R8POLY
Polynomials with R8 Coefficients

R8POLY, a MATLAB 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 MATLAB library which defines Legendre product polynomials, creating a multivariate polynomial as the product of univariate Legendre polynomials.

MONOMIAL, a MATLAB 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.

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

r8poly_test

Source Code:

• r8_sign.m, returns the sign of an R8.
• r82poly2_print.m, prints a second order polynomial in two variables;
• r82poly2_type.m, analyzes a second order polynomial in two variables.
• r82poly2_type_print.m, prints the meaning of the output from R82POLY2_TYPE.
• r8mat_inverse_3d.m, computes the inverse of a 3 by 3 R8MAT;
• r8mat_print.m, prints an R8MAT;
• r8mat_print_some.m, prints some of an R8MAT;
• r8poly_degree.m, returns the degree of a polynomial;
• r8poly_deriv.m, returns the derivative of a polynomial;
• r8poly_lagrange_0.m, evaluates the Lagrange factor at a point;
• r8poly_lagrange_1.m, evaluates the first derivative of the Lagrange factor at a point;
• r8poly_lagrange_2.m, evaluates the second derivative of the Lagrange factor at a point;
• r8poly_lagrange_coef.m, returns the coefficients of a Lagrange polynomial;
• r8poly_lagrange_factor.m, evaluates the polynomial Lagrange factor at a point;
• r8poly_lagrange_val.m, evaluates the IPOL-th Lagrange polynomial;
• r8poly_order.m, returns the order of a polynomial.
• r8poly_print.m, prints a polynomial;
• r8poly_shift.m, adjusts the coefficients of a polynomial for a new argument.
• r8poly_value.m, evaluates a polynomial using a naive method;
• r8poly_value_horner.m, evaluates a polynomial using Horner's method;
• r8poly_value_fast.m, evaluates a polynomial, using the coefficient ordering that is the opposite of that which Matlab's polyval() assumes, and using Matlab's presumably faster, but more obscure, linear algebra approach.
• r8poly_value_2d.m, evaluates a polynomial of X and Y of total degree M, using a coefficient ordering that begins with the constant term.
• r8poly_values_horner.m, evaluates a polynomial, using Horner's method.
• r8poly2_ex.m, finds the extremal point of a parabola determined by three points.
• r8poly2_ex2.m, finds the extremal point of a parabola determined by three points.
• r8poly2_root.m, returns the two roots of a quadratic polynomial.
• r8poly2_rroot.m, returns the real parts of the two roots of a quadratic polynomial.
• r8poly2_val.m, evaluates a parabola defined by three data values.
• r8poly2_val2.m, evaluates a parabolic interpolant through tabular data.
• r8poly3_root.m, returns the three roots of a cubic polynomial.
• r8poly4_root.m, returns the four roots of a quartic polynomial.
• r8r8_print.m, prints an R8R8, that is, a pair of R8's;
• r8vec_even.m, returns an R8VEC of N values evenly spaced between given limits;
• r8vec_even_select.m, returns the I-th of N evenly spaced values;
• r8vec_is_distinct.m, is true if all entries of an R8VEC are distinct;
• r8vec_linspace.m, returns an R8VEC of values evenly spaced between given limits.
• r8vec_print.m, prints an R8VEC;
• r8vec_transpose_print.m, prints the "transpose" of an R8VEC.
• roots_to_r8poly.m, converts polynomial roots to polynomial coefficients;
• timestamp.m, prints the current YMDHMS date as a timestamp;