the sorted array.
  If down is false sort in increasing order (default is decreasing order).
  This is a translation of the CERNLIB routine sortzv (M101)
  based on the quicksort algorithm.
  NOTE that the array index must be created with a length >= n1
  before calling this function.

 Calculates hash index from any char string.
 Based on precalculated table of 256 specially selected random numbers.

   For string:  i = TMath::Hash(string,nstring);
   For int:     i = TMath::Hash(&intword,sizeof(int));
   For pointer: i = TMath::Hash(&pointer,sizeof(void*));

   Limitation: for ntxt>256 calculates hash only from first 256 bytes

              V.Perev

 Calculates hash index from any char string.
 Based on precalculated table of 256 specially selected numbers.
 These numbers are selected in such a way, that for string
 length == 4 (integer number) the hash is unambigous, i.e.
 from hash value we can recalculate input (no degeneration).

 The quality of hash method is good enough, that
 "random" numbers made as R = Hash(1), Hash(2), ...Hash(N)
 tested by <R>, <R*R>, <Ri*Ri+1> gives the same result
 as for libc rand().

 For string:  i = TMath::Hash(string,nstring);
 For int:     i = TMath::Hash(&intword,sizeof(int));
 For pointer: i = TMath::Hash(&pointer,sizeof(void*));

              V.Perev

 Computation of the modified Bessel function I_0(x) for any real x.

 The algorithm is based on the article by Abramowitz and Stegun [1]
 as denoted in Numerical Recipes 2nd ed. on p. 230 (W.H.Press et al.).

 [1] M.Abramowitz and I.A.Stegun, Handbook of Mathematical Functions,
     Applied Mathematics Series vol. 55 (1964), Washington.

--- NvE 12-mar-2000 UU-SAP Utrecht

 Computation of the modified Bessel function K_0(x) for positive real x.

 The algorithm is based on the article by Abramowitz and Stegun [1]
 as denoted in Numerical Recipes 2nd ed. on p. 230 (W.H.Press et al.).

 [1] M.Abramowitz and I.A.Stegun, Handbook of Mathematical Functions,
     Applied Mathematics Series vol. 55 (1964), Washington.

--- NvE 12-mar-2000 UU-SAP Utrecht

 Computation of the modified Bessel function I_1(x) for any real x.

 The algorithm is based on the article by Abramowitz and Stegun [1]
 as denoted in Numerical Recipes 2nd ed. on p. 230 (W.H.Press et al.).

 [1] M.Abramowitz and I.A.Stegun, Handbook of Mathematical Functions,
     Applied Mathematics Series vol. 55 (1964), Washington.

--- NvE 12-mar-2000 UU-SAP Utrecht

 Computation of the modified Bessel function K_1(x) for positive real x.

 The algorithm is based on the article by Abramowitz and Stegun [1]
 as denoted in Numerical Recipes 2nd ed. on p. 230 (W.H.Press et al.).

 [1] M.Abramowitz and I.A.Stegun, Handbook of Mathematical Functions,
     Applied Mathematics Series vol. 55 (1964), Washington.

--- NvE 12-mar-2000 UU-SAP Utrecht

 Computation of the Integer Order Modified Bessel function K_n(x)
 for n=0,1,2,... and positive real x.

 The algorithm uses the recurrence relation

               K_n+1(x) = (2n/x)*K_n(x) + K_n-1(x)

 as denoted in Numerical Recipes 2nd ed. on p. 232 (W.H.Press et al.).

--- NvE 12-mar-2000 UU-SAP Utrecht

 Computation of the Integer Order Modified Bessel function I_n(x)
 for n=0,1,2,... and any real x.

 The algorithm uses the recurrence relation

               I_n+1(x) = (-2n/x)*I_n(x) + I_n-1(x)

 as denoted in Numerical Recipes 2nd ed. on p. 232 (W.H.Press et al.).

--- NvE 12-mar-2000 UU-SAP Utrecht

Inline Functions

           Double_t Pi()
           Double_t E()
           Double_t Sin(Double_t x)
           Double_t Cos(Double_t x)
           Double_t Tan(Double_t x)
           Double_t SinH(Double_t x)
           Double_t CosH(Double_t x)
           Double_t TanH(Double_t x)
           Double_t ASin(Double_t x)
           Double_t ACos(Double_t x)
           Double_t ATan(Double_t x)
           Double_t ATan2(Double_t y, Double_t x)
           Double_t Exp(Double_t x)
           Double_t Power(Double_t x, Double_t y)
           Double_t Log(Double_t x)
           Double_t Log10(Double_t x)
              Int_t Finite(Double_t x)
              Int_t IsNaN(Double_t x)
             Long_t Sqrt(Long_t x)
             Long_t Hypot(Long_t x, Long_t y)
            Short_t Abs(Short_t d)
              Int_t Abs(Int_t d)
             Long_t Abs(Long_t d)
            Float_t Abs(Float_t d)
           Double_t Abs(Double_t d)
             Bool_t Even(Long_t a)
             Bool_t Odd(Long_t a)
            Short_t Sign(Short_t a, Short_t b)
              Int_t Sign(Int_t a, Int_t b)
             Long_t Sign(Long_t a, Long_t b)
            Float_t Sign(Float_t a, Float_t b)
           Double_t Sign(Double_t a, Double_t b)
            Short_t Min(Short_t a, Short_t b)
           UShort_t Min(UShort_t a, UShort_t b)
              Int_t Min(Int_t a, Int_t b)
             UInt_t Min(UInt_t a, UInt_t b)
             Long_t Min(Long_t a, Long_t b)
            ULong_t Min(ULong_t a, ULong_t b)
            Float_t Min(Float_t a, Float_t b)
           Double_t Min(Double_t a, Double_t b)
            Short_t Max(Short_t a, Short_t b)
           UShort_t Max(UShort_t a, UShort_t b)
              Int_t Max(Int_t a, Int_t b)
             UInt_t Max(UInt_t a, UInt_t b)
             Long_t Max(Long_t a, Long_t b)
            ULong_t Max(ULong_t a, ULong_t b)
            Float_t Max(Float_t a, Float_t b)
           Double_t Max(Double_t a, Double_t b)
            Short_t Range(Short_t lb, Short_t ub, Short_t x)
              Int_t Range(Int_t lb, Int_t ub, Int_t x)
             Long_t Range(Long_t lb, Long_t ub, Long_t x)
            ULong_t Range(ULong_t lb, ULong_t ub, ULong_t x)
           Double_t Range(Double_t lb, Double_t ub, Double_t x)
            Float_t NormCross(Float_t* v1, Float_t* v2, Float_t* out)
           Double_t NormCross(Double_t* v1, Double_t* v2, Double_t* out)
            TClass* Class()
            TClass* IsA() const
               void ShowMembers(TMemberInspector& insp, char* parent)
               void Streamer(TBuffer& b)
               void StreamerNVirtual(TBuffer& b)
              TMath TMath()
              TMath TMath(TMath&)
               void ~TMath()