mask - return a subset of an array

Syntax: any mask(any x, float condition)
Description: Return all elements of x for which condition is true.
  • x and condition are grids they are first converted to arrays
  • If all elements of condition are false, mask returns undef
  • mask is useful for reducing the size of datasets by removing unwanted elements.
  • You must remember to perform the same mask on any similar datasets. e.g. 
    z = mask(z,x>0);
y = mask(y,x>0);
x = mask(x,x>0);

    If you are using a dataset in the condition you must remember to mask that dataset last. Alternatively, or if you have a complex condition you can evaluate the condition first:

    mymask = (x>0) and (y<0);
x = mask(x, mymask);
y = mask(y, mymask);
z = mask(z, mymask);
  • If you want to avoid changing the size of your datasets then you can instead mark points as invalid with undef and the if function: 
    z = if((x>0) and (y<0), undef, z);
Code sample 1: x = rnd(100);  y = rnd(100);

#Find the elements of x that are less than 0.1
lineNums = mask(1:100, x<.1);

for i in lineNums
  printf("x[%d] = %g, y[%d] = %g\n", i, x[i], i, y[i]);
endfor
Code sample 2: #find all arguments containing ".gsl"

argv = "Gsharp" // "bob.gsl" // "dave.gsl" // "-bs";
GSLfiles = mask(argv, (argv-".gsl")<>argv);
See also: if

match - find text substring

Syntax: string match(string t, string pattern)
Description: match is included for backwards compatibility - it has been replaced by strstr.

match returns a substring of t matching the specified pattern.

  • ? - selects a character
  • <space> - ignores a character
  • * - selects one or more characters
Examples: pattern match("abcdef",pattern)
"*   "
" ? * "
"a ? * "
"b*" 		"abc"
"bde"
"ace"
undef
See also: strstr, strchr, strrchr

matdet - matrix determinant

Syntax: float matdet(float matrix)
Description: Return determinant of a matrix.
Examples: matrix matdet(matrix)
a  b
c  d 		ad - bc
See also: matinv, matmul, matsolve

matinv, matsolve - matrix inverse and matrix solve

Syntax: float matinv(float matrix)
float matsolve(float M, float D)
Description: matinv returns the inverse of matrix.
matsolve solves simultaneous equations.

If M is a matrix, N is matinv(M) and I is the identity matrix (M.I=M and I.M=M) then:

  • M.N = I and
  • N.M = I
  • If M.X = D, where D is known and X is not then:
    Multiply both sides by N:   
     N.(M.X) = N.(D)
    which is the same as: 
     (N.M).X  = N.D
    which simplifies to: 
     X = N.d
    or in GSL: 
     x = matmul(matinv(M),D);
     
  • Rather than use x = matmul(matinv(M),D) you can use: 
    x = matsolve(M,D);
Examples:

To solve the simultaneous equations:

3x + 2y = 4
x - y = 6

write as M.x = d where

M x d
3   2
1  -1		 x
y		 4
6		 
M = (3,2)//(1,-1);
d = 4//6;
#x = matmul(matinv(M),d);
x = matsolve(M,d);
See also: matdet, matmul, matsolve

 matmul - multiply matrices

Syntax: float matmul(float M, float N)
Description: Return the matrix multiplication of M and N
  • matmul(M,N) is equivalent to: 
    sumx(repeatz(transpose(M),sizey(N))*repeaty(N,sizey(M)))
  • matmul(M,N) may be different from matmul(N,M)
See also: matdet, matinv, matsolve

max - maximum of dataset

Syntax: float max(float x)
Description: Return maximum value of x
Examples: x max(x)
1
3
2 		3
Code sample 1: x = rnd(100);  y = rnd(100);

echo("The highest value of y can be found where x equals:");
echo(mask(x,y=max(y));

See also: min, max2, maxx

 max2 - maximum of corresponding elements

Syntax: float max2(float a, float b)
Description: Return the maximum values of corresponding elements of a and b
Examples: a b max2(a,b)
1  1
3  4 		4  3
2  1 		4  3
3  4
Code sample 1: x = rnd(100);
x = max2(x,0.5);
See also: min, max, maxx

maxx - maximum of each column

Syntax: float maxx(float x)
Description: Return the maximum value of each column of x
  • The result is returned as a column dataset
  • To find the maximum of each row use maxx(transpose(x))
Examples: x maxx(x)
1  3  5
2  4  6 		2
4
6
See also: max

member - check existence of dataset

Syntax: float member(string dataset)
Description: Returns true if dataset can be found in the current folder
  • This function is the simplest way to check for the existence of a dataset if you are unsure of the current folder. If you know the folder is WORK then you can use exists(WORK.mydataset) instead.
Code sample: 
if not member("grid")  grid = bilinear(x,y,z,20,20);
See also: exists

message_level - set which messages to suppress

Syntax: message_level(float errors, float warnings, float information, float user)
Description:

Exactly the same as set_messages()
See also: set_messages

middayrange - return range of dates

Syntax: date middayrange(date d, float s)
Description: identical to dayrange
See also: dayrange

midhourrange - return range of times

Syntax: time midhourrange(string times, float hstep)
Description: Return a range of times which can be found within the extremes of times and are an integer multiple of hstep hours since 00:30:00
Example: times midhourrange(times,3)
9:02:01
12:00:00
19:02:01 		9:30:00
12:30:00
15:30:00
18:30:00
See also:

minuterange, secondrange, hourrange

midminuterange - return range of times

Syntax: time midminuterange(string times, float mstep)
Description: Return a range of times which can be found within the extremes of times and are an integer multiple of mstep minutes since 00:00:30
Example: times midminuterange(times,7)
9:06:15
9:29:59 		9:06:30
9:13:30
9:20:30
9:27:30
See also:

minuterange, secondrange, hourrange

midmonthrange - return range of dates

Syntax: date midmonthrange(string dates, float dstep)
Description: Return all the month middles that can be found within the extremes of dates starting with the first one and then with a step of dstep
Example: dates midmonthrange(dates,2)
29/6/1970
25/12/1970 		16-JUL-1970
16-SEP-1970
16-NOV-1970
See also:

monthrange, dayrange, yearrange

midquarterrange - return range of dates

Syntax: date midquarterrange(string dates, float dstep)
Description: Return all the mid quarter dates that can be found within the extremes of dates starting with the first one and then with a step of dstep
Example: dates midquarterrange(dates,2)
1/4/2000
25/12/2000 		16-MAY-2000
16-NOV-2000
See also:

quarterrange, monthrange, dayrange, yearrange

midsecondrange - return range of times

Syntax: time midsecondrange(string times, float mstep)
Description: Identical to secondrange
See also:

secondrange

midweekrange - return range of dates

Syntax: date midweekrange(string dates, float dstep)
Description: Return all the Thursdays that can be found within the extremes of dates starting with the first one and then with a step of dstep
Example: dates midweekrange(dates,2)
29/6/70
2/8/70 		02-JUL-1970
16-JUL-1970
30-JUL-1970
See also:

weekrange, quarterrange, monthrange, dayrange, yearrange

midyearrange - return range of dates

Syntax: date midyearrange(string dates, float dstep)
Description: Return all the July 2nd's that can be found within the extremes of dates starting with the first one and then with a step of dstep
Example: dates midyearrange(dates,2)
29/6/70
2/8/73 		02-JUL-1970
02-JUL-1972
See also:

weekrange, quarterrange, monthrange, dayrange, yearrange

min - minimum of dataset

Syntax: float min(float x)
Description: Return minimum value of x
Examples: x min(x)
1
3
2 		1
Code sample 1: x = rnd(100);  y = rnd(100);

echo("The lowest value of y can be found where x equals:");
echo(mask(x,y=min(y));

See also: max, min2, minx

 min2 - minimum of corresponding elements

Syntax: float min2(float a, float b)
Description: Return the minimum values of corresponding elements of a and b
Examples: a b min2(a,b)
1  1
3  4 		4  3
2  1 		1  1
2  1
Code sample 1: x = rnd(100);
x = min2(x,0.5);
See also: min, minx

minutenumber - return minute part of a time

Syntax: float minutenumber(string t)
Description: Return the minute part of a time dataset t.
  • t can either be a time dataset or a string in one of the formats supported by the function timeformat1.
Example: t minutenumber(t)
12:00:00
14:59:59 		00
59
Sample code: 
#This function calculates the angles of the hands of a clock
function set_hands()
  T = time;
  SecondHand = secondnumber(T)*6;
  BigHand    = (360*minutenumber(T)+SecondHand)/60;
  LittleHand = (360*hournumber(T)+BigHand)/12;
endfunction
See also:

hournumber, secondnumber, totime

minuterange - return time range

Syntax: time minuterange(string times, float hstep)
Description: Return a range of times which can be found within the extremes of times and are an integer multiple of hstep minutes since midnight
Example: times minuterange(times,6)
"00:3:20"
"00:21:21" 		00:06:00
00:12:00
00:18:00
See also:

hourrange, secondrange, midhourrange

minx - minimum of each column

Syntax: float minx(float x)
Description: Return the minimum value of each column of x
  • The result is returned as a column dataset
  • To find the minimum of each row use minx(transpose(x))
Examples: x minx(x)
1  3  5
2  4  6 		1
3
5
See also: min

mod - modulus - remainder from integer division

Syntax: float mod(float x, float y)
Description: Returns the remainder after integer division of x by y.

For example: mod(1989,100) = 89

  • div(x,y)*y + mod(x,y) is equivalent to x
Examples: x mod(x,2)
-3
-2
-1
0
1
2
3		 -1 
0 
-1
0
1
0
1
Code sample: 
years = yearnumber(dates);
years2digits = mod(years,100);
See also: div

monthnumber - extract month number from a date dataset

Syntax: float monthnumber(date d)
Description: Extract the month number of each element of d
Examples: d monthnumber(d)
13-MAR-2000
14-APR-2000		 3
4
Sample code: 
#This list of dates is missing the year

A1 = "13/9" // "2/10" // "1/1" // "5/5" //
     "12/8" // "25/12" // "4/2";
mydates = dateformat1(A1+"/98");
dd = daysince(mydates);
offset = accum(diff(dd)<0);
d = daynumber(mydates);
m = monthnumber(mydates);
y = yearnumber(mydates)+offset;
mydates = todate(y,m,d);
See also: todate, daynumber, yearnumber

monthrange - return range of dates

Syntax: date monthrange(string dates, float dstep)
Description: Return all the first days of the month that can be found within the extremes of dates starting with the first one and then with a step of dstep
Example: dates monthrange(dates,2)
29/6/1970
25/12/1970 		01-JUL-1970
01-SEP-1970
01-NOV-1970
See also:

midmonthrange, dayrange, yearrange

moveavg - return moving average

Syntax: float moveavg(float x, float nx)
Description: Return a moving average of x. The value returned is an average of each element and the nx-1 elements before it.
  • The returned dataset has the same size as x
  • The first nx-1 values are an average of all the elements up to that point.
Example: x moveavg(x,3)
1
2
3
4
5 		1
1.5
2
3
4
Sample code: 
#A function where the value returned is an average of each
#element and the nx-1 elements around it.
#Special treatment is performed at the beginning and the end
function float movingavg(float x, float nx)
  float n1, n2, a;

  n1 = nint(nx/2);
  n2 = size(x)+n1-1;
  x = x//repeatx(undef,nx);
  a = moveavg(x,nx);
  return slicex(a,n1:n2);

endfunction
See also:

avg, movesum

movesum - return moving sum

Syntax: float movesum(float x, float nx)
Description: Return a moving sum of x. The value returned is the sum of each element and the nx-1 elements before it.

See moveavg for details

See also:

moveavg, sum, accum

 

 

 

 

 

 

 

 

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