XDL Complete Function Reference

Version: 1.2 Date: December 31, 2025 Total Functions: 500+

Mathematical Functions
Array Functions
Statistical Functions
String Functions
I/O Functions
Graphics Procedures
Machine Learning Functions
DataFrame Functions
Python Integration
Linear Algebra
Signal Processing
Image Processing
System Functions

Mathematical Functions

Trigonometric

Function	Description	Example
`SIN(x)`	Sine	`y = SIN(!PI/2)`
`COS(x)`	Cosine	`y = COS(0)`
`TAN(x)`	Tangent	`y = TAN(!PI/4)`
`ASIN(x)`	Arc sine	`y = ASIN(1)`
`ACOS(x)`	Arc cosine	`y = ACOS(0)`
`ATAN(x)`	Arc tangent	`y = ATAN(1)`

Hyperbolic

Function	Description	Example
`SINH(x)`	Hyperbolic sine	`y = SINH(1)`
`COSH(x)`	Hyperbolic cosine	`y = COSH(0)`
`TANH(x)`	Hyperbolic tangent	`y = TANH(1)`
`ASINH(x)`	Inverse hyperbolic sine	`y = ASINH(1)`
`ACOSH(x)`	Inverse hyperbolic cosine	`y = ACOSH(1)`
`ATANH(x)`	Inverse hyperbolic tangent	`y = ATANH(0.5)`

Exponential & Logarithmic

Function	Description	Example
`EXP(x)`	Exponential (e^x)	`y = EXP(1)`
`ALOG(x)`	Natural log	`y = ALOG(2.718)`
`ALOG10(x)`	Base-10 log	`y = ALOG10(100)`
`SQRT(x)`	Square root	`y = SQRT(16)`

Rounding & Conversion

Function	Description	Example
`ABS(x)`	Absolute value	`y = ABS(-5)`
`FLOOR(x)`	Floor	`y = FLOOR(3.7)`
`CEIL(x)`	Ceiling	`y = CEIL(3.2)`
`ROUND(x)`	Round	`y = ROUND(3.5)`
`FIX(x)`	Truncate to integer	`y = FIX(3.9)`

Type Conversion

Function	Description	Example
`BYTE(x)`	Convert to byte (0-255)	`b = BYTE(100)`
`INT(x)`	Convert to 16-bit integer	`i = INT(3.7)`
`UINT(x)`	Convert to unsigned 16-bit	`u = UINT(100)`
`LONG(x)`	Convert to 32-bit integer	`l = LONG(100)`
`ULONG(x)`	Convert to unsigned 32-bit	`u = ULONG(100)`
`LONG64(x)`	Convert to 64-bit integer	`l = LONG64(100)`
`ULONG64(x)`	Convert to unsigned 64-bit	`u = ULONG64(100)`
`FLOAT(x)`	Convert to 32-bit float	`f = FLOAT(100)`
`DOUBLE(x)`	Convert to 64-bit double	`d = DOUBLE(100)`
`STRING(x)`	Convert to string	`s = STRING(42)`
`COMPLEX(re, im)`	Create complex number	`c = COMPLEX(1, 2)`
`DCOMPLEX(re, im)`	Create double complex	`c = DCOMPLEX(1, 2)`

Special Functions

Function	Description	Example
`FFT(x)`	Fast Fourier Transform	`f = FFT(signal)`
`RANDOMU(seed, n)`	Uniform random	`r = RANDOMU(seed, 100)`
`RANDOMN(seed, n)`	Normal random	`r = RANDOMN(seed, 100)`
`MESHGRID(x, y)`	Create mesh grid	`[xx, yy] = MESHGRID(x, y)`
`ERF(x)`	Error function	`y = ERF(1.0)`
`ERFC(x)`	Complementary error function	`y = ERFC(1.0)`
`GAMMA(x)`	Gamma function	`y = GAMMA(5)`
`LNGAMMA(x)`	Log gamma function	`y = LNGAMMA(100)`
`FACTORIAL(n)`	Factorial (n!)	`y = FACTORIAL(5)`
`BESELJ(x, n)`	Bessel J function	`y = BESELJ(1.0, 0)`
`BESELY(x, n)`	Bessel Y function	`y = BESELY(1.0, 0)`
`BESELI(x, n)`	Modified Bessel I	`y = BESELI(1.0, 0)`
`BESELK(x, n)`	Modified Bessel K	`y = BESELK(1.0, 0)`

Array Functions

Array Generation

Function	Description	Example
`FINDGEN(n)`	Float indices [0, n-1]	`x = FINDGEN(100)`
`INDGEN(n)`	Integer indices	`x = INDGEN(100)`
`DINDGEN(n)`	Double indices	`x = DINDGEN(100)`
`BINDGEN(n)`	Byte indices	`x = BINDGEN(256)`
`LINDGEN(n)`	Long indices	`x = LINDGEN(100)`
`FLTARR(dims)`	Float array (zeros)	`a = FLTARR(10, 10)`
`DBLARR(dims)`	Double array (zeros)	`a = DBLARR(10, 10)`
`INTARR(dims)`	Integer array	`a = INTARR(10)`
`BYTARR(dims)`	Byte array	`a = BYTARR(256)`
`LONARR(dims)`	Long array	`a = LONARR(100)`
`STRARR(dims)`	String array	`s = STRARR(10)`

Array Manipulation

Function	Description	Example
`N_ELEMENTS(x)`	Number of elements	`n = N_ELEMENTS(arr)`
`WHERE(condition)`	Find indices	`idx = WHERE(arr GT 0)`
`REFORM(arr, dims)`	Reshape array	`b = REFORM(a, 5, 20)`
`TRANSPOSE(arr)`	Transpose	`b = TRANSPOSE(a)`
`REVERSE(arr)`	Reverse array	`b = REVERSE(a)`
`SORT(arr)`	Sort indices	`idx = SORT(arr)`
`SHIFT(arr, s)`	Circular shift elements	`b = SHIFT(arr, 2)`
`ROTATE(arr, dir)`	Rotate 2D array	`b = ROTATE(img, 1)`
`REPLICATE(val, n)`	Replicate value	`a = REPLICATE(0, 100)`
`REBIN(arr, dims)`	Resize by averaging	`b = REBIN(a, 100, 100)`
`CONGRID(arr, dims)`	Resize with interpolation	`b = CONGRID(a, 256, 256)`
`MAKE_ARRAY(dims)`	Create array	`a = MAKE_ARRAY(10, 10)`
`ARRAY_EQUAL(a, b)`	Compare arrays	`eq = ARRAY_EQUAL(a, b)`
`UNIQ(arr)`	Find unique elements	`u = arr[UNIQ(arr)]`
`HISTOGRAM(arr)`	Compute histogram	`h = HISTOGRAM(data)`

Array Statistics

Function	Description	Example
`MIN(arr)`	Minimum value	`m = MIN(arr)`
`MAX(arr)`	Maximum value	`m = MAX(arr)`
`MEAN(arr)`	Mean	`m = MEAN(arr)`
`TOTAL(arr)`	Sum	`s = TOTAL(arr)`

Moving Averages

Function	Description	Example
`SMOOTH(arr, w)`	Boxcar smooth	`s = SMOOTH(arr, 5)`
`MOVING_AVERAGE(arr, w)`	Simple MA	`ma = MOVING_AVERAGE(arr, 10)`
`WMA(arr, w)`	Weighted MA	`wma = WMA(arr, 10)`
`EMA(arr, w)`	Exponential MA	`ema = EMA(arr, 10)`
`CUMULATIVE_AVERAGE(arr)`	Cumulative avg	`ca = CUMULATIVE_AVERAGE(arr)`

Statistical Functions

Basic Statistics

Function	Description	Example
`VARIANCE(arr)`	Variance	`v = VARIANCE(data)`
`STDDEV(arr)`	Standard deviation	`s = STDDEV(data)`
`MEDIAN(arr)`	Median	`m = MEDIAN(data)`
`MOMENT(arr)`	Statistical moments	`mom = MOMENT(data)`
`MEANABSDEV(arr)`	Mean absolute deviation	`mad = MEANABSDEV(data)`
`SKEWNESS(arr)`	Skewness	`sk = SKEWNESS(data)`
`KURTOSIS(arr)`	Kurtosis	`k = KURTOSIS(data)`
`CORRELATE(x, y)`	Correlation coefficient	`r = CORRELATE(x, y)`

Probability Distributions

Function	Description	Example
`GAUSS_PDF(x, mu, sigma)`	Gaussian PDF	`p = GAUSS_PDF(x, 0, 1)`
`T_PDF(x, df)`	Student’s t PDF	`p = T_PDF(x, 10)`
`CHISQR_PDF(x, df)`	Chi-squared PDF	`p = CHISQR_PDF(x, 5)`

Curve Fitting

Function	Description	Example
`LINFIT(x, y)`	Linear fit (y = a + bx)	`coef = LINFIT(x, y)`
`POLY_FIT(x, y, n)`	Polynomial fit	`coef = POLY_FIT(x, y, 2)`
`REGRESS(x, y)`	Multiple regression	`result = REGRESS(x, y)`

Interpolation

Function	Description	Example
`INTERPOL(y, x, xnew)`	Linear interpolation	`ynew = INTERPOL(y, x, xnew)`
`SPLINE(x, y, xnew)`	Cubic spline	`ynew = SPLINE(x, y, xnew)`
`BILINEAR(z, x, y)`	Bilinear interpolation	`znew = BILINEAR(z, xnew, ynew)`

String Functions

Function	Description	Example
`STRLEN(s)`	String length	`n = STRLEN('hello')`
`STRPOS(s, sub)`	Find substring	`pos = STRPOS(s, 'abc')`
`STRMID(s, start, len)`	Substring	`sub = STRMID(s, 0, 5)`
`STRUPCASE(s)`	Uppercase	`u = STRUPCASE(s)`
`STRLOWCASE(s)`	Lowercase	`l = STRLOWCASE(s)`
`STRING(x)`	Convert to string	`s = STRING(123)`
`STRTRIM(s, flag)`	Trim whitespace	`t = STRTRIM(s, 2)`
`STRJOIN(arr, delim)`	Join strings	`s = STRJOIN(['a','b'], ',')`
`STRSPLIT(s, delim)`	Split string	`arr = STRSPLIT('a,b,c', ',')`
`STRCOMPRESS(s)`	Compress whitespace	`c = STRCOMPRESS(s)`
`STRCMP(s1, s2)`	Compare strings	`eq = STRCMP('abc', 'ABC')`
`STRREPLACE(s, old, new)`	Replace in string	`r = STRREPLACE(s, 'old', 'new')`
`STREGEX(s, pattern)`	Regex match	`m = STREGEX(s, '[0-9]+')`
`STRMATCH(s, pattern)`	Wildcard match	`m = STRMATCH(s, '*.txt')`

I/O Functions

File Operations

Function/Procedure	Description	Example
`PRINT, args`	Print to console	`PRINT, 'Hello'`
`OPENR, unit, file`	Open for reading	`OPENR, 1, 'data.txt'`
`OPENW, unit, file`	Open for writing	`OPENW, 2, 'out.txt'`
`OPENU, unit, file`	Open for read/write	`OPENU, 1, 'data.bin'`
`READF, unit, var`	Read formatted	`READF, 1, data`
`WRITEF, unit, data`	Write formatted	`WRITEF, 2, data`
`READ, var`	Read from stdin	`READ, input`
`READS, str, var`	Read from string	`READS, line, val`
`READU, unit, var`	Read binary data	`READU, 1, arr`
`WRITEU, unit, data`	Write binary data	`WRITEU, 1, arr`
`CLOSE, unit`	Close file	`CLOSE, 1`
`GET_LUN`	Get free unit	`lun = GET_LUN()`
`FREE_LUN, unit`	Free unit	`FREE_LUN, lun`
`POINT_LUN, unit, pos`	Seek position	`POINT_LUN, 1, 0`
`EOF(unit)`	Check end of file	`IF EOF(1) THEN ...`
`FLUSH, unit`	Flush buffer	`FLUSH, 1`

File System

Function	Description	Example
`FILE_TEST(path)`	Test file exists	`IF FILE_TEST('f.txt') THEN ...`
`FILE_INFO(path)`	Get file metadata	`info = FILE_INFO('f.txt')`
`FILE_SEARCH(pattern)`	Search for files	`files = FILE_SEARCH('*.dat')`
`FILE_MKDIR(path)`	Create directory	`FILE_MKDIR, 'subdir'`
`FILE_DELETE(path)`	Delete file	`FILE_DELETE, 'temp.txt'`
`FILE_COPY(src, dst)`	Copy file	`FILE_COPY, 's.txt', 'd.txt'`
`FILE_MOVE(src, dst)`	Move/rename file	`FILE_MOVE, 'old', 'new'`
`FILEPATH(file)`	Get full path	`p = FILEPATH('data.txt')`
`READ_JPEG(file)`	Read JPEG image	`img = READ_JPEG('photo.jpg')`

Graphics Procedures

Basic Plotting

Procedure	Description
`PLOT, y`	2D line plot
`PLOT, x, y`	2D line plot with x
`OPLOT, x, y`	Overplot on existing
`PLOTS, x, y`	Draw polyline
`XYOUTS, x, y, text`	Draw text
`AXIS`	Draw axis

3D Plotting

Procedure	Description
`SURFACE, z`	3D surface plot
`SHADE_SURF, z`	Shaded surface
`CONTOUR, z`	Contour plot
`PLOT3D, x, y, z`	3D line plot
`ISOSURFACE`	Isosurface rendering

Image Display

Procedure	Description
`TV, img`	Display image
`TVSCL, img`	Display scaled image
`IMAGE_DISPLAY, img`	Enhanced image display

Window Management

Procedure	Description
`WINDOW, n`	Create window
`WSET, n`	Set active window
`WDELETE, n`	Delete window
`ERASE`	Clear window
`DEVICE`	Device settings

Charting (ECharts)

Procedure	Description
`CHART_PLOT`	Interactive line chart
`CHART_SCATTER`	Scatter chart
`CHART_BAR`	Bar chart
`CHART_CONTOUR`	Contour chart
`SURFACE3D`	3D surface chart
`SCATTER3D`	3D scatter chart

Machine Learning Functions

XDLML Functions (50+)

See ML Complete Reference for full documentation.

Categories:

Data utilities: XDLML_PARTITION, XDLML_SHUFFLE
Normalizers: XDLML_*_NORMALIZER
Activation functions: XDLMLAF_*
Loss functions: XDLMLLF_*
Optimizers: XDLMLOPT_*
Neural networks: XDLML_FEEDFORWARDNEURALNETWORK
SVM: XDLML_SUPPORTVECTORMACHINE*
Cross-validation: XDLML_KFOLD, XDLML_STRATIFIEDKFOLD

Linfa ML Functions (Native Rust)

See Linfa ML Reference for full documentation.

Function	Description
`ML_KMEANS_FIT`	Train K-Means
`ML_KMEANS_PREDICT`	Predict clusters
`ML_LINEAR_FIT`	Train linear regression
`ML_LINEAR_PREDICT`	Predict values
`ML_PCA_FIT`	Fit PCA
`ML_PCA_TRANSFORM`	Transform data
`ML_ACCURACY`	Classification accuracy
`ML_MSE`	Mean squared error
`ML_R2_SCORE`	R² coefficient

DataFrame Functions (Polars)

See DataFrame Reference for full documentation.

Function	Description
`DF_READ_CSV`	Read CSV file
`DF_READ_PARQUET`	Read Parquet file
`DF_READ_JSON`	Read JSON file
`DF_CREATE`	Create from arrays
`DF_WRITE_CSV`	Write to CSV
`DF_WRITE_PARQUET`	Write to Parquet
`DF_HEAD`	First N rows
`DF_TAIL`	Last N rows
`DF_SELECT`	Select columns
`DF_FILTER`	Filter rows
`DF_SORT`	Sort by column
`DF_GROUPBY`	Group and aggregate
`DF_JOIN`	Join DataFrames
`DF_SHAPE`	Get dimensions
`DF_COLUMNS`	Get column names
`DF_TO_ARRAY`	Convert to XDL array
`DF_DROP`	Free memory

Python Integration

See Python Integration for full documentation.

Function	Description
`PYTHON_IMPORT(module)`	Import Python module
`PYTHON_CALL(mod, func, args)`	Call Python function
`PYTHON_CALL_KW(mod, func, args, kwargs)`	Call with keywords

Linear Algebra

Function	Description
`IDENTITY(n)`	Identity matrix
`INVERT(matrix)`	Matrix inverse
`DETERM(matrix)`	Determinant
`TRANSPOSE(matrix)`	Transpose
`CROSSP(a, b)`	Cross product
`DOTP(a, b)`	Dot product
`NORM(arr)`	Vector norm
`DIAGONAL(matrix)`	Diagonal elements
`TRACE(matrix)`	Matrix trace
`SVDC(matrix)`	SVD decomposition
`LA_EIGENVAL(matrix)`	Eigenvalues
`LUDC(matrix)`	LU decomposition
`LUSOL(lu, b)`	Solve LU system

Signal Processing

Function	Description
`A_CORRELATE(x, lag)`	Auto-correlation
`C_CORRELATE(x, y)`	Cross-correlation
`DIGITAL_FILTER(x, coef)`	Digital filter
`HILBERT(x)`	Hilbert transform
`MEDIAN_FILTER(x, w)`	Median filter

Image Processing

Function	Description
`CONVOL(img, kernel)`	Convolution
`DILATE(img, struct)`	Morphological dilation
`ERODE(img, struct)`	Morphological erosion
`SOBEL(img)`	Sobel edge detection
`ROBERTS(img)`	Roberts cross
`PREWITT(img)`	Prewitt operator
`GAUSSIAN_FILTER(img, sigma)`	Gaussian blur
`THRESHOLD(img, val)`	Binary threshold

System Functions

General

Function/Procedure	Description	Example
`HELP`	Display help	`HELP`
`CD, path`	Change directory	`CD, '/home/user'`
`SPAWN, cmd`	Execute system command	`SPAWN, 'ls -la'`
`WAIT, seconds`	Pause execution	`WAIT, 2.5`
`STOP`	Stop execution	`STOP`
`CATCH, var`	Error handling	`CATCH, err`

Timing

Function	Description	Example
`SYSTIME()`	Current time string	`t = SYSTIME()`
`SYSTIME(1)`	Seconds since epoch	`s = SYSTIME(1)`
`TIC()`	Start timer	`TIC`
`TOC()`	Elapsed time (seconds)	`elapsed = TOC()`
`JULDAY(m, d, y)`	Julian day number	`jd = JULDAY(12, 25, 2024)`
`CALDAT(jd)`	Calendar date from Julian	`date = CALDAT(jd)`

Type Inspection

Function	Description	Example
`SIZE(x)`	Array dimensions info	`dims = SIZE(arr)`
`N_ELEMENTS(x)`	Number of elements	`n = N_ELEMENTS(arr)`
`TYPENAME(x)`	Type name as string	`t = TYPENAME(x)`
`ISA(x, type)`	Check type	`IF ISA(x, 'FLOAT') THEN ...`

Structure Functions

Function	Description	Example
`CREATE_STRUCT(tags, vals)`	Create structure	`s = CREATE_STRUCT('a', 1, 'b', 2)`
`N_TAGS(struct)`	Number of fields	`n = N_TAGS(mystruct)`
`TAG_NAMES(struct)`	Field names	`names = TAG_NAMES(mystruct)`

System Variables

Variable	Description
`!PI`	Pi (float)
`!DPI`	Pi (double)
`!E`	Euler’s number
`!RADEG`	Radians to degrees
`!DTOR`	Degrees to radians
`!NULL`	Null value
`!TRUE`	Boolean true
`!FALSE`	Boolean false
`!VERSION`	XDL version
`!DIR`	Installation directory
`!PATH`	Search path

Keywords

Control Flow

IF condition THEN statement
IF condition THEN BEGIN ... END ELSE BEGIN ... END

FOR var = start, end DO statement
FOR var = start, end, step DO BEGIN ... END

WHILE condition DO statement
WHILE condition DO BEGIN ... END

REPEAT statement UNTIL condition
REPEAT BEGIN ... END UNTIL condition

FOREACH item, collection DO statement

SWITCH expression OF
  value1: statement
  value2: BEGIN ... END
  ELSE: default_statement
ENDSWITCH

CASE expression OF
  value1: statement
  value2: statement
  ELSE: default
ENDCASE

BREAK
CONTINUE
RETURN [, value]

Definitions

FUNCTION name, param1, param2, KEYWORD=keyword
  ; function body
  RETURN, result
ENDFUNCTION

PRO name, param1, param2, KEYWORD=keyword
  ; procedure body
ENDPRO

Operators

Type	Operators
Arithmetic	`+`, `-`, `*`, `/`, `^`, `MOD`
Comparison	`EQ`, `NE`, `LT`, `GT`, `LE`, `GE`
Logical	`AND`, `OR`, `NOT`, `XOR`
Assignment	`=`, `+=`, `-=`, `*=`, `/=`
Matrix	`#` (multiply), `##` (transpose multiply)
Pointer	`->`
Range	`:`

Feature Flags

Flag	Description	Functions
`python`	Python integration	`PYTHON_*`
`dataframes`	Polars DataFrames	`DF_*`
`ml`	Linfa ML	`ML_*`
`rustpython`	RustPython	`RUSTPY_*`

Build with flags:

cargo build --features "python,dataframes,ml"