![[Previous Document]](http:/Images/Left.gif)
![[Back to CSI Home Page]](http:/Images/Home.gif)
![[Next Document]](http:/Images/Right.gif)
List of Statements Available in MLAB
1. Assignment Statement
2. TYPE Statement
3. PRINT Statement
4. FUNCTION Statement
5. INITIAL Statement
6. CONSTRAINTS Statement
7. FIT Statement
8. WINDOW Statement
9. FRAME Statement
10. IMAGE Statement
11. FRAMEBOX and IMAGEBOX Statements
12. DRAW Statement
13. AXIS Statement
14. TITLE Statement
15. The 3D-DRAW Statement
16. The 3D-View Control Statement
17. BLANK and UNBLANK Statements
18. VIEW and UNVIEW Statement
19. PLOT Statement
20. DELETE Statement
21. SAVE, SSAVE, RESAVE, and RESSAVE Statements
22. USE and REUSE Statements
23. FOR Statement
24. BREAK and DONE Statements
25. IF Statement
26. DO Statement
27. EDIT Statement
28. HELP Statement
29. RESET Statement
30. EXIT Statement
List of MLAB functions in each extension package
0. Base MLAB system
· Basic Scalar and Matrix Arithmetic Operators
+,- unary and binary addition and subtraction
* multiplication
/ division
^ exponentiation
· Relational Operators
<, <=, =, >=, >, NOT= relational (comparison) operators
· Boolean Operators
NOT, AND, OR logical negation, and, or
· Conditional Computation Operator
IF-THEN-ELSE conditional operator
· Matrix Manipulation Operators
: sequence generator
:: fixed step sequence generator
:! fixed-size sequence generator
[ ] matrix subscripting
ROW row submatrix construction
COL column submatrix construction
' transpose of a matrix
& row-wise concatenation
&' column-wise concatenation
^^ row-wise replication
^^ ' column-wise replication
# vector cross product
ON function application operator
*' element-by-element multiplication
/' element-by-element division
· String Operators
+ string concatenation
^^ string replication
<, <=, =, >=, > relational (comparison) string operators
· Other basic functions
ABS absolute value function
ACOS inverse trigonometric cosine function
ASIN inverse trigonometric sine function
ATAN2 2-argument inverse trigonometric tangent function
ATAN inverse trigonometric tangent function
BARGRAPH construct bar graph matrix
CDIV complex division
CEILING ceiling function
COLORN assign a color number each number
COLORX color number for an (R,G,B) triple
COLSUM sum of the columns of a matrix
COL column submatrix construction
COMPRESS censor a matrix
CORE available workspace
COS trigonometric cosine function
CPOW complex exponentiation
CPROD complex multiplication
CPR polar-to-rectangular conversion
CROSS tensor product of matrices
CRP rectangular-to-polar conversion
CURVEM extract data of a curve or axis
DIGAMMA derivative of the logarithmic Gamma function
DIVISORS divisors of an integer
DTYPE data type of an object
EGCD extended greatest common divisor
ETIME elapsed time
EVAL evaluate by substitution
EXP exponential function
FACTOR prime factors of an integer
FLOOR floor function
FRAMEM extract limit numbers of the frame of a window
GAMMA Gamma function
GETSTRINGS displays a form and returns user entries
IMAGEM extract limit numbers of the image of a window
INTEGRAL definite integral
INT integer part function
KREAD read from the keyboard one or more numbers
KSREAD read a string from the keyboard
LABELM extract label numbers of a curve or axis
LINLOG evaluate a function or data for linlog drawing
LIST construct a matrix from a list
LN natural (base e) logarithm function
LOGGAMMA logarithmic gamma function
LOGLIN evaluate a function or data for loglin drawing
LOGLOG evaluate a function or data for log-log drawing
LOG logarithm function
MAPPLY apply a function to matrix indices
MAXCOL column index of maximum element in matrix
MAXROW row index of maximum element in matrix
MAXV maximum element of a matrix
MAX maximum of list of scalars
MEAN trimmed arithmetic mean
MENUCHOICE display a menu and return user choice
MESH interleave two matrices by rows or columns
MINCOL column index of minimum element in matrix
MINROW row index of minimum element in matrix
MINV minimum element of a matrix
MIN minimum of list of scalars
MOD modulus (integer division remainder) function
MSIZE size of a matrix
NCOLS number of columns of a matrix
NROWS number of rows of a matrix
ON function application operator
POINTS evaluate function(s) on a list of argument vectors
PPOLAR parameterized polar functions for cartesian drawing
PRIMES list of primes up to argument
PRODUCT product of a sequence
PROOT zeros of a polynomial (real or complex)
PSUM partial row sums of a matrix
PTSIZEM extract pointsize matrix of a curve or axis
QROMB definite integral
READON read a matrix from a file without closing
READ read a matrix from a file
ROOT zero of a function of one argument
ROTATE rotate a matrix by rows or columns
ROWSUM sum of the rows of a matrix
ROW row submatrix construction
RPOLAR evaluate radial polar function for cartesian drawing
SEC trigonometric secant function
SIGN sign function
SIN trigonometric sine function
SORT sort a matrix on a column
SQRT square root function
STDDEV standard deviation
STEPGRAPH construct step function graph matrix
STRDATE build a string with the current date
STRTIME build a string with the current time
STRVAL build a string from a defined object
SUBSTR get a substring of a string
SUM sum of a sequence
TAN trigonometric tangent function
TITLESTR get the string of a title
TPOLAR evaluate azimuthal polar function for cartesian drawing
TYPEOUT type-out a value from within a function
VAR variance
WINDOWM extract limit numbers of a window
1. Ordinary-differential equation (ODE) solving
INTEGRATE solve ordinary differential equations
ITERATE solve first order difference equations
2. Curve-fitting
FIT Marquardt-Levenberg non-linear curve-fitting
EWT estimated weights for curve-fitting
3. Optimization
LINPROG linear programming by the simplex method
MAXIMIZE maximize a function
MINIMIZE minimize a function
SIMPLEX linear programming by the simplex method
4. Advanced linear algebra
BAND build a diagonally-banded matrix
COND condition number of a matrix
DET matrix determinant
DIAG build a matrix by diagonals
DOT scalar product of vectors
EIGEN matrix eigenvalues and eigenvectors
GETDIAG extract diagonals of a matrix
INVERSE matrix inverse
LENGTH vector length
LINEQ solve linear equations
MNORM matrix norms
MRHO spectral radius of a matrix
QRFAC QR-factorization of a matrix
RANK matrix rank
SHAPE restructure a matrix
SVD singular value decomposition
TRACE matrix trace
5. Special functions
ACOSECH inverse hyperbolic cosecant function
ACOSEC inverse trigonometric secant function
ACOSH inverse hyperbolic cosine function
ACOTANH inverse hyperbolic cotangent function
ACOTAN inverse trigonometric tangent function
AIRYD Airy Function Ai derivative
AIRY Airy function Ai
ALEG associated Legendre function
ASECH inverse hyperbolic secant function
ASEC inverse trigonometric secant function
ASINH inverse hyperbolic sine function
ATANH inverse hyperbolic tangent function
BAIRYD Airy Function Bi Derivative
BAIRY Airy Function Bi
BERNUM Bernoulli number
BERPOL Bernoulli polynomial
BESSI modified Bessel function of the first kind
BESSJ Bessel function of the first kind
BESSK modified Bessel function of the second kind
BESSY Bessel function of the second kind
BETA Beta function
BINCOEF binomial coefficient
CE1 complete elliptic integral of the first kind
CE2 complete elliptic integral of the second kind
CE3 complete elliptic integral of the third kind
CEL general complete elliptic integral
COSD trigonometric cosine function (argument in degrees)
COSECH hyperbolic cosecant function
COSEC trigonometric cosecant function
COSHINT hyperbolic cosine integral function
COSH hyperbolic cosine function
COSINT cosine integral function
COTANH hyperbolic cotangent function
COTAN trigonometric cotangent function
DAWSON Dawson's integral
EL2 general elliptic integral of the second kind
ELLRC degenerate elliptic integral
ELLRD elliptic integral of the second kind
ELLRF elliptic integral of the first kind
ELLRJ elliptic integral of the third kind
ERFC complementary error function
ERF error function
EULNUM Euler number
EULPOL Euler polynomial
EXPINTN Yth order exponential integral function
EXPINT exponential integral function
IBETA incomplete beta function
IGAMMA incomplete Gamma function
JACOBIAM Jacobian am elliptic function
JACOBICD Jacobian cd elliptic function
JACOBICN Jacobian cn elliptic function
JACOBICS Jacobian cs elliptic function
JACOBIDC Jacobian dc elliptic function
JACOBIDN Jacobian dn elliptic function
JACOBIDS Jacobian ds elliptic function
JACOBINC Jacobian nc elliptic function
JACOBIND Jacobian nd elliptic function
JACOBINS Jacobian ns elliptic function
JACOBISC Jacobian sc elliptic function
JACOBISD Jacobian sd elliptic function
JACOBISN Jacobian sn elliptic function
JBETA function used in derivative of beta distribution fn
JGAMMA function used in derivative of gamma distribution fn
LE1 Legendre elliptic integral of the first kind
LE2 Legendre elliptic integral of the second kind
LEG Legendre function
LOG10 base-10 logarithm function
LOG2 base-2 logarithm function
LOGINT logarithmic integral function
NPRIME the X-th prime number
PARTD distinct partitions of an integer
PARTU unrestricted partitions of an integer
RFACT rising factorial function
SECH hyperbolic secant function
SIND trigonometric sine function (argument in degrees)
SINHINT hyperbolic sine integral function
SINH hyperbolic sine function
SININT sine integral function
SPENCE Spence's dilogarithm
STIRL1 Stirling number of the first kind
STIRL2 Stirling number of the second kind
TAND trigonometric tangent function (argument in degrees)
TANH hyperbolic tangent function
THETA1 Jacobi's first theta function
THETA2 Jacobi's second theta function
THETA3 Jacobi's third theta function
THETA4 Jacobi's fourth theta function
THETAC Neville's c theta function
THETAD Neville's d theta function
THETAN Neville's n theta function
THETAS Neville's s theta function
6. Signal analysis functions
CONVOLVE convolution
CROSSCORR cross-correlation of sets of vectors
CROSSCOV covariance of sets of vectors
DECONV inverse convolution (deconvolution)
DFT discrete Fourier transform
IDFT discrete inverse Fourier transform
LMAX local maxima of 2D curve
LMIN local minima of 2D curve
RDUP thresholded duplicate removal
REALDFT amplitude/phase real discrete Fourier transform
7. Cluster analysis functions
ALINK average linkage dendrogram
ASCALE translation to zero mean and scaling to unit variance
CENTROID centroid linkage dendrogram
CHULL convex hull
CLINK complete linkage dendrogram
CLUSTERR clustering error
CLUSTINFO cluster summary table
COPHEN cophenetic correlation of a dendrogram
DCIRCLES matrix for circumcircles of Delaunay triangulation
DELAUN Delaunay triangulation
DELCURVE construct matrix for drawing Delaunay triangulation
DENCURVE dendrogram tree matrix for drawing
DISTS Minkowsky p-metric, Euclidean distance
FISHERRK Fisher's rank-correlation
INCON inconsistency coefficients of a dendrogram
KMEANS K-means clustering
MST minimal spanning tree
NLM dimensionality reduction using nonlinear mapping
PRCOMP principal components of a covariance matrix
RSCALE minimum/maximum scaling
SLINK single linkage dendrogram
TREECURVE tree/graph matrix for drawing
TREEGROUP regroups clusters from a dendrogram tree
VORCURVE construct matrix for drawing Voronoi diagram
VORREGIONS compute Voronoi diagram
VORSTAT edge-count, area and perimeter of Voronoi regions
WARD Ward's linkage dendrogram
8. Density functions, distribution functions, and inverse distribution fns
ASTUTD absolute non-central Student's t density
ASTUTF absolute non-central Student's t distribution function
ASTUTI inverse non-central absolute Student's t dist. function
BETAD non-central beta density function
BETAF non-central beta distribution function
BETAI inverse non-central Beta distribution function
BINOMD binomial density function
BINOMF binomial distribution function
BINOMI inverse binomial distribution function
CAUCHYD Cauchy distribution density function
CAUCHYF Cauchy distribution function
CAUCHYI inverse Cauchy distribution function
CHISQD non-central chi-squared density function
CHISQF non-central chi-squared distribution function
CHISQI inverse non-central chi-squared distribution function
EXPD exponential distribution density function
EXPF exponential distribution function
EXPI inverse exponential distribution function
GAMMAD gamma distribution density function
GAMMAF gamma distribution function
GAMMAI inverse Gamma distribution function
GAUSSD normal density function
GAUSSF normal distribution function
GAUSSI inverse gaussian distribution function
GEOMD geometric distribution density function
GEOMF geometric distribution function
GEOMI inverse geometric distribution function
GUMBELD Gumbel (extreme value) density function
GUMBELF Gumbel extreme value distribution function
GUMBELI inverse Gumbel distribution function
HGEOMD hypergeometric distribution density function
HGEOMF hypergeometric distribution function
HGEOMI inverse hypergeometric distribution function
HNORMD halfnormal density function
HNORMF halfnormal distribution function
HNORMI inverse halfnormal distribution function
KSMF Kolmogorov-Smirnov distribution function
LAPLACED Laplace distribution density function
LAPLACEF Laplace distribution function
LAPLACEI inverse Laplace distribution function
LNORMD lognormal distribution density function
LNORMF lognormal distribution function
LNORMI inverse lognormal distribution function
LOGISD logistic distribution density function
LOGISF logistic distribution function
LOGISI inverse logistic distribution function
LOGSERD logarithmic series distribution density function
MWD Mann-Whittney-Wilcoxon rank-sum test density function
MWF Mann-Whitney-Wilcoxon rank-sum distribution function
NBIND negative binomial distribution density function
NBINF negative binomial distribution function
NBINI inverse negative binomial distribution function
PARETOD Pareto distribution density function
PARETOF Pareto distribution function
PARETOI inverse Pareto distribution function
POISSD Poisson density function
POISSF Poisson distribution function
POISSI inverse Poisson distribution function
QFD singly non-central F density function
QFF singly non-central F-distribution function
QFI inverse singly non-central F-distribution function
SPEARD Spearman rank-correlation test density function
SPEARF Spearman rank-correlation distribution function
STUTD non-central Student's t density function
STUTF non-central Student's t distribution function
STUTI inverse non-central Student's t distribution function
TRID triangular distribution density function
TRIF triangular distribution function
TRII inverse triangular distribution function
UNID uniform distribution density function
UNIF uniform distribution function
UNII inverse uniform distribution function
WEIBD Weibull distribution density function
WEIBF Weibull distribution function
WEIBI inverse Weibull distribution function
WILCD Wilcoxon signed-rank test density function
WILCF Wilcoxon signed-rank distribution function
9. Statistics computations and tests
ACTSURV actuarial survival curve estimate
AVDEV average absolute deviation
CDF empirical cumulative distribution function
CENTROPY conditional entropy of a contingency table
CHISQ1T chi-square test on data versus expected values
CHISQ2T chi-square test on two data sets
CHISQFA chi square test rejection error probability
CHISQFB chi square test acceptance error probability
CHISQFD chi square test rms average bucket deviation
CHISQFN chi square test degrees of freedom
CHISQFT chi-square test on histogram vs. cdf
CORR2T correlation-coefficient test
CORR correlation matrix
COV covariance matrix
CTABT chi-square test on contingency table
ENTROPY entropy of a probability density function
HBPOWER Mantel-Haenszel test power simulation
HISTO compute a histogram matrix
JENTROPY entropy of a contingency table
JUNCERT joint uncertainty of a contingency table
KEN1T Kendall's paired-sample tau correlation coef. test
KEN2T Kendall's tau test on a contingency table
KMSURV Kaplan-Meier survival curve estimation
KS1T Kolmogorov-Smirnov 1-sample test
KS2T Kolmogorov-Smirnov 2-sample test
KSF1T Kolmogorov-Smirnov 1-sample test on a cdf
KSF2T Kolmogorov-Smirnov 2-sample test on 2 cdf's
KURTT D'Agostino's kurtosis test for normality
KURT kurtosis
KWT Kruskal-Wallis multi-sample rank-sum test
LEVENET Levene's test for equality of variances
MAVDEV moving absolute average deviation
MEDIAN median
MHT Mantel-Haenszel-Armitage-Cochran test
MMEAN moving mean
MMEDIAN moving median
MODE mode
MQUANTILE moving quantile
MSTDDEV moving standard deviation
MVAR moving variance
MWT Mann-Whittney-Wilcoxon rank-sum test
NORMT D'Agostino's omnibus test for normality
PEART Pearson correlation test on bivariate normal data
QFA rejection error prob. of the variance-ratio F-test
QFB variance-ratio F-test acceptance error probability
QFE variance-ratio F-test alternate hyp. variance ratio
QFN variance-ratio F-test sample size
QFT F-test for equal variances
RANKORDER rank ordering
SKEWT D'Agostino's skewness test for normality
SKEW skew
SPEART Spearman rank-correlation test on two data sets
STUTFA rejection error prob. of the t-test for equal means
STUTFB acceptance error probability of t-test for equal means
STUTFN sample size of the t-test for equal means
STUTFT sample size ratio of the t-test for equal means
SURV2T Mantel-Haenszel test on 2 group survival data
SURVT Mantel-Haenszel test on multiple group survival data
TDT Student's t test for equal means (unequal variances)
THOMAST Thomas' test
TMT Student's t test against a postulated constant mean
TPT Student's t test for equal means (paired samples)
TST Student's t test for equal means (equal variances)
UNCERT uncertainty of a contingency table
WIL1T Wilcoxon 1-sample signed-rank test
WIL2T Wilcoxon 2-sample paired data signed-rank test
10. Spline smoothing
DINTERP 2D function derivative interpolation
INTERPOLATE 2D and 3D function interpolation
INTERP 2D and 3D function interpolation
LOOKUP interpolate linearly into a tabular function of 1 variable
SMOOTH smooth a tabular function of 1 or 2 variables
SPLINEP spline interpolate parametric plane or space curve
SPLINE spline interpolation of plane or space curve
SMOOTHSPLINE optimal smoothing spline
MONOT monotonic smoother
11. Random number generators
BETARAN non-central beta-distributed random number
BINRAN binomial-distributed random number
CAUCHYRAN Cauchy-distributed random number
CHISQRAN non-central chi squared-distributed random number
EXPRAN exponential-distributed random number
FRAN singly non-central F-distributed random number
GAMRAN gamma-distributed random number
GEOMRAN geometric-distributed random number
GUMBELRAN Gumbel (extreme value) random number
HNORMRAN half normal-distributed random number
IRAN integer-valued random number
LAPLACERAN Laplace-distributed random number
LNORMRAN lognormal-distributed random number
LOGISRAN logistic-distributed random number
NBINRAN negative binomial-distributed random number
NORMRAN normal random number
PARETORAN Pareto-distributed random number
POISRAN Poisson-distributed random number
RANPERM random permutation of random combination
RAN uniform random number
STUTRAN Student't t-distributed random number
TRIRAN triangular-distributed random number
WEIBRAN Weibull-distributed random number
12. 3D graphics and contour maps
CONTOUR level lines of a surface
FILL fill lines of a polygon