Calculate Polynomials from Zeros or Values

Calculate either the monic polynomial with specified zeros, or the Lagrange interpolation polynomial through the (x,y) points.

poly.calc(x, y, tol=sqrt(.Machine$double.eps), lab=dimnames(y)[[2]])

Arguments

x

numeric vector specifying either the zeros of the desired polynomial if this is the only non-missing argument, or the x-values for Lagrange interpolation.

y

numeric vector or matrix specifying the y-values for the Lagrange interpolation polynomial. If y is a matrix, nrow(y) must equal length(x), and each column of y is used separately with x.

tol

An absolute value tolerance, below which coefficients are treated as zero.

lab

If y is a matrix, lab is used as the names vector for the list result.

Details

If y is a matrix, the result is a list of polynomials using each column separately.

If x only is given, repeated zeros are allowed. If x and y are given, repeated values in the x vector must have identical y values associated with them (up to tol), otherwise the first y-value only is used and a warning is issued.

Value

Either a polynomial object, or a list of polynomials, as appropriate. In the latter case the object is of class "polylist".

See also

polynomial

Examples

poly.calc(rep(1,3))
#> -1 + 3*x - 3*x^2 + x^3 
## -1 + 3*x - 3*x^2 + x^3 
poly.calc(0:4, (0:4)^2 + 1)
#> 1 + x^2 
## 1 + x^2 
poly.calc(0:4, cbind(0:4, (0:4)^2 + 1), lab = letters[1:2])
#> List of polynomials:
#> $a
#> x 
#> 
#> $b
#> 1 + x^2 
#> 
## List of polynomials:
## $a:
## x
##
## $b:
## 1 + x^2