This feature allows you to create a new column based on a formula.
Calculated columns are useful in data analysis; for example, you might define a column that is the derivative of another column with respect to time, a smoothed version of a sensor column, or the ratio of two sensor columns. Calculated columns can be graphed or used in further analysis.
The new calculated column can be a function of another column or columns, or it may be defined by a rule that does not depend on other columns. Arithmetic operators ("^", "*", "/", "+", "-"), parentheses, and other mathematical functions can be used to create a new column based on one or more existing columns. For example, if you have current and potential data, you can use a new column to calculate the power (current times potential). This definition is shown here.
You can create a calculated column by choosing New Calculated Column from the Data menu. You can edit calculated columns by either double-clicking the column name in the data table or choosing Column Options from the Data menu.
Name
The long name is used in graph axis labels, column headings and menus whenever there is sufficient room. You cannot use a quotation character (“) in the Name.
Short Name
The Short Name is used in graph axis labels, column headings, and menus whenever there is limited room. If you do not enter a Short Name, the first letter of the Name will be used.
Units
The Unit follows the Name in graph axis labels and column headings. If the units that you enter are not the same as a visible line on the active graph window, you will be warned that your column will not be automatically shown in the graph. You can either re-enter units that match a visible line, or click on the y-axis label in the graph window and select your column to be drawn.
You can choose special symbols (including subscripts and superscripts) to be included in all of the above fields by clicking .
A Calculated Column resides in a particular Data Set. Choose which Data Set will receive the new column. If Add to All Similar Data Sets, is checked, copies of the calculated column will be added to Data Sets that share the same column names. For example, you might want to create a smoothed version of the data from an accelerometer, and you want such a column in each of your stored runs. To do this, add a calculated column to the Latest Data Set, and check Add to All Similar Data Sets to add to all similar data sets.
Equations can contain column names, mathematical functions, constants, and parameters. If you want your equation to include data from a column, you can choose column names from the Variables (Columns) drop-down menu or you can type existing column names (inside quotation marks). If you choose a sensor column as a variable, a Display During Live Readouts checkbox will appear. If you select this option, the readouts for the calculated column will be displayed on the toolbar.
You may also enter mathematical functions by choosing them from the Functions drop-down menu or by typing them (see below for function definitions). For example, if you have a column named "X", and you want to create a column whose values are the square roots of the values in "X", select sqrt() from the Functions menu, then select X from the Variables (Columns) menu. Your equation would look like this:
sqrt("X")
Let's suppose you named your new column "Root". If "X" had the values: 4, 25, and 64, then "Root" would have the values: 2, 5, and 8. If you changed any of the values in "X", "Root" would also change. "Root" is linked to and dependent on the column "X". If you delete "X", "Root" will also be deleted.
Mathematical functions can be used alone or in combination with others; you can nest functions, use arithmetic operators inside functions, and use parentheses to group operations. For example, a valid expression (assuming you have columns named "X" and "Y"), is:
sin(("X" + "Y") / sqrt(3))
If the the equations are not mathematically legal (e.g. square roots of negative numbers), a blank cell will be displayed. Any further expression based on that cell will also result in a blank cell.
To insert a specific parameter into a calculated column's equation, select its name from the Parameters drop-down menu. A parameter is a place to store an adjustable numeric value. The parameter can be referred to in calculated columns, trigger level thresholds, and similar fields.
When you include a column as part of an equation, you can enter only the column name or you can enter the full name. The full name specifies the data set and the column name (for example, Run 1 | Time). The difference is subtle but can be useful. When you enter just the column name, you are saying that you want the calculated column to use a column of that name in the data set in which the calculated column is located. When you give the full name, you are referring to a specific column in a specific data set, regardless of in which data set you have placed your calculated column.
For example, let's say you have two sets of data that each contain 3 columns: X, Y, and a calculated column called CC. If the CC equation is "X" + "Y", the values in the Run 1 calculated column will be the sum of Run 1 X and Run 1 Y and the values in the Run 2 calculated column will be the sum of Run 2 X and Run 2 Y. However, if the CC equation is "Run 1 | X" + "Y", Run 1 CC will be the sum of Run 1 X and Run 1 Y and Run 2 CC will be the sum of Run 1 X and Run 2 Y. To select the full name, choose Variables (Columns) > Choose Specific Column.
- Trigonometric functions will use degrees or radians as set in the Settings for (file name) in the File menu.
Function |
Description |
analysis > |
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("X", startRow, endRow) Takes all columns named "X" and extracts startRow to endRow for each of those columns, appending the values into a single column. |
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datasets("X") Appends the dataset names of all datasets that have a column named "X". Use analysis and datasets together to create a graph (analysis on the vertical axis and datasets on the horizontal). for example, if you had 3 datasets as follows: DS1 DS2 DS3 X X Y 1 11 21 2 12 22 and then added analysis("X", 1, 1) and datasets("X") you would get: datasets analysis DS1 1 DS2 11 |
beats per minute |
BeatsPerMinute("Signal", "Time", intervalInSeconds,
minPercent, maxPercent, noise) Returns the number of beats per minute of the values in "Signal" vs. "Time". This function is similar to the rate function except that the interval given here is always in seconds and the returned value is always in minutes. For example, if "Time" is in seconds then: beatsPerMinute("Signal", "Time", interval, min, max, noise) = 60 * rate("Signal", "Time", interval, min, max, noise) |
blood pressure > |
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The measured arterial pressure when the heart is at
rest. "Pressure" and a "Time" column as inputs and return a single
number. diastolic("Pressure", "Time") "Pressure": Pressure values from the BPS "Time": Time the pressure values were recorded Returns the smaller number of blood pressure |
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meanArterialPressure("Pressure", "Time") "Pressure": Pressure values from the BPS "Time": Time the pressure values were recorded Returns the pressure value at the max peak used for blood pressure calculations. |
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Oscillations("Pressure", "Time") "Pressure": Pressure values from the BPS "Time": Time the pressure values were recorded Returns the Oscillations of the peaks and valleys used to calculate systolic and other blood pressure values. |
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OscillatoryPeaks("Pressure", "Time") "Pressure": Pressure values from the BPS "Time": Time the pressure values were recorded Returns the peaks used to calculate systolic, diastolic, and pulse (the "high" values in "Oscillations"). |
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pulse("Pressure", "Time") "Pressure": Pressure values from the BPS "Time": Time the pressure values were recorded Returns the pulse using the inputs from the Blood Pressure Sensor (similar results, different algorithm as the other beats-per-minute functions) |
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systolic("Pressure", "Time") "Pressure": Pressure values from the BPS "Time": Time the pressure values were recorded The measured arterial pressure when the heart contracts. Returns the larger number of blood pressure |
boolean > |
For the boolean functions a 1 is considered true, 0 false and anything else an invalid input |
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AND(X, Y) return 1 if and only if X and Y are both 1 |
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NOT(X) return 1 if X is 0; 0 if X is 1 |
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OR(X, Y) return 1 if X or Y is 1 |
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XOR(X, Y) return 1 if X or Y is 1 but not both |
calculus > |
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derivative("Y", "X") "Y": A column of real numbers "X": Optional. A column of real numbers The numerical derivative is the weighted average of the slope of 'n' points around each point. You can set 'n' in Settings for (Name). If you don't supply an "X" column, the program will find one. |
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derivativeSG("Y", "X") "Y": A column of real numbers "X": Optional. A column of real numbers Savitsky-Golay derivative. Fits a polynomial to 'n' points around each point and computes the derivative of the polynomial at that point. You can set 'n' in Settings for (Name). If you don't supply an "X" column, the program will find one. |
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derivativeTimeShift("Y", "X") Returns the derivative of "Y" with respect to "X". This function is specifically designed to be used with photogate and picket fence data. The derivatives returned are adjusted to estimate values at the start of the timing interval, instead of the midpoint. For details see The Physics Teacher, Vol 35, April 1997, p. 220. The article written by William Leonard is entitled "The Dangers of Automated Data Analysis." Average velocity during the time interval is equal to the instantaneous velocity at midpoint of the time interval. Where |
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integral("Y","X") "Y": A column of real numbers "X": Optional. A column of real numbers The numerical integral is the running sum of the areas of rectangles calculated by the midpoint rule. The i'th rectangle is (Yi - Y(i-1)) / (Xi - X(i-1)). If you don't supply an "X" column, the program will find one. |
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secondDerivative("Y", "X") "Y": A column of real numbers "X": Optional. A column of real numbers Calculates the numerical second derivative of "Y" with respect to "X". If you don't supply an "X" column, the program will find one. |
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secondDerivativeSG("Y", "X") "Y": A column of real numbers "X": Optional. A column of real numbers Savitsky-Golay second derivative. Fits a polynomial to 'n' points around each point and computes the second derivative of the polynomial at that point. You can set 'n' in Settings for (Name). If you don't supply an "X" column, the program will find one. |
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secondDerivativeTimeShift("Y", "X") "Y": A column of real numbers "X": Optional. A column of real numbers Numerical time-shifted second derivative. Calculates the second numerical derivative of "Y" with respect to "X". The values are shifted so that the derivatives are calculated at the midpoints between each two values. If you don't supply an "X" column, the program will find one. |
collapse |
collapse("X") Returns a column with all non-numerical cells (blanks and text) removed. |
collapseIndirect |
collapseIndirect(X, Y) Returns a column of only the rows in "X" corresponding to rows in "Y" that have valid numerical cells. |
constant |
Constant(x, num) x: A real number num: A real number or a column Generates a constant column filled with the value 'x'. The number of values in the returned column is num, or if a column was passed in, the size of the passed-in column. |
delta |
delta ("X") "X": A column of real numbers Returns a column of values where the i'th value is the i'th value in "X" minus the (i-1)'th value in "X". |
digital filtering > |
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("Y", "X", "ripple", "freqCutoff") "Y": The data column to be filtered "X": The associated time column for "Y" "ripple": The ripple allowed in the pass-band "freqCutoff": Cut-off frequency (-3dB), in hertz Applies a Chebyshev low-pass filter. For "ripple", enter a value that is a percent of the pass-band. To apply a Butterworth low-pass filter, set "ripple" to 0. |
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("Y", "X", "ripple", "freqCutoff") "Y": The data column to be filtered "X": The associated time column for "Y" "ripple": The ripple allowed in the pass-band "freqCutoff": Cut-off frequency (-3dB), in hertz Applies a Chebyshev high-pass filter. For "ripple", enter a value that is a percent of the pass-band. To apply a Butterworth high-pass filter, set ripple to 0. |
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("Y", "X", "lowFreq", "highFreq") "Y": The data column to be filtered "X": The associated time column for "Y" "lowFreq": Low frequency cut-off (-3dB), in hertz "highFreq": High frequency cut-off (-3dB), in hertz Ripple is automatically set to zero and is not adjustable. The function returns the signal with the frequencies outside the designated frequency range removed. |
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("Y", "X", "lowFreq", "highFreq") "Y": The data column to be filtered "X": The associated time column for "Y" "lowFreq": Low frequency cut-off (-3dB), in hertz "highFreq": High frequency cut-off (-3dB), in hertz Ripple is automatically set to zero and is not adjustable. The function returns the signal with the frequencies inside the designated frequency range removed. |
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("Y", "X", "decayConstant") "Y": The data column to be filtered "X": The associated time column for "Y" "decayConstant": A value in seconds that determines the decay of "Y" Applies an exponential time decay to the signal. |
ElectrophoresisInterpolate |
ElectrophoresisInterpolate("Std. Dist", "Std. BP",
"Dist") "Std. Dist": Distances from the standard "Std. BP": Base Pair Counts from the standard "Dist": Distances to interpolate Returns a column of base pair counts based on the Electrophoresis curve fit for "Std. Dist" vs. "Std. BP" given "Dist". Will NOT work if curve fit has been deleted. This function is used automatically when doing a Gel Analysis (Electrophoresis). |
exp |
exp("X") "X": A column of real numbers Returns the exponent, exp(x) = e^x, where e is the natural log base (2.17...). |
integer |
integer("X") Extracts the integral part of values in "X". |
interpolate |
interpolate("X") Fills in missing values using linear interpolation. |
ln |
ln("X") "X": A column of real numbers larger than 0 Returns the natural logarithm. If b = ln(a) then e^b = a (Where e is the constant 2.17...). |
log |
log("X") "X": A column of real numbers larger than 0 (Log base 10) If b = log(a) then 10^b = a. |
modulo |
modulo("X", n) "X": A column of integers n: An integer larger than 0 Returns the remainder of each of the numbers in "X" when divided by n. |
photogate > |
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BlockedMidTimes("Time", "Gate1", "Gate2") "Time": Optional. A column of real numbers (the times of events) "Gate1": A column of photogate states (1's and 0's) "Gate2": Optional. A column of photogate states (1's and 0's) Calculate the average times between blocked events from Gate 1 to Gate 2. If you don't enter a "Time" column, the program will find one. If you don't enter "Gate2", "Gate1" will be used. |
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BlockedToBlocked("Time", "Gate1", "Gate2") "Time": Optional. A column of real numbers (the times of events) "Gate1": A column of photogate states (1's and 0's) "Gate2": Optional. A column of photogate states (1's and 0's) Returns a column of the times between successive blocked events in gate 1 and blocked events in gate 2. If you don't enter a "Time" column, the program will find one. If you don't enter "Gate2", "Gate1" will be used. |
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BlockedToUnblocked("Time", "Gate1", "Gate2") "Time": Optional. A column of real numbers (the times of events) "Gate1": A column of photogate states (1's and 0's) "Gate2": Optional. A column of photogate states (1's and 0's) Returns a column of the times between successive blocked events in gate 1 and unblocked events in gate 2. If you don't enter a "Time" column, the program will find one. If you don't enter "Gate2", "Gate1" will be used. |
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Blocked to Unblocked MidTimes "Time": Optional. A column of real numbers (the times of events) "Gate1": A column of photogate states (1's and 0's) "Gate2": Optional. A column of photogate states (1's and 0's) Calculate the average time between the blocked events in gate 1 and unblocked events in gate 2. If you don't enter a "Time" column, the program will find one. If you don't enter "Gate2", "Gate1" will be used. |
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DerivativeTimeShift ("Y", "X") Returns the derivative of "Y" with respect to "X". This function is specifically designed to be used with photogate and picket fence data. The derivatives returned are adjusted to estimate values at the start of the timing interval, instead of the midpoint. For details see The Physics Teacher, Vol 35, April 1997, p. 220. Average velocity during the time interval is equal to the instantaneous velocity at midpoint of the time interval. Where |
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PendulumPeriod("Time", "Gate1") "Time": Optional. A column of real numbers (the times of events) "Gate1": A column of photogate states (1's and 0's) Calculate the time between every other blocked event on Gate 1. If you don't enter a "Time" column, the program will find one. |
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secondDerivativeTimeShift("Y", "X") "Y": A column of real numbers "X": Optional. A column of real numbers Numerical time-shifted second derivative. Calculates the second numerical derivative of "Y" with respect to "X". The values are shifted so that the derivatives are calculated at the midpoints between each two values. If you don't supply an "X" column, the program will find one. |
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UnblockedToBlocked("Time", "Gate1", "Gate2") "Time": Optional. A column of real numbers (the times of events) "Gate1": A column of photogate states (1's and 0's) "Gate2": Optional. A column of photogate states (1's and 0's) Returns a column of the times between successive unblocked events in gate 1 and blocked events in gate 2. If you don't enter a "Time" column, the program will find one. If you don't enter "Gate2", "Gate1" will be used. |
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UnblockedToUnblocked("Time", "Gate1", "Gate2") "Time": Optional. A column of real numbers (the times of events) "Gate1": A column of photogate states (1's and 0's) "Gate2": Optional. A column of photogate states (1's and 0's) Returns a column of the times between successive unblocked events in gate 1 and unblocked events in gate 2. If you don't enter a "Time" column, the program will find one. If you don't enter "Gate2", "Gate1" will be used. |
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Unblocked to Blocked MidTimes "Time": Optional. A column of real numbers (the times of events) "Gate1": A column of photogate states (1's and 0's) "Gate2": Optional. A column of photogate states (1's and 0's) Calculate the average time between unblocked events in gate 1 and blocked events in gate 2. If you don't enter a "Time" column, the program will find one. If you don't enter "Gate2", "Gate1" will be used. |
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UnblockedMidTimes("Time", "Gate1", "Gate2") "Time": Optional. A column of real numbers (the times of events) "Gate1": A column of photogate states (1's and 0's) "Gate2": Optional. A column of photogate states (1's and 0's) Calculate the average times between unblocked events from Gate 1 to Gate 2. If you don't enter a "Time" column, the program will find one. If you don't enter "Gate2", "Gate1" will be used. |
rate |
rate("Y", "X", t, m1, m2, n) "Y": A column of real numbers "X": Optional. A column of real numbers t: Optional. Time interval m1: Optional. Minimum threshold m2: Optional. Maximum threshold n: Optional. Noise threshold Returns the rate of "Y" with respect to "X", where t is the time interval measured, m1 is min percentage threshold, m2 is max percentage threshold, and n is noise threshold. "X", t, m1, m2, and noise are all optional with default values "X" is time column, t = 1/10 the range, m1 = 40%, m2 = 60%, and noise = 0. Details |
rotary motion > |
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("Data Column", "Time Column", "Min Percent", "Max
Percent", "Time Interval") "Data Column": Data for which you want to calculate amplitude "Time Column": Associated time column for "Data Column" "Min Percent": Threshold used to detect valleys "Max Percent": Threshold used to detect peaks "Time Interval": Period of time over which amplitude is calculated (in the time units of the experiment) Calculates peak to peak amplitude. For Min and Max Percent, enter values between 0 and 100. Smaller values are more sensitive to noise and thus more sensitive to real cycles. Larger values are less sensitive to noise; too large of a value may filter out real cycles. "Time Interval" ends at the row at which the value is calculated (the current time). |
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("Data Column", "Time Column", "Min Percent", "Max
Percent", "Time Interval") "Data Column": Data for which you want to calculate period "Time Column": Associated time column for "Data Column" "Min Percent": Threshold used to detect valleys "Max Percent": Threshold used to detect peaks "Time Interval": Period of time over which period is calculated (in the time units of the experiment) Calculates the period of an oscillating function. For Min and Max Percent, enter values between 0 and 100. Smaller values are more sensitive to noise and thus more sensitive to real cycles. Larger values are less sensitive to noise; too large of a value may filter out real cycles. "Time Interval" ends at the row at which the value is calculated (the current time). |
round |
round("X") "X": A column of real numbers Round. Returns the closest integer to x. If x is equidistant to two integers, round(x) gives the largest of the two (e.g., round(0.5) = 1). |
smoothAve |
smoothAve("X") "X": A column of real numbers Returns a column of moving averages of the values in "X". The width of the "window" to use when averaging points can be set in Settings for (Name)... |
statistics > |
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abs("X") "X": A column of real numbers Absolute value. If x less than 0, then abs(x) = -x. Otherwise, abs(x) = x. |
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ceiling("X") "X": A column of real numbers Returns the smallest integer larger than or equal to x. |
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floor("X") "X": A column of real numbers Returns the largest integer smaller than or equal to x. |
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max("X") "X": A column of real numbers Compares all the values in a single column and returns a single number-the largest number in the column. |
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max2("X", "Y") "X": column of real numbers "Y": A column of real numbers or a single number. Compares all the values in a column against a real number (e.g max2("X", 5.1)) |
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mean("X") "X": A column of real numbers Arithmetic mean. Returns the sum of all the values in "X" divided by the number of values. |
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Median("X"). "X": A column of real numbers If m = median("X"), then half the numbers in "X" are greater than (or equal) to m, and half are less than or equal. |
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min("X") "X": A column of real numbers Compares all the values in a single column ,and returns a single number-the smallest number in the column. |
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min("X", "Y") "X": A column of real numbers "Y": A column of real numbers or a single number Compares all the values in a column against a real number (e.g min2("X", 5.1)) |
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NumRows("X") "X": A column of real numbers Returns a single value-the number of rows in the column. |
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randInt(min, max, num): min: A real number max: A real number num: A real number or a column Random Integer. Returns a column of random integers between min and max (inclusive). The size of the returned column is num. If num is a column, then the size will be the number of rows in that column. |
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randReal(min, max, num) min: A real number max: A real number num: A real number or a column Random Real. Returns a column of random real numbers between min and max (inclusive). The size of the returned column is num. If num is a column, then the size will be the number of rows in that column. |
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stddev("X") "X": A column of real numbers Standard Deviation. Returns a column representing the standard deviations of each of the numbers in a column. |
step |
step(start, increment, num, first, skip) start: Start value increment: Increment value num: Number of values to generate first: Optional. First non-empty row skip: Optional. Rows to skip between each value Generates a column "num" rows long starting with "start" and incrementing by "increment". "num" can be a positive integer or a column name. Optional parameters: "first" is the first non-empty row and "skip" is the number of rows to skip between each value. |
StepColumnBase |
stepColumnBased("X", start, increment, first, skip) start: Start value increment: increment value first: Optional. First non-empty row skip: Optional. Row to skip between each value Generates a column based on non-empty values in column "X" starting with "start" and incrementing by "increment." "First" is the first non-empty row and "skip" is the number of rows to skip between each value. |
subset |
subset("X", startRow, step) "X": A column of real numbers startRow: An integer larger than 0 step: An integer larger than 0 Extract a subset. Returns a column extracted from "X" starting with 'startRow' by 'step'. For example, subset("X", 1, 2) will get every second row of "X" starting with row 1. |
sum |
Sum("X") "X": A column of real numbers Returns a column whose n'th value is the sum of the values in "X" from row 1 to n. |
sqrt |
Square root. "X": A column of non-negative real
numbers. If x is the square root of y, then x*x = y. |
trigonometric > |
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sin("X") "X": A column of real numbers In a right triangle with angle between two sides 'x', sin(x) is the length of the opposite side divided by the hypotenuse. |
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cos("X") "X": A column of real numbers In a right triangle with angle between two sides 'x', cos(x) is the length of the adjacent side divided by the hypotenuse. |
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tan("X") "X": A column of real numbers In a right triangle with angle between two sides 'x', tan(x) is the length of the opposite side divided by the adjacent side. |
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asin("X") "X": A column of real numbers between -1 and 1 Arcsine function. asin(x) = the angle whose sine is x. |
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acos("X") "X": A column of real numbers between -1 and 1 Arccosine function. acos(x) = the angle whose cosine is x. |
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atan("X") "X": A column of real numbers Arctangent function. atan(x) = the angle whose tangent is x. The result will be between -pi/2 and pi/2. |
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sinh("X") "X": A column of real numbers Hyperbolic sine. |
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cosh("X") "X": A column of real numbers Hyperbolic cosine. |
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tanh("X") "X": A column of real numbers Hyperbolic tangent. |
Value |
Value(n, "X") n: Number of rows backwards (when n < 0) or forwards (n >0) in column "X" to extract a value from. "X": Column from which to extract values . Create a new column from another column by extracting offset values. |
If data are imported from an experiment file, you may want to specify the independent column. For example, if the imported data included "time" in the first column but you wanted to calculate the derivative of pH with respect to volume, you have to define the derivative as derivative("pH","Volume").