Algol 60 Procedures Libraries
Library NumAl of Algol 60 procedures in numerical mathematics.
NumAl 1 library part 1 with complex number operations, Vector and Matrix arithmetic, long integer and double precision arithmetic, matrix triangulation, determinant calculation, matrix inversion, linear equation solution, Cholesky decomposition, Householder triangulation, linear least squares problem, Sin/cosine/Fourier series, continued fractions, Orthogonal polynomials
NumAl 2 library part 2 with vector sorting, matrix eigenvalues and eigenvectors, Gram-Schmidt method, singular values of matrix, roots of polynomials, definite integrals, function minimization, initial value problem FOR ordinary differential equations
NumAl 3 library part 3 with an initial value problem, two points boundary value problem, estimation of unknown variables in a system of first orderdifferensial equations, value of PI and E, parameters of computer arithmetic, hyperbolic functions, exponential integrals, The gamma function, The error function, the sine integral SI(X) ald the cosine integral CI(X), Bessel functions, Airy functions
NumAl original Original texts of NumAl library
Proposal of Algol 60 standard library in numerical mathematics.
(proposal is in development...)
Multi integer arithmetics:
Multi integer is integer array with dimension.
MintNeg( ) - negate multi integer
MintAdd( ) - addition of two multi integers
MintMult( ) - multi integer multiplication
MintDiv( ) - multi integer division
MintRes( ) - multi integer residual of division
MintDivisor( ) - multi integer minimal divisor
Fractional arithmetics:
Fraction = couple of two integers, numerator and denominator.
FracAdd() - addition of two fractions
Frac() - multiplication of two fractions
Frac() - division of two fractions
Frac() - chain presentation of fraction
Complex arithmetics:
complex number = couple of real numbers (real part and imaginery part)
CompAdd() - addition of two complex numbers
CompMult() - multiplication of two complex numbers
CompDiv() - division of two complex numbers
CompNorm() - norm of complex number
CompTrig() - trigonometric form (r, arg) of complex number
CompExp() - exponent of complex number
CompLn() - logarithm of complex number
Real vectors:
Real vector = real 1-dim array
OutVector() - vector output to file in text form
InVector() - vector input from text file
VectGen() - generation of vector with values (a + i * s)
VectRand() - generation of vector with random components from 0 to 1.0
VectCopy() - copying of vector to another vector
VectAddNumber() - addition of scalar to vector
VectAdd() - addition of two vectors
VectMultNumber() - multiplication of vector to scalar
VectScalarMult() - scalar multiplication of two vectors
VectNorm() - Euclid norm of vector
VectAngle() - angle between two vectors
Real square matrices:
Real square matrix = real square 2-dim array
OutMatrix() - matrix output to file in text form
InMatrix() - matrix input from text file
MatrDiag() - generation of matrix with const value on diagonal
MatrDiag3() - generation of three diagonal matrix matrix with const values on diagonal and upper/lower sub diagonals
MatrGen() - generation of matrix with values (a + i*s1 + j*s2)
MatrRand() - generation of matrix with random components from 0 to 1.0
MutrCopy() - copying of matrix to another matrix
MatrAddNumber() - addition of scalar to matrix
MatrAdd() - addition of two matrices
MatrMultNumber() - multiplication of matrix to scalar
MatrMultVect() - multiplication of matrix to vector
MatrMult() - multiplication of matrix to another matrix
MatrTranspose() - multiplication of matrix to another matrix
MatrDeterm() - determinant of matrix
Linear equations and Linear algebra:
LinalgGauss(matr, vect, vect) -
LinalgEigen() -
Analytical Geometry on Plane:
point (x,y), line coefficients (a,b,c), line segment (x1,y1,x2,y2)
GeomInPoint() - point coordinates reading
GeomOutPoint() - point coordinates writing
GeomInLine() - line coefficients reading
GeomOutLine() - line coefficients writing
GeomPointShift() - point shift
GeomPointRadius() - point shift
GeomDist() - distance between points
Polynomials and their roots:
polynomial represented as real 1-dim array with polynomials coefficients
PolyCalc() - fast polynomial value calculation
PolyAdd() - addition of two polynomials
PolyMult() - multiplication of two polynomials
Poly2Roots() - roots of second order polynomial
Poly3Root() - real root of third order polynomial
PolyDivision() - division of two polynomials
Fourier series:
FourierFFT() - fast Fourier transform
FourierInverse() - Inverse Fourier transform
Non-linear equations:
Differential equations (initial value problems):
Differential equations (boundary value problems):
Numerical integration and differentiation:
Time series filtration:
Time series represented as Real vector
Interpolation:
Regression analysis:
Statistical calculations:
StatAverage() - average value of data collection
StatAveStd() - average value and Standard Deviation of data collection
StatMedian() - median value of data collection
StatCorr() - correlation value between two data vectors
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