provisdom.math.series — provisdom/math 2.67

chebyshev-derivative-fn clj

(chebyshev-derivative-fn degree derivative)

(chebyshev-derivative-fn degree
                         derivative
                         {:provisdom.math.series/keys [second-kind?]
                          :or {second-kind? false}})

Returns a chebyshev-derivative function. Can optionally use first kind (default) or set second-kind? to true. Will use numerical derivative when necessary.

chebyshev-polynomial-factors-to-regular-polynomial-factors clj

(chebyshev-polynomial-factors-to-regular-polynomial-factors chebyshev-factors)

(chebyshev-polynomial-factors-to-regular-polynomial-factors
  chebyshev-factors
  {:provisdom.math.series/keys [second-kind?] :or {second-kind? false}})

Returns polynomial factors a (i.e., a0 + a1 * x + a2 * x^2 +...) from chebyshev factors (i.e., b0 + b1 * x + b2 * (2x^2 - 1) + ...). Can optionally use first kind (default) or set second-kind? to true.

chebyshev-polynomial-fn clj

(chebyshev-polynomial-fn degree)

(chebyshev-polynomial-fn degree
                         {:provisdom.math.series/keys [second-kind?]
                          :or {second-kind? false}})

Returns a chebyshev polynomial function of degree. Can optionally use first kind (default) or set second-kind? to true.

continued-fraction clj

(continued-fraction term-series)

Returns the continued fraction series for a term-series: a0 + (1 / (a1 + 1 / (a2 + 1 / (a3 + ...

generalized-continued-fraction clj

(generalized-continued-fraction a-term-series b-term-series)

Returns the generalized continued fraction series: a0 + (b0 / (a1 + b1 / (a2 + b2 / (a3 + ...

polynomial-2D-count clj

(polynomial-2D-count end-degree)

(polynomial-2D-count end-degree
                     {:provisdom.math.series/keys [start-degree]
                      :or {start-degree 0}})

Returns the number of elements in 2D between start-degree and end-degree.

polynomial-2D-fn-by-basis-count clj

(polynomial-2D-fn-by-basis-count basis-count)

(polynomial-2D-fn-by-basis-count basis-count
                                 {:provisdom.math.series/keys [start-degree
                                                               chebyshev-kind]
                                  :or {start-degree 0 chebyshev-kind 0}})

cheybshev-kind can be 0 (default), 1, or 2, where 0 means a regular polynomial. Order retains x to the highest powers first, e.g., [1 x y x^2 xy y^2 x^3 (x^2 × y) (y^2 × x) y^3]. Returns a function that takes two numbers (an x and a y) and returns a vector.

polynomial-2D-fn-by-degree clj

(polynomial-2D-fn-by-degree end-degree)

(polynomial-2D-fn-by-degree end-degree
                            {:provisdom.math.series/keys [start-degree
                                                          chebyshev-kind]
                             :or {start-degree 0 chebyshev-kind 0}})

cheybshev-kind can be 0 (default), 1, or 2, where 0 means a regular polynomial. Order retains x to the highest powers first, e.g., [1 x y x^2 xy y^2 x^3 (x^2 × y) (y^2 × x) y^3]. Returns a function that takes two numbers (an x and a y) and returns a vector.

polynomial-fn clj

(polynomial-fn end-degree)

(polynomial-fn end-degree
               {:provisdom.math.series/keys [start-degree chebyshev-kind]
                :or {start-degree 0 chebyshev-kind 0}})

Cheybshev-kind can be 0 (default), 1, or 2, where 0 means a regular polynomial. Returns a function that takes a number and returns a vector.

polynomial-fns clj

(polynomial-fns end-degree)

(polynomial-fns end-degree
                {:provisdom.math.series/keys [start-degree chebyshev-kind]
                 :or {start-degree 0 chebyshev-kind 0}})

Cheybshev-kind can be 0 (default), 1, or 2, where 0 means a regular polynomial. Returns a collection of functions that each take a number and return a number.

polynomial-ND-fn clj

(polynomial-ND-fn end-degree)

(polynomial-ND-fn end-degree
                  {:provisdom.math.series/keys [chebyshev-kind]
                   :or {chebyshev-kind 0}})

Returns a function that takes a vector [x y z ...] and returns a vector. Terms are sorted by order and then by dimension, e.g., [1 x y z x^2 xy xz y^2 yz z^2 x^3 (x^2 × y) (x^2 × z) (x × y^2) (x × y × z) (x × z^2) y^3 (y^2 × z) (y × z^2) z^3].

polynomial-ND-fn-without-cross-terms clj

(polynomial-ND-fn-without-cross-terms end-degree)

(polynomial-ND-fn-without-cross-terms
  end-degree
  {:provisdom.math.series/keys [chebyshev-kind] :or {chebyshev-kind 0}})

Returns a function that takes a vector [x y z ...] and returns a vector. Terms are sorted by order and then by dimension, e.g., [1 x y z x^2 y^2 z^2 x^3 y^3 z^3].

power-series-derivative-fn clj

(power-series-derivative-fn term-series)

Returns a function that takes a number and returns the derivative of the power series of a value 'x' using a term-series: (a_n × x^n).

power-series-fn clj

(power-series-fn term-series)

Returns a function that takes a number and returns the power series of a value 'x' using a term-series: (a_n × x^n).

power-series-integral-fn clj

(power-series-integral-fn term-series)

Returns a function that takes a number and returns the integral of the power series of a value x using a term-series: (a_n × x^n).

sum-convergent-series clj

(sum-convergent-series term-series)

(sum-convergent-series
  term-series
  {:provisdom.math.series/keys [kahan? converged-pred error-pred]
   :or {kahan? false
        converged-pred (fn [sum i val]
                           (and (>= i 10)
                                (or (<= (m/abs val) m/quad-close)
                                    (<= (m/abs (m/div val sum)) m/quad-close))))
        error-pred (fn [sum i val] (> i 10000))}})

Returns the sum of a convergent series. The functions converged-pred and error-pred take the sum, an index, and the next series value. Options: ::kahan? (default false) -- set to true for greater floating-point summation accuracy. ::converged-pred -- predicate indicating that series has converged (default is that index >= 10 AND the abs value is <= m/quad-close or the abs value is m/quad-close times smaller than the abs sum) ::error-pred -- predicate indicating an error (default is that index is > 10000).