Module: AppMath::Basics

Defined in:
lib/appmath_basics.rb

Overview

A Module which collects simple utility functions.

Class Method Summary collapse

Class Method Details

.cut(x) ⇒ Object

Returns the nearest number to x, which up to sign and power of 10 is one of the numbers in the array c in the function body. For instance,

c = [1,2,5,7.5,10]

In a sense, here cutting is a more drastic version of rounding. It will be used in order to create reasonable axis subdivsion in graphical representation of data.



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# File 'lib/appmath_basics.rb', line 86

def Basics.cut(x)
  fail "x is not a number" if x.nan?
  fail "x is not finite" if x.infinite?
  c = [R.c1,R.c2,R.c5,R.c(7.5),R.c10]
  return R.c0 if x.zero? 
  s = Basics.sign(x)
  y1 = x.abs
  ylog = y1.log10
  ylogInt = ylog.floor
  yMantisse = ylog - ylogInt
  y = R.c10 ** yMantisse
  fail "Basics.cut(): !(1 <= y)" if !(R.c1 <= y)
  fail "Basics.cut(): !(y < 10)" if !(y < R.c10)
  i = 0
  while y > c[i] 
    i += 1
  end
  cd = c.length
  fail "unexpected failure in function Basics.cut" if i < 0 || i >= cd
  yu = c[i] # yu is the smallest c[k] which is larger or equal to y

  if i==0
    yf = yu
  else
    fail "unexpected failure in function Basics.cut" if (i-1) < 0 || (i-1) >= cd
    yl = c[i-1]
    yf = yu-y <y -yl ? yu : yl # now yf is the c[k] which is nearest to y

  end
  return yf.ldexp(ylogInt) * s # sign and exponent are restored

end

.inf(a, b) ⇒ Object

Returns the smaller of the two numbers a and b.



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# File 'lib/appmath_basics.rb', line 58

def Basics.inf(a, b)
  a < b ? a : b
end

.sign(a) ⇒ Object

Returns the sign of a as a real number.



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# File 'lib/appmath_basics.rb', line 63

def Basics.sign(a)
  if a > R.c0
    R.c1
  elsif a < R.c0
    -R.c1
  else
    R.c0
  end
end

.sign2(a, b) ⇒ Object

Returns ‘a with the sign of b’. Programming idiom frequently used in the ‘Numerical Recipes in C’ by Press et al.



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# File 'lib/appmath_basics.rb', line 75

def Basics.sign2(a, b)
  b >= R.c0 ? a.abs : -a.abs
end

.sup(a, b) ⇒ Object

Returns the larger of the two numbers a and b.



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# File 'lib/appmath_basics.rb', line 53

def Basics.sup(a, b)
  a <= b ? b : a
end