provisdom.math.derivatives — provisdom/math 2.67

derivative-fn clj

(derivative-fn number->number)

(derivative-fn number->number
               {:provisdom.math.derivatives/keys [derivative h type accuracy]
                :or {derivative 1 type :central}})

Returns a numerical derivative function. Function number->number takes and returns a number. Note that derivative-fn will not be accurate when inputs or outputs are so large when divided by ::h that they lose precision. Options: ::derivative - can be 0 or 1 (default) to 8 ::h - (default is m/sgl-close for 1st deriv, 10x less for others) is the denominator, which is equal to (dx ^ ::derivative), where 'dx' is the small change (smaller ::h isn't usually better, changes to ::h can be important) ::type - can be :central (default), :forward, or :backward ::accuracy - can be 2, 4, 6, or 8 for central (no 8 for 3rd or 4th deriv), and 1-6 for forward or backward (no 6 for 4th deriv). (default ::accuracy is 2 for ::derivative <= 2, else 6. ::accuracy is ignored for ::derivative > 4 and default accuracies are used.

gradient-fn clj

(gradient-fn v->number)

(gradient-fn v->number
             {:provisdom.math.derivatives/keys [h type accuracy]
              :or {h m/sgl-close type :central accuracy 2}})

Returns a numerical gradient function. Function v->number takes a vector and returns a number. The output function takes and returns a vector. Options: ::h (default m/sgl-close) is the denominator, which is equal to 'dx', where 'dx' is the small change (smaller ::h isn't usually better, changes to ::h can be important) ::type can be :central (default), :forward, or :backward ::accuracy can be 2 (default), 4, 6, or 8 for :central, and 1-6 for :forward or :backward.

hessian-fn clj

(hessian-fn v->number)

(hessian-fn v->number
            {:provisdom.math.derivatives/keys [h type accuracy]
             :or {h (* m/sgl-close 0.1) type :joint-central accuracy 2}})

Returns a numerical Hessian function. Function v->number takes a vector and returns a number. The output function takes a vector and returns a symmetric matrix. Options: ::h -- (default m/sgl-close / 10) is the denominator, which is equal to (dx * dx), where 'dx' is the small change (smaller ::h isn't usually better, changes to ::h can be important) ::type can be :joint-central (default), :central, :forward, or :backward ::accuracy can be 2 (default, only choice for :joint-central); 2, 4, 6, and 1-6 for :forward or :backward.

jacobian-fn clj

(jacobian-fn v->v)

(jacobian-fn v->v
             {:provisdom.math.derivatives/keys [h type accuracy]
              :or {h m/sgl-close type :central accuracy 2}})

Returns a numerical jacobian function. Function v->v takes a vector and returns a vector. The output function takes a vector and returns a matrix, where each row is the gradient of f's output. Options: ::h -- (default m/sgl-close) is the denominator, which is equal to 'dx', where 'dx' is the small change (smaller ::h isn't usually better, changes to ::h can be important) ::type -- can be :central (default), :forward, or :backward ::accuracy -- can be 2 (default), 4, 6, or 8 for :central, and 1-6 for :forward or :backward.

partial-derivative-x-of-fxy clj

(partial-derivative-x-of-fxy fxy)

(partial-derivative-x-of-fxy fxy
                             {:provisdom.math.derivatives/keys [h]
                              :or {h m/sgl-close}})

partial-derivative-y-of-fxy clj

(partial-derivative-y-of-fxy fxy)

(partial-derivative-y-of-fxy fxy
                             {:provisdom.math.derivatives/keys [h]
                              :or {h m/sgl-close}})

second-partial-derivative-xx-of-fxy clj

(second-partial-derivative-xx-of-fxy fxy)

(second-partial-derivative-xx-of-fxy fxy
                                     {:provisdom.math.derivatives/keys [h]
                                      :or {h (* m/sgl-close 0.1)}})

second-partial-derivative-xy-of-fxy clj

(second-partial-derivative-xy-of-fxy fxy)

(second-partial-derivative-xy-of-fxy fxy
                                     {:provisdom.math.derivatives/keys [h]
                                      :or {h (* m/sgl-close 0.1)}})

second-partial-derivative-yy-of-fxy clj

(second-partial-derivative-yy-of-fxy fxy)

(second-partial-derivative-yy-of-fxy fxy
                                     {:provisdom.math.derivatives/keys [h]
                                      :or {h (* m/sgl-close 0.1)}})