SAS/IML Software: Features

Features

Matrices and Matrix Operators
- Matrix Operators
Control Statements
Functions and Call Routines
IML Modules and Subroutines
Graphics Commands

Matrices and Matrix Operators

The fundamental IML data object is a two-dimensional (row-by-column) numeric or character matrix. Matrices are useful for representing data and are very efficient for working with data. For example, suppose you measured the daily high temperatures in September for six different cities and want to convert the readings from Fahrenheit to Celsius. You could write code such as

  do i=1 to 30;
    do j=1 to 6;
      C[i,j]=5*(F[i,j]-32)/9;
    end;
  end;

where C[1,6] is the temperature in Celsius on September 1 for city 6. Such operations can be very slow and difficult to program for complex formulas and large datasets; however, in SAS/IML you load your data into matrix F and simply write

  C=5*(F-32)/9;

Matrix Operators

Basic operators are provided that perform: arithmetic operations on each element of the matrix (elementwise operations, as illustrated in the previous example), matrix operations, concatenation of matrices, comparisons between and within matrices, subscripting of matrices, and subscript reduction (for example, take the sum of squares of each row of a matrix).

Control Statements

These statements direct the flow of execution of IML statements, and enable program modularization. The control statements include IF-THEN...ELSE, DO...END, iterative DO, DO WHILE, DO UNTIL, GOTO, LINK, RETURN, STOP, and ABORT.

Functions and Call Routines

The power of the SAS/IML language is released with the many matrix functions and call routines provided, ranging from general matrix functions to complex numerical integration and optimization routines. The following lists some of the operations that can be performed:

General Matrix Functions

absolute values, exponentials, remainders, powers of matrix elements
find elements in a matrix satisfying given conditions
cumulative sums, horizontal direct product, and trace
create block diagonal, identity, diagonal, transposed matrices
reshape a matrix
find set difference, set union, or set intersection of matrices; remove duplicates from matrices

Linear Algebraic and Statistical Functions

solve an ordinary differential equation
perform numerical integration
compute eigenvalues and eigenvectors for symmetric and unsymmetric matrices; create orthonormal eigenvectors
compute inverses, generalized inverses, Moore-Penrose inverses, and determinants
compute Gram-Schmidt orthonormal factorization
perform Cholesky, singular value, and complete orthogonal decomposition
perform QR decomposition by Householder rotation or the Gram-Schmidt process
solve linear programs, linear systems, and systems of linear equations
compute the first nonzero roots of a Bessel function of the first kind and the derivative of the Bessel function at each root
perform discrete sequential tests

Time Series Functions

compute ARMA model autocovariance sequence, log likelihood and residuals
simulate a univariate ARMA time series
compute autocovariance estimates for time series
generate a Hankel ,Toeplitz, or block Toeplitz matrix
perform finite Fourier transformations and inverse FFTs
Kalman filtering
- perform covariance filtering and prediction
- perform fixed-interval smoothing
- perform diffuse covariance filtering and prediction
- perform diffuse fixed-interval smoothing
TIMSAC (TIMe Series Analysis and Control) routines (developed by the Institute of Statistical Mathematics, Japan)
- Bayesian seasonal adjustment modeling
- time series decomposition analysis
- locally stationary univariate and multivariate AR model fitting
- univariate, multivariate, and periodic AR model fitting
- ARMA model forecasting and forecast error variance
- polynomial roots or ARMA coefficients computation
- time-varying coefficient AR model estimation

Numerical Analysis Functions

solve ordinary differential equations
perform numerical integration
nonlinear optimization
- optimization methods available:
  - Conjugate Gradient Method
  - Double Dogleg Method
  - Nelder-Mead Simplex Method
  - Newton-Raphson Method
  - Newton-Raphson Ridge Method
  - (Dual) Quasi-Newton Method
  - Quadratic Optimization Method
  - Trust-Region Method
- methods for solving nonlinear least-squares problems:
  - Levenberg-Marquardt Least-Squares Method
  - Hybrid Quasi-Newton Least-Squares Methods
- compute finite difference approximations for first- and second-order derivatives
- determine a feasible point subject to boundary and linear constraints

IML Modules and Subroutines

You can extend the power of SAS/IML by writing your own functions and routines and storing them as "modules" in libraries. Libraries can contain both functions and subroutines; functions can be invoked in assignment statements or expressions, while subroutines can be invoked using CALL or RUN statements. IML automatically loads, resolves, and executes a module when you use it.

The IMLMLIB Module Library contains several modules which may be used as though they were built-in functions of IML. The IMLMLIB modules enable you to:

convert a matrix into a column vector
compute correlation coefficients
draw box and whisker diagrams
draw probability contours for x-y data
draw scatter plots of x-y data
compute the median of numeric data
perform quadratic regression
compute quartiles
perform regression analysis
convert a matrix into a row vector
replace substrings
standardize numeric data
print matrices in tabular format

Graphics Commands

A powerful set of commands, called graphics primitives, are provided to create customized displays. Several basic commands are GDRAW (for drawing a line), GPOINT (for plotting points), and GPOLY (for drawing a polygon). A set of attributes such as color and linestyle can be associated with each primitive. Collections of graphics primitives can be saved as a segment, which can be included in subsequent graphs; graphs can be included on the same page.

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