R8POLY
Polynomials with R8 Coefficients

R8POLY is a FORTRAN90 library which contains a number of utilities for polynomials with R8 coefficients, that is, using double precision or 64 bit real arithmetic.

Licensing:

The computer code and data files made available on this web page are distributed under the GNU LGPL license.

Languages:

R8POLY is available in a C++ version and a C version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

LEGENDRE_PRODUCT_POLYNOMIAL, a FORTRAN90 library which defines Legendre product polynomials, creating a multivariate polynomial as the product of univariate Legendre polynomials.

MONOMIAL, a FORTRAN90 library which enumerates, lists, ranks, unranks and randomizes multivariate monomials in a space of M dimensions, with total degree less than N, equal to N, or lying within a given range.

FORTRAN90, a MATLAB library which adds, multiplies, differentiates, evaluates and prints multivariate polynomials in a space of M dimensions.

Source Code:

• r8poly.f90, the source code.

Examples and Tests:

• r8poly_test.f90, a sample calling program.
• r8poly_test.txt, the output file.

List of Routines:

• R8_SIGN returns the sign of an R8.
• R82POLY2_PRINT prints a second order polynomial in two variables.
• R82POLY2_TYPE analyzes a second order polynomial in two variables.
• R82POLY2_TYPE_PRINT prints the meaning of the output from R82POLY2_TYPE.
• R8POLY2_EX finds the extremal point of a parabola determined by three points.
• R8POLY2_EX2 finds extremal point of a parabola determined by three points.
• R8POLY2_ROOT returns the two roots of a quadratic polynomial.
• R8POLY2_RROOT returns the real parts of the roots of a quadratic polynomial.
• R8POLY2_VAL evaluates a parabola defined by three data values.
• R8POLY2_VAL2 evaluates a parabolic interpolant through tabular data.
• R8POLY3_ROOT returns the three roots of a cubic polynomial.
• R8POLY4_ROOT returns the four roots of a quartic polynomial.
• R8POLY_DEGREE returns the degree of a polynomial.
• R8POLY_DERIV returns the derivative of a polynomial.
• R8POLY_LAGRANGE_0 evaluates the Lagrange factor at a point.
• R8POLY_LAGRANGE_1 evaluates the first derivative of the Lagrange factor.
• R8POLY_LAGRANGE_2 evaluates the second derivative of the Lagrange factor.
• R8POLY_LAGRANGE_COEF returns the coefficients of a Lagrange polynomial.
• R8POLY_LAGRANGE_FACTOR evaluates the polynomial Lagrange factor at a point.
• R8POLY_LAGRANGE_VAL evaluates the IPOL-th Lagrange polynomial.
• R8POLY_ORDER returns the order of a polynomial.
• R8POLY_PRINT prints out a polynomial.
• R8POLY_SHIFT adjusts the coefficients of a polynomial for a new argument.
• R8POLY_VALUE evaluates a polynomial using a naive method.
• R8POLY_VALUE_2D evaluates a polynomial in 2 variables, X and Y.
• R8POLY_VALUE_HORNER evaluates a polynomial using Horner's method.
• R8POLY_VALUES_HORNER evaluates a polynomial using Horner's method.
• R8R8_PRINT prints an R8R8.
• R8VEC_EVEN returns an R8VEC of evenly spaced values.
• R8VEC_EVEN_SELECT returns the I-th of N evenly spaced values in [ XLO, XHI ].
• R8VEC_INDICATOR1 sets an R8VEC to the indicator vector (1,2,3,...).
• R8VEC_IS_DISTINCT is true if the entries in an R8VEC are distinct.
• R8VEC_LINSPACE creates a vector of linearly spaced values.
• R8VEC_PRINT prints an R8VEC.
• R8VEC_TRANSPOSE_PRINT prints an R8VEC "transposed".
• R8VEC2_PRINT prints an R8VEC2.
• ROOTS_TO_R8POLY converts polynomial roots to polynomial coefficients.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.