TMath

A small math function collection based on the Taylor expansion series.

Building the project

• Download the source files from the master-tree
• To build the project, you need to have g++ and make installed
• And you need to run export CC=g++
• If everything is ready, run make and ...
• ... your libtmath.a library file is ready in the lib folder

How to use

Just build it as described above, include the header files and link the library. The library uses the types TMath::DOUBLE(long double) and TMath::LONG(long long) for parameters and return values.

What is included?

Mathematical functions

Function	Description
sin(DOUBLE x)	sine of x
asin(DOUBLE x)	arcsine of x
sinh(DOUBLE x)	hyperbolic sine of x
cos(DOUBLE x)	cosine of x
acos(DOUBLE x)	arccosine of x
cosh(DOUBLE x)	hyperbolic cosine of x
tan(DOUBLE x)	tangent of x
atan(DOUBLE x)	arctangent of x
cot(DOUBLE x)	cotangent of x
acot(DOUBLE x)	arccotangent of x
coth(DOUBLE x)	hyperbolic cotangent of x
sec(DOUBLE x)	secant of x
asec(DOUBLE x)	arcsecant of x
sech(DOUBLE x)	hyperbolic secant of x
cosec(DOUBLE x)	cosecant of x
acsc(DOUBLE x)	arccosecant of x
csch(DOUBLE x)	hyperbolic cosecant of x
floor(DOUBLE x)	next lower integer of x
ceil(DOUBLE x)	next higher integer of x
mod(LONG x, LONG y)	the remainder of the division x / y
exp(DOUBLE x)	natural exponential function
sqrt(DOUBLE x)	squareroot of x
root(DOUBLE x, DOUBLE n)	n-th root of x
ln(DOUBLE x)	natural logarithm of x
lg(DOUBLE x)	common logarithm of x
lb(DOUBLE x)	binary logarithm of x
log(DOUBLE x, DOUBLE n)	logarithm with base n of x
pow(DOUBLE x, DOUBLE n)	x to the power of n
pow(LONG x, LONG n)	x to the power of n
pow(DOUBLE x, LONG n)	x to the power of n
fac(LONG n)	factorial of n
facd(LONG n)	factorial of n using floating point
oddfac(LONG n)	odd-factorial of n
oddfacd(LONG n)	odd-factorial of n using floating point
rad(DOUBLE x)	degrees to radiant
deg(DOUBLE x)	radiant to degrees
abs(DOUBLE x)	absolute value of x
equal(DOUBLE x, DOUBLE y)	floating-point number equality
equal(DOUBLE x, DOUBLE y, DOUBLE eps)	floating-point number equality with a variance of epsilon

Vector class

To initialize a new vector just use initializer lists (like Vector {1, 2, 3}) or create a null-vector using Vector(n) (where n is the number of dimensions).

Operation	Description
a[n]	Access the n-th element of the vector a
a.at(n)	Access the n-th element of the vector a as a constant
a + b	Adds vector a and b
a - b	Subtracts vector a from b
a * s	Scales the vector by the factor s
a / s	Scales the vector by the factor 1 / s
a == b	Tests if vector a is equal to b
a != b	Tests if vector a is not equal to b
a.equal(b, e)	Tests if the vector a is equal to b with the accuracy e
a.dot(b)	Dot product of a and b.
a.cross(b)	Cross product of a and b
a.norm()	Normalized copy of the vector a
a.length()	Length of vector a
a.dim()	Dimensions of vector a
a.to_string()	Generates a string representation of the vector a

Matrix class

To initialize a new matrix you can use initializer lists (like Matrix{{1, 0}, {0, 1}}) or create a null-matrix using Matrix(x, y) (where x is the number of cols and y the number of rows).

Operation	Description
m[n]	Access the n-th row of the matrix
m[n][x]	Access the element at row n and col x
m.at(n)	Access the n-th row of the matrix as a constant
m.at(n, x)	Access the element at row n and col x as a constant
m * v	Multiply matrix m with vector v
m * a	Multiply matrix m with matrix a
m * s	Multiply matrix m with scalar s
-m	Negate matrix m
a + b	Add the matrices
a - b	Subtract the matrices
a.equal(b, e)	Tests if the matrix a is equal to b with the accuary e
a == b	Tests if the matrix a is equal to b
a != b	Tests if the matrix a is not equal to b
a.colCount()	Get the number of matrix cols
a.rowCount()	Get the number of matrix rows
a.to_string()	Generate a string representation of the matrix
identity(n)	Generates an identity matrix of dimension n

What is planned?

• Statistics
• Numerics (e.g. solvers for ODE/PDE/LS)