For entering mathematical formulas there are several special variables and constants, most of which are directly connected to the contents or indices of the data matrix. Please note that not all constants and special variables are available for the calculation of chemical maps (those which are not avaiable are displayed in the table below in gray color):
| Identifier |
Type |
Explanation |
| Pi |
const |
R/O |
The number Pi (3.14159...) |
| NCol |
const |
R/O |
Number of columns of the data matrix |
| NRow |
const |
R/O |
Number of rows of the data matrix |
| NLay |
const |
R/O |
Number of layers of the data matrix |
| NTsl |
const |
R/O |
Number of time slots of the data matrix |
| Cx |
var |
R/W |
Data in column x (x = 1..NCol) |
| Rx |
var |
R/W |
Data in row x (x =1..NRow) |
| Lx |
var |
R/W |
Data in layer x (x =1..NLay) |
| Tx |
var |
R/W |
Data in time slot x (x =1..NTsl) |
| Cx:y |
var |
R/W |
Data in columns x to y (x,y = 1..NCol) |
| Rx:y |
var |
R/W |
Data in row x to y (x,y = 1..NRow) |
| CuRv:CxRy |
var |
R/W |
Data in a rectangular area of the data matrix which is bounded by the columns Cu and Cx and the rows Rv and Ry. |
| All |
var |
W/O |
All data of the data matrix; the identifier "All" is only allowed in the left part of an equation. |
| ° |
var |
R/O |
Current reference cell. This symbol indicates the value of the currently referenced cell when iterating through a range of cells. |
| Cix |
var |
R/O |
Column index of the data matrix |
| Rix |
var |
R/O |
Row index of the data matrix |
| Lix |
var |
R/O |
Layer index of the data matrix |
| Tix |
var |
R/O |
Time slot index of the data matrix |
The following operators are currently available for mathematical transformations:
| Operator |
Function |
Explanation |
Example |
| + |
summation |
x+y |
c1+c2+c7 calculates the sum of the columns 1, 2, and 7 |
| - |
subtraction |
x-y |
r5-r7 computes the difference between row 5 and 7 |
| * |
multiplication |
x*y |
|
| / |
division |
x/y |
|
| # |
modulo |
x#y, the modulo function returns the remainder of integer division of round(x)/round(y) |
c3#5 returns the values in column 3 modulo 5 |
| ^ |
exponentiation |
x^y , x,y..any real values |
|
| () |
parentheses |
parentheses can be used to change operator precedence |
(c1+c2)*(c3+c4) is different from c1+c2*c3+c4 |
| ABS |
absolute value |
abs(x), x..any real number |
|
| ARCCOS |
inverse cosine |
arccos(x) |
|
| ARCSIN |
inverse sine |
arcsin(x) |
|
| ARCTAN |
inverse tangens |
arctan(x) |
|
| COS |
cosine |
cos(x), x..angle in radians |
cos(c1) returns the cosine of the values in column 1 (assuming that the column contains angles measured in radians) |
| EXP |
exponent |
exp(x) |
|
| FRAC |
decimal part of a real number |
frac(x) |
frac(-3.822) returns the value -0.822 |
| GAUSS |
random number |
generates normally distributed random numbers with zero mean and unit standard deviation |
c1:=0.2*gauss+6.5 fills the column 1 with normally distributed random numbers having a mean of 6.5 and a standard deviation of 0.2 |
| INT |
integer part of a real number |
int(x) |
|
| LG |
decadic logarithm |
lg(x) |
|
| LN |
natural logarithm |
ln(x) |
|
| MEAN |
returns the mean of a list of columns or rows |
mean(list), the list contains a list of columns or rows separated by commas; a range of neighboring columns/rows/layers may be abbreviated by the ':' sign. |
mean(r8:10,r5) calculates the mean of the rows 5, 8, 9, and 10. |
| NDDENS |
density of the standard normal distribution |
nddens(x) |
|
| NDINT |
integral of the standard normal distribution from
-infinity to x |
ndint(x) |
|
| NDQUANT |
quantile of the standard normal distribution for a probability x |
ndquant(x) |
|
| RAND |
uniformly distributed random numbers |
random(x), x..amplitude of noise (mean = 0.0) |
rand(8) creates uniformly distributed random numbers in the range of -4 to +4 |
| ROUND |
rounding to integer |
round(x) |
|
| SIGN |
returns the sign of variable x |
sign(x) |
|
| SIN |
sine |
sin(x), x..angle in radians |
sin(c1+pi/2) returns the sine of the values in column 1 plus pi/2 (assuming that the column contains angles measured in radians) |
| SQR |
square |
sqr(x) |
|
| SQRT |
square root |
sqrt(x), with x >= 0. Negative numbers generate an error message |
|
| SUM |
returns the sum of a list of columns or rows |
sum(list), the list contains a list of columns or rows separated by commas; a range of neighboring columns/rows/layers may be abbreviated by the ':' sign. |
sum(c2,c8:11) calculates the sum of the columns 2, 8, 9, 10, and 11. |
| TAN |
tangens |
tan(x), x..angle in radians |
tan(c4) returns the tangens of the values in column 4 (assuming the column contains angles measured in radians) |
| VAR |
returns the variance of a list of columns or rows |
var(list), the list contains a list of columns or rows separated by commas; a range of neighboring columns/rows/layers may be abbreviated by the ':' sign. |
var(c1:4,c7,c9) calculates the variance of the columns 1, 2, 3, 4, 7, and 9. |
Appendix 
