As for multiple expressions like an example listed below, each expression is separated by @, and the last one includes y= at the beginning. A range of the loop variable is specified by using x=<::>. The arguments are start, end and step values from the left. Here, abc and def are user definition variables, and pi is a registered constant. (Both a user definition variable and a registered constant are configured by alphabetic characters only or those plus numeric characters.)
x = < -2*pi: 2*pi: 0.01*pi > @
abc = 2 * x @
def = 3 * x @
y = sin( abc ) + cos( def )
But when an expression is used alone as following, y= may be omitted. (It is imperative on ByeGraph.)
2+3*(log(sin(2*pi^2))+6.8)
Parameters are specified by ={,,,} and allowed to hold up to 16 elements. Each parameter can include user definition variables, functions and so on. Here, sita is a user definition variable, and kRad is a registered constant.
x = < 0: 360: 1 > @
sita = { 0, 45, 90 } @
y = sin( kRad * ( x + sita ) )
| Kinds | Key words, supplements |
| Variable | x, y Normally x is used as the loop variable. y is only used at the left side of the last expression line. |
| User definition variable | alphabetic characters only or alphabetic + numeric characters. [ex] var, abc01 |
| Registered constant | alphabetic characters only or alphabetic + numeric characters. [ex] pi, K0, ep0 |
| Global variable | _M0 - _M15 For looping these value are kept. The initial values are 0 by default. '_M0(+)=A' and '_M0(-)=A' are also available. |
| Global variable initializer | ginit<> initializes _M0~_M15 with particular values. [ex] _M0=ginit<10> |
| Loop counter | #LOOP contains the current loop count value. No substitution. |
| Parameter counter | #PARAM contains the current parameter count value. No substitution. |
| Row depth constant for fread source | #FREADMAX stands for the row's depth of the source data for fread/fread2. |
| Separator | @ |
| Substitution | = |
| Range of loop variable | <::> Start, end and step values from the left. [ex] x=<-2*pi:2*pi:0.01*pi> |
| Parameters | {,,,} Up to 16 elements are allowed. [ex] sita={a,b,c} |
| Numeric value | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, e, E |
| Sign | +, - |
| Operator | +, -, *, /, ^ |
| Relation operator | >、<、≥、≤、=、≠ |
| Parenthesis | (,) |
| Math function | ln(), log(), exp(), sin(), cos(), tan(), asin(), acos(), atan(), sqrt(), abs(), fmod(,), inv() |
| File reading function | fread() requires an argument that is a column data number counting from zero. fread2(,) requires two arguments, for row and column. In these, you need to specify a file for reading data. |
| Array data reading function | dread(,) The array data defined in the %data header are read. Two arguments are respectively a row and a column data number counting from zero. |
| Sum function | sum('exp',k=m:n) The partial sum of 'exp' (m:start, n:end). |
| Switch function | switch('test',A:B) If 'test' results in true (>=1), it returns A. Otherwise, B. |
| Comment mark | ! is inserted at the beginning of comment lines. But it is allowed to insert in the middle of a line except for the expression headers. |
| [Note] •• fmod(a,b) outputs the remainder of a ÷ b. •• Considering priority of operators ( +,- << *,/ << ^ ), evaluation for values is done from the left. Using parentheses, '()', the priority can be changed. •• Radian is used as a unit for an angle of trigonometric functions. •• <::>, {,,,} or ginit<> must be used alone on the right side of an expression. (=a*<::> is not allowed. ) •• The relation operators ( >、<、≥、≤、=、≠ ) are allowed to use only inside the 'test' expression of switch('test',A:B). •• The sum or switch function is not allowed to include itself in it. | |
Expression headers are provided for specifying optional settings to expressions or their results.
| Names | Functions |
| %data | The array data defined between %data and %end are read by dread(,) function. |
| %format | Specify the formats of calculation results. As parameters, f (Real), e (Exponential real), d (Integer), y (Integer, divided every three figures) and s (Strings) are prepared. |
| %external | Specify the source file for the file read functions (fread / fread2). |
| %statout (Only for CalcLoop) |
Calculate and output statistics constants (sum, average, and so on) for each column of calculation results after looping is completed. |
| %gout (Only for CalcLoop) |
Output values of the global variables under the calculation results after looping is completed. |
By using file reading functions in expressions you can add several calculation processes into original data which were taken by inquiry or experiment. There are two types of file reading functions: fread for sequential access and fread2 for random access. Applied examples of the fread function are shown below.
[Example] Read the x and y data, calculate omg=2*pi*x from x and multiply y and omg^2.
0.0 1 2 0.1 2 4 0.2 3 6 0.3 4 8 0.4 5 10 : : :
Specification for the loop variable x (x=<::>) is not necessary because data are read by the fread function. The loop count depends on the number of the row depth of the source file.
! Specify formats
%format f e
x = fread(0) @
omg = 2*pi*x @
w = { 1, 2 } @
y = fread(w)*omg^2
The results are as follows.
0.0 0.000e+00 0.000e+00 0.1 7.896e-01 1.579e+00 0.2 4.737e+00 9.475e+00 0.3 1.421e+01 2.842e+01 0.4 3.158e+01 6.317e+01 : : :
From the version 1.8, reading strings becomes possible. Here is an example about it.
[Example] Let's try to add calculated column data newly into the 5th and 6th blank columns which have labels only. (These labels are made to remain.) And the %statout header is used for calculating statistics data for each column.
Name Math English Science Total Average JAMES 78 81 58 MARY 68 83 63 JOHN 72 77 71 PATRICIA 91 68 69 ROBERT 77 71 88 LINDA 88 82 59 MICHAEL 90 72 74 BARBARA 69 71 58 WILLIAM 78 79 63 ELIZABETH 81 83 70 DAVID 65 71 58 JENNIFER 88 83 81
Being switched by the switch function in the following expressions, labels are outputted on the first row (the loop counter #LOOP=0) and then calculation results (the sum and average values among 2nd to 4th columns) are outputted on the other rows.
%external "~/tmp/Grades.txt" 0
!calculate statistics data for each column
%statout avg max min n dev
%format s d
x=fread(0)@
z=sum(fread(k),k=1:3)@
y={fread(1),fread(2),fread(3),
switch(#LOOP=0,fread(4):z),
switch(#LOOP=0,fread(5):z/3)}
The results are as follows.
Name Math English Science Total Average JAMES 78 81 58 217 72 MARY 68 83 63 214 71 JOHN 72 77 71 220 73 PATRICIA 91 68 69 228 76 ROBERT 77 71 88 236 79 LINDA 88 82 59 229 76 MICHAEL 90 72 74 236 79 BARBARA 69 71 58 198 66 WILLIAM 78 79 63 220 73 ELIZABETH 81 83 70 234 78 DAVID 65 71 58 194 65 JENNIFER 88 83 81 252 84 --------- ---- ------- ------- ----- ------- N 12 12 12 12 12 AVG 79 77 68 223 74 DEV 9 6 10 16 5 MAX 91 83 88 252 84 MIN 65 68 58 194 65
CalcEngine is the expression analysis library used in CalcLoop, CalcLoop Plus and ByeGraph.
| Version | Corresponding version to CalcLoop/ByeGraph |
Additional functions |
| CE1.0 (2006/05/06) |
CL1.0, BG1.0 | |
| CE2.0 (2007/07/26) |
CL1.5, BG1.2, BG1.3, BG1.4, BG1.5 | - dread function - sum function - switch function - Expression headers + %data + %format (d/f/e/y) (BG, from ver.1.3) + %symbol (Only for BG) + %yscale (Only for BG) |
| CE2.1 (2008/12/15) |
CL1.6, BG1.6 | - Global variable initializer ginit - fread2 function - #LOOP counter, #PARAM counter - #FREADMAX constant - %format (s) header (CL, from ver.1.8) - %xstrings header (Only for BG) |
| CE2.2 (2009/05/15) |
BG1.7 | - %external header (CL, from ver.1.8) - Reading strings |
| CE2.3 (2009/06/30) |
CL1.8 | - %gout header (Only for CL) - %statout header (Only for CL) |
| CE2.4 (2009/10/31) |
BG1.8 | - %label header (Improved) |
| CE2.4.1 (2010/04/10) |
BG1.9 | - %rangeLin/log, %axislabel headers |