Mathematical Functions
Mathematical Functions are used to modify data in the Data | Data | Transform command.
The expression evaluator supports 32-bit signed integer numbers, double-precision floating-point numbers, a boolean value, a text string of 0 to 256 characters, and time stamp values.
Variable names must begin with a column letter (i.e. A), row number (i.e. _1), or cell location (i.e. A2), which may be followed by other letters, numbers, or underscores (_), up to a maximum of 256 characters per variable name.
The variable names are not case sensitive. For example, sum(a..z), sum(A..z), and sum(A..Z) all refer to the same variable.
The mathematical expression can consist of constants, variables (such as column letters), or functions (outlined below). The formulas follow standard precedence rules. Spaces are used in the equation for clarity.
Formulas are specified using standard precedence rules. Operators, in order of decreasing precedence, are:
( ) |
parentheses |
- |
minus (or negative sign) |
* / |
multiplication and division |
+ - |
addition and subtraction |
The expression evaluator treats operators with the following precedence:
!, NOT, ~
*, /, %
+, -
<<, >>
<, >, <=, >=
==,!=,<>
&
^, XOR
|
&&, AND
||, OR
?:
IF
Operators of equal precedence are evaluated from left to right within the equation. Parentheses are used to override precedence, and expressions with the parentheses are performed first.
The following built-in functions are supported.
All trigonometric functions are carried out in radians. If the data are in degrees, use the d2r(x) conversion function (in the Miscellaneous Functions section below) to convert degree data to radians and then use the trigonometric functions.
sin(x) |
sine of angle x |
cos(x) |
cosine of angle x |
tan(x) |
tangent of angle x, the value of x must not be an odd multiple of P/2 |
asin(x) |
Arcsine in the range -P/2 to P/2, x must be between -1 and 1 |
acos(x) |
Arccosine in the range 0 to , x must be between -1 and 1 |
atan(x) |
Arctangent in the range -P/2 toP /2 |
atan2(y,x) |
Arctangent of y/x in the range -P to P |
j0(x) j1(x) jn(n,x) |
Bessel functions of the first kind at x of orders 0, 1, and n, respectively |
y0(x) y1(x) yn(n,x) |
Return the Bessel functions of the second kind at x, of orders 0, 1, and n, respectively. For y0, y1, and yn, the value of x must not be negative |
exp(x) |
exponential function of x (e to the x) |
sinh(x) |
hyperbolic sine of angle x |
cosh(x) |
hyperbolic cosine of angle x |
tanh(x) |
hyperbolic tangent of angle x |
ln(x) |
natural logarithm (base e) of x, x must be positive |
log10(x) |
base 10 logarithm of x, x must be positive |
pow(x,y) |
x raised to the yth power Error conditions result if: x is zero and y is negative or zero, x is negative and y is not an integer, an overflow results. |
min(x,y) |
smaller of x and y |
max(x,y) |
larger of x and y |
randn(x,y) |
an approximately normally (Gaussian) distributed real random number with mean x and standard deviation y |
randu(x) |
a uniformly distributed real random number with mean of x from the interval [0,x] |
row() |
returns the row number |
ceil(x) |
next whole number greater than or equal to x |
floor(x) |
next whole number less than or equal to x |
pi() |
returns the value of Pi. To limit to a specific number of digits, use Round(Pi(),y), where Y is the number of digits after the decimal point. |
round(x,y) |
X rounded to the nearest number with Y digits after the decimal point |
sqrt(x) |
square root of x, x must not be negative |
fabs(x) |
absolute value of x |
fmod(x,y) |
floating point remainder of x/y, if y is zero, fmod returns zero |
d2r(x) |
convert angle x from degrees to radians. Example: sin(d2r(30)) computes the sine of 30 degrees. Sin(30) computes the sine of 30 radians. |
r2d(x) |
convert angle x from radians to degrees. |
Statistical Functions of Intervals
sum(a..z) |
calculates the sum of a range of columns in a row |
sum(_1.._5) |
calculates the sum of a range of rows in a column |
avg(a..z) |
calculates the average of a range of columns in a row |
avg(_1.._5) |
calculates the average of a range of rows in a column |
std(a..z) |
calculates the (population) standard deviation of a range of columns in a row |
std(_1.._5) |
calculates the population standard deviation of a range of rows in a column |
rowmin(a..z) |
finds the minimum value of a range of columns in a row |
rowmin(_1.._5) |
finds the minimum value of a range of rows in a column |
rowmax(a..z) |
finds the maximum value of a range of columns in a row |
rowmax(_1.._5) |
finds the maximum value of a range of rows in a column |
The Statistical Functions of Intervals functions operate row-wise on an interval of columns or column-wise on an interval of rows.
For example, SUM(A..Z) computes the sum of the twenty-six columns A, B, C, ..., Z. It does this for each row separately.
Replace 'a..z' by any valid interval of columns or rows, such as W..AC or _4.._612. There must be exactly two periods between the column or row labels. The labels may be given in reverse order, such as SUM(Z..A).
String Comparison
atof(x) |
convert a string x to floating point value |
atoi(x) |
convert a string x to an integer value |
strlen(x) |
length of string x in characters |
strcmp(x,y) |
compare string x with y and return 1 if x>y, -1 if x<y, or 0 if x=y |
stricmp(x,y) |
compare string x with y without regard to the case of any letters in the strings |
strncmp(x,y,z) |
compare the first z character of string x with y |
strnicmp(x,y,z) |
compare the first z characters of string x with y without regard to the case of any letters in the strings |
String comparison functions work with strings, not numbers. Any rows or columns containing numbers result in blanks. In each of the string comparison functions, 1 is returned if string x is greater than string y, -1 is returned if string x is less than string y, and 0 if string x = string y. In the three-parameter comparison functions, the third parameter, z, specifies the number of characters to compare. For example, a z value of 3 compares the x and y strings' first three characters and ignores any characters after the third.
The comparisons are based on the standard ASCII table:
numeric values (disregarded in string comparisons as mentioned above)
cells starting with a space character
common punctuation
numeric text (numbers entered as text)
less common punctuation
uppercase letters
even less common punctuation
lower case letters
uncommon punctuation
blank cells (disregarded in string comparisons)
This is the ASCII table order. The table is read left to right, top to bottom. Items
appearing toward the upper left corner are less than the items
appearing toward the lower left corner.
Boolean Expressions
Boolean expressions include:
logical Operators (and, or, xor, not),
Comparison Operators (=, <>, <, >, <=, >=),
the IF Function - IF(condition,true_value,false_value)
The words AND, OR, XOR, NOT, and IF are reserved keywords and may not be used as variable names.
Logical Operators (and, or, xor, not)
SYMBOL |
NAME |
DESCRIPTION |
AND |
AND |
The result is true if both operands are true. |
&& |
AND |
The result is true if both operands are true. |
! |
Logical NOT |
Inverts the boolean value. True becomes false, false becomes true. |
NOT |
Logical NOT |
Inverts the boolean value. True becomes false, false becomes true. |
& |
AND |
The result is true if both operands are true. |
| |
OR |
The result is true is either of the two operands is true |
^ |
Exclusive -OR (XOR) |
|
XOR |
Exclusive-OR (XOR) |
Same as ^ |
|| |
OR |
The result is true is either of the two operands is true. |
OR |
OR |
The result is true is either of the two operands is true. |
Comparison Operators (=, <>, <, >, <=, >=)
SYMBOL |
NAME |
DESCRIPTION |
~ |
Bitwise NOT |
Inverts the bits in an integer |
* |
Multiply |
Multiplies the two operands |
/ |
Divide |
Divides the first operand by the second |
% |
Remainder |
Integer remainder of the first operand divided by the second. |
+ |
Add |
Adds the two operands |
- |
Subtract |
Subtracts the second operand from the first |
<< |
Shift Left |
Shifts the operand to the left |
>> |
Shift Right |
Shifts the operand to the right |
< |
Less Than |
In the example, A1 < B1, the result is true if A1 is less than B1. |
<= |
Less Than or Equal To |
Result is true if the ordinal value of p1 is less than or equal to p2 |
> |
Greater Than |
Result is true if the ordinal value of p1 is greater than p2 |
>= |
Greater Than or Equal To |
Result is true if the ordinal value of p1 is greater than or equal to p2 |
== |
Equal To |
Result is true if the operands have identical values |
!= |
Not Equal To |
Result is true if the operands do not have identical values |
<> |
Nor Equal To |
Result is true if the operands do not have identical values |
IF Function - IF(condition,true_value,false_value)
SYMBOL |
NAME |
EXAMPLE |
DESCRIPTION |
IF |
Conditional Evaluation |
IF(p1,p2,p3) |
IF (condition,true_value,false_value) i.e. If p1 is true, the result will be p2. If p1 is false, the result will be p3. |
IF |
Conditional Evaluation |
p1?p2:p3 |
condition?true_value:false_value i.e. If p1 is true, the result will be p2. If p1 is false, the result will be p3. |
Examples
In Data | Data | Transform replace X,Y, and Z with column letters (A), row numbers (remember the underscore, _1 is row 1), or cell locations (A1).
Equation |
Mathematical Function Syntax
|
|
pow(x,2) |
|
ln(x) |
|
log10(x) |
|
(1-exp(-X)) |
|
(1-exp(-(pow(x,2)))) |
|
1-(sin(x)/x) |
|
pow(x,2)/(1+(pow(x,2))) |
|
(2 * X)-pow(x,2) |
|
(pow(x,2)+pow(y,2))*(sin(8*atan(x*y))) |
See Also
