-- The MIT License (MIT)
--
-- Copyright (c) 2023 Leandro Pereira de Lima e Silva
-- 
-- Permission is hereby granted, free of charge, to any person obtaining a copy
-- of this software and associated documentation files (the "Software"), to deal
-- in the Software without restriction, including without limitation the rights
-- to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
-- copies of the Software, and to permit persons to whom the Software is
-- furnished to do so, subject to the following conditions:
-- 
-- The above copyright notice and this permission notice shall be included in all
-- copies or substantial portions of the Software.
-- 
-- THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-- IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-- FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-- AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-- LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-- OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
-- SOFTWARE.

create or replace function npv(
    "values" numeric[],
    rate numeric,
    months numeric default 12,
    derivative bool default false)
returns numeric
as $$
declare
    ret double precision;
    k integer;
begin
    ret := 0;
    for i in 1..array_length(values, 1) loop
        k := case when derivative then -i else 1 end;
        ret := ret + k * values[i] / (1 + rate) ^ ((i - 1)  * (months / 12));
    end loop;
    return ret;
end;
$$ language plpgsql;

create or replace function irr(
    "values" numeric[],
    months numeric default 12,
    guess numeric default 0.1,
    tol numeric default 1e-12,
    maxiter integer default 100)
returns numeric
as $$
declare
    val double precision;
    der double precision;
    new_guess double precision;
begin
    for j in 1..maxiter loop
        val = npv(values, guess, months);
        der = npv(values, guess, months, derivative := true);
        new_guess := guess - val / der;
        if abs(guess - new_guess) <= tol then
            return guess;
        end if;
        guess := new_guess;
    end loop;
    return null;
end;
$$ language plpgsql;