goalseek (as in Excel)

[jazper]

I use GoalSeek a fair amount in spreadsheets.  It's fast enough, but I confess I don't understand how it works.  Googling produced discussions about Newton Rhapson, something that Computer Science and Math students seem to know about.  Having last looked at math a half century ago on finishing my schooling, I can't pick up what it's about.  



Recently some other clever mathematical stuff was added to newLISP.  Has anybody ever tried something like GoalSeek in newLISP?  If so, I'd appreciate an explanation of the algorithm.  



As an example, I use it in spreadsheets to arrive at what a payment instalment will be over [n] months, at a certain rate of interest.  It isn't simply a matter of dividing sum of principle + interest by number of months, because interest is compounded monthly.  It looks to me like GoalSeek is able to cope with this, as though it calculates the a root of compound interest.  Microsoft gives an simple explanation of the algorithm which didn't help me at all.  Perhaps it just iterates, adding a cent at a time, until its guess subtracted from target is close enough to zero.  I'd imagine it would be easier to bisect, as in a binary search, but I can't get my head around the code even in pseudocode.  Any ideas?

[xytroxon]

I have never used them, but you should be able to find what you want here:



http://www.newlisp.org/downloads/newlisp_manual.html#financial">//http://www.newlisp.org/downloads/newlisp_manual.html#financial



Financial math functions



fv    returns the future value of an investment

irr    calculates the internal rate of return

nper    calculates the number of periods for an investment

npv    calculates the net present value of an investment

pv    calculates the present value of an investment

pmt    calculates the payment for a loan



-- xytroxon

[xytroxon]

Also be sure to use floating point math functions for any calculations, that is: add sub mul div, instead of: + - * /



http://www.newlisp.org/downloads/newlisp_manual.html#floating_point">http://www.newlisp.org/downloads/newlis ... ting_point">http://www.newlisp.org/downloads/newlisp_manual.html#floating_point



Floating point math and special functionsabs   returns the absolute value of a number



acos   calculates the arc-cosine of a number

acosh   calculates the inverse hyperbolic cosine of a number

add   adds floating point or integer numbers and returns a floating point number

array   creates an array

array-list   returns a list conversion from an array

asin   calculates the arcsine of a number

asinh   calculates the inverse hyperbolic sine of a number

atan   calculates the arctangent of a number

atanh   calculates the inverse hyperbolic tangent of a number

atan2   computes the principal value of the arctangent of Y / X in radians

beta   calculates the beta function

betai   calculates the incomplete beta function

binomial   calculates the binomial function

ceil   rounds up to the next integer

cos   calculates the cosine of a number

cosh   calculates the hyperbolic cosine of a number

crc32   calculates a 32-bit CRC for a data buffer

dec   decrements a number in a variable, list or array

div   divides floating point or integer numbers

erf   calculates the error function of a number

exp   calculates the exponential e of a number

factor   factors a number into primes

fft   performs a fast Fourier transform (FFT)

floor   rounds down to the next integer

flt   converts a number to a 32-bit integer representing a float

gammai   calculates the incomplete Gamma function

gammaln   calculates the log Gamma function

gcd   calculates the greatest common divisor of a group of integers

ifft   performs an inverse fast Fourier transform (IFFT)

inc   increments a number in a variable, list or array

inf?   checks if a floating point value is infinite

log   calculates the natural or other logarithm of a number

min   finds the smallest value in a series of values

max   finds the largest value in a series of values

mod   calculates the modulo of two numbers

mul   multiplies floating point or integer numbers

NaN?   checks if a float is NaN (not a number)

round   rounds a number

pow   calculates x to the power of y

sequence   generates a list sequence of numbers

series   creates a geometric sequence of numbers

sgn   calculates the signum function of a number

sin   calculates the sine of a number

sinh   calculates the hyperbolic sine of a number

sqrt   calculates the square root of a number

sub   subtracts floating point or integer numbers

tan   calculates the tangent of a number

tanh   calculates the hyperbolic tangent of a number

uuid    returns a UUID (Universal Unique IDentifier)

[jazper]

Thanks, xytroxon.  I will have to roll my own Goal Seek.  Perhaps some of these functions will help.