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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