Quick Tip: Create User-Defined Inverse Hyperbolic Functions

Posted May 28, 2021 by James, Vertica Field Chief Technologist

Business card that says Expert Tips,

Vertica includes a ton of built-in mathematical functions to help you on your analytic journey, and creating new ones is quick and easy.

Let’s create the inverse hyperbolic functions:

    ACOSH – To compute the inverse (arc) hyperbolic cosine of its argument.
    ASINH – To compute the inverse (arc) hyperbolic sine of its argument.
    ATANH – To compute the inverse (arc) hyperbolic tangent of its argument.

Example:

verticademos=> CREATE OR REPLACE FUNCTION acosh(x FLOAT) RETURN FLOAT
verticademos-> AS
verticademos-> BEGIN
verticademos->   RETURN ln(x + sqrt((x^2-1)));
verticademos->
verticademos-> END;
CREATE FUNCTION

verticademos=> SELECT acosh(2.352409615);
      acosh
------------------
1.49999999988576
(1 row)

verticademos=> CREATE OR REPLACE FUNCTION asinh(x FLOAT) RETURN FLOAT
verticademos-> AS
verticademos-> BEGIN
verticademos->   RETURN ln(x + sqrt((x^2+1)));
verticademos->
verticademos-> END;
CREATE FUNCTION

verticademos=> SELECT asinh(2.129279455);
      asinh
------------------
1.49999999995969
(1 row)

verticademos=> CREATE OR REPLACE FUNCTION atanh(x FLOAT) RETURN FLOAT
verticademos-> AS
verticademos-> BEGIN
verticademos->   RETURN (ln(((1 + x) / (1 - x)))) / 2;
verticademos->
verticademos-> END;
CREATE FUNCTION

verticademos=> SELECT atanh(0.9051482536);
      atanh
------------------
1.49999999975172
(1 row)

Have fun!