Mathematical Functions

Mathematical Functions are used to modify data with the Data | Data | Transform command in the worksheet or create function plots in the plot window.

Data Types

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

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.

Precedence

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.

Operators of equal precedence are evaluated from left to right within the equation. Parentheses are used to override precedence, and expressions within parentheses are performed first.

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:

1. !, NOT, ~

2. *, /, %

3. +, -

4. <<, >>

5. <, >, <=, >=

6. ==,!=,<>

7. &

8. ^, XOR

9. |

10. &&, AND

11. ||, OR

12. ?:

13. IF

Built-in Functions

The following built-in functions are supported:

Trigonometric Functions

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 in radians
cos(x)	cosine of angle x in radians
tan(x)	tangent of angle x in radians, the value of x must not be an odd multiple of P/2 radians.
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 P, x must be between -1 and 1
atan(x)	Arctangent in the range -P/2 to P/2
atan2(y,x)	Arctangent in the range -P to P

Bessel Functions

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.

Exponential Functions

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 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.

Miscellaneous Functions

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 from the interval [0,x]
row()	row number
ceil(x)	smallest integer that is greater than or equal to x
floor(x)	largest integer 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 argument in degrees to radians, for example: sin(d2r(30)) computes the sine of 30 degrees
r2d(x)	convert argument in radians to degrees

Statistical Functions of an Interval

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 an interval of columns operate row-wise on an interval of columns. For example, SUM(A..Z) computes the sum of the twenty-six columns A, B, C, ..., Z separately for each row. You can replace A..Z with any valid interval of columns, e.g., C..H or W..AC. There must be exactly two periods between the column labels. Columns may be given in reverse order, i.e., SUM(Z..A).

The statistical functions of an interval of rows operate column-wise on an interval of rows. For example, SUM(_1.._5) computes the sum of the 5 rows 1, 2, 3, 4, 5 separately for each column. You can replace _1.._5 with any valid interval of rows, e.g., _3.._12 or _34.._413. There must be exactly two periods between the row labels. Rows may be given in reverse order, i.e., SUM(_5.._1).

String Comparison

atof(x)	converts string to floating-point number
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.

The comparisons are based on the standard ASCII table:

1. numeric values (disregarded in string comparisons as mentioned above)

2. cells starting with a space character

3. common punctuation

4. numeric text (numbers entered as text)

5. less common punctuation

6. uppercase letters

7. even less common punctuation

8. lower case letters

9. uncommon punctuation

10. 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, i.e., 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 if either of the two operands are true
^	Exclusive-OR (XOR)
XOR	Exclusive-OR (XOR)	Same as ^
\|\|	OR	The result is true if either of the two operands are true
OR	OR	The result is true if either of the two operands are true

Comparison Operators (=, <>, <, >, <=, >=)

SYMBOL	NAME	DESCRIPTION
~	Bitwise NOT	Inverts the bits in an integer
*	Multiple	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	Result is true if the value of p1 is less than the value of p2
<=	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
<>	Not 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

Conditional Evaluation

IF(p1,p2,p3)

IF(condition,true_value,false_value)

If p1 is true, the result will be p2. If p1 is false, the result will be p3

Conditional Evaluation

p1?p2:p3

condition?true_value:false_value

If p1 is true, the result will be p2. If p1 is false, the result will be p3

Examples

The following are examples of mathematical function syntax. If you use Data | Data | Transform in the worksheet, replace X, Y, and Z with column letters (A is column A), row numbers (_1 is row 1), or cell locations (A1).

Equation	Mathematical Function Syntax
$image\mte-x2.png$	pow(x,2)
$image\mte-lnx.png$	ln(x)
$image\mte-log10x.png$	log10(x)
$image\mte-1ex.png$	(1-exp(-X))
$image\mte-1-ex2.png$	(1-exp(-(pow(x,2))))
$image\mte-1-sinx.png$	1-(sin(x)/x)
$image\mte-1-x2-1x2.png$	pow(x,2)/(1+(pow(x,2)))
$image\mte-2x-x2.png$	(2 * X)-pow(x,2)
$image\mte-x2y2sin.png$	(pow(x,2)+pow(y,2))(sin(8atan(x*y)))