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-- 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;