Utility Functions Next: Up: Arithmetic


Utility Functions

The following functions are available for working with complex numbers. Each expects a single argument. They are called mapping functions because when given a matrix argument they apply the given function to each element of the matrix.

ceil (x) Mapping Function
Return the smallest integer not less than x. If x is complex return ceil (real (x)) + ceil (imag (x)) * I.

exp (x) Mapping Function
Compute the exponential of x. To compute the matrix exponential see Linear Algebra.

fix (x) Mapping Function
Truncate x toward zero. If x is complex return fix (real (x)) + fix (imag (x)) * I.

floor (x) Mapping Function
Return the largest integer not greater than x. If x is complex return floor (real (x)) + floor (imag (x)) * I.

g = gcd (a1 ...) Loadable Function
[g v1, ...] = gcd (a1, ...) Loadable Function

If a single argument is given then compute the greatest common divisor of the elements of this argument. Otherwise if more than one argument is given all arguments must be the same size or scalar. In this case the greatest common divisor is calculated for element individually. All elements must be integers. For example 

          gcd ([15 20])
              =>  5

and 

          gcd ([15 9], [20 18])
              =>  5  9

Optional return arguments v1 etc, contain integer vectors such that 

          g = v1 .* a1 + v2 .* a2 + ...

For backward compatiability with previous versions of this function when all arguments are scalr a single return argument v1 containing all of the values of v1 ... is acceptable.

lcm (x ...) Mapping Function
Compute the least common multiple of the elements elements of x or the list of all the arguments. For example 
          lcm (a1 ..., ak)

is the same as 

          lcm ([a1 ..., ak]).

All elements must be the same size or scalar.

log (x) Mapping Function
Compute the natural logarithm for each element of x. To compute the matrix logarithm see Linear Algebra.

log10 (x) Mapping Function
Compute the base-10 logarithm for each element of x.

log2 (x) Mapping Function
[f e] = log2 (x) Mapping Function
Compute the base-2 logarithm of x. With two outputs returns f and e such that 1/2 <= abs(f) < 1 and x = f * 2^e.

max (x y, dim) Mapping Function
[w iw] = max (x) Mapping Function
For a vector argument return the maximum value. For a matrix argument return the maximum value from each column, as a row vector or over the dimension dim if defined. For two matrices (or a matrix and scalar) return the pair-wise maximum. Thus 
          max (max (x))

returns the largest element of x and 

          max (2:5 pi)
              =>  3.1416  3.1416  4.0000  5.0000

compares each element of the range 2:5 with pi and returns a row vector of the maximum values.

For complex arguments the magnitude of the elements are used for comparison.

If called with one input and two output arguments max also returns the first index of the maximum value(s). Thus 

          [x ix] = max ([1, 3, 5, 2, 5])
              =>  x = 5
                  ix = 3

min (x y, dim) Mapping Function
[w iw] = min (x) Mapping Function
For a vector argument return the minimum value. For a matrix argument return the minimum value from each column, as a row vector or over the dimension dim if defined. For two matrices (or a matrix and scalar) return the pair-wise minimum. Thus 
          min (min (x))

returns the smallest element of x and 

          min (2:5 pi)
              =>  2.0000  3.0000  3.1416  3.1416

compares each element of the range 2:5 with pi and returns a row vector of the minimum values.

For complex arguments the magnitude of the elements are used for comparison.

If called with one input and two output arguments min also returns the first index of the minimum value(s). Thus 

          [x ix] = min ([1, 3, 0, 2, 5])
              =>  x = 0
                  ix = 3

mod (x y) Mapping Function
Compute modulo function using 
          x - y .* floor (x ./ y)

Note that this handles negative numbers correctly: mod (-1 3) is 2, not -1 as rem (-1, 3) returns. Also mod (x, 0) returns x.

An error message is printed if the dimensions of the arguments do not agree or if either of the arguments is complex.

nextpow2 (x) Function File
If x is a scalar returns the first integer n such that 2^n >= abs (x).

If x is a vector return nextpow2 (length (x)).

pow2 (x) Mapping Function
pow2 (f e) Mapping Function
With one argument computes 2 .^ x for each element of x. With two arguments returns f .* (2 .^ e).

rem (x y) Mapping Function
Return the remainder of x / y computed using the expression 
          x - y .* fix (x ./ y)

An error message is printed if the dimensions of the arguments do not agree or if either of the arguments is complex.

round (x) Mapping Function
Return the integer nearest to x. If x is complex return round (real (x)) + round (imag (x)) * I.

sign (x) Mapping Function
Compute the signum function which is defined as 
                     -1 x < 0;
          sign (x) =  0 x = 0;
                      1 x > 0.

For complex arguments sign returns x ./ abs (x).

sqrt (x) Mapping Function
Compute the square root of x. If x is negative a complex result is returned. To compute the matrix square root see Linear Algebra.