B.2 A Summary of Frequently Used SAS/IML Operators 420
B.3 A Summary of Functions and Subroutines 420
B.3.1 Mathematical Functions 420
B.3.2 Probability Functions 421
B.3.3 Descriptive Statistical Functions 421
B.3.4 Matrix Query Functions 422
B.3.5 Matrix Reshaping Functions 422
B.3.6 Linear Algebra Functions 423
B.3.7 Set Functions 423
B.3.8 Formatting Functions 424
B.3.9 Module Statements 424
B.3.10 Control Statements 425
B.3.11 Statements for Reading and Writing SAS Data Sets 425
B.3.12 Options for Printing Matrices 425
The SAS/IML language contains over 300 built-in functions and subroutines. There are also hundreds of functions in Base SAS software that you can call from SAS/IML programs.
The best overview of these many functions is Chapter 23, "Language Reference" (SAS/IML User's Guide). The section "Overview" lists the SAS/IML functions according to their functionality; the section "Base SAS Functions Accessible from SAS/IML Software" lists the Base SAS functions according to their functionality.
This appendix presents tables that list functions discussed in this book and also related functions that were not explicitly used in this book but that are used often in practice.
The SAS/IML language provides standard elementwise operators such as addition, subtraction, multiplication, and division. See Section 2.12 for details. The following table lists frequently used SAS/IML operators:
Table B.1. Frequently Used SAS/IML Operators
Statement | Description |
|---|---|
& | Logical AND |
| | Logical OR |
^ | Logical negation |
- | Elementwise unary negation |
+ | Elementwise addition |
- | Elementwise subtraction |
# | Elementwise multiplication |
/ | Elementwise division |
## | Elementwise power |
* | Matrix multiplication |
** | Matrix power |
` | Matrix transpose |
|| | Horizontal concatenation of matrices |
// | Vertical concatenation of matrices |
A complete list of operators is available in the Chapter 23, "Language Reference" (SAS/IML User's Guide).
The SAS/IML language does not have bitwise logical operators; use the BAND, BNOT, BOR, and BXOR functions for bitwise operations.
This section lists many of the SAS/IML functions and subroutines that are used in statistical data analysis. For a complete list of functions, see the "Overview" section of the Chapter 23, "Language Reference" (SAS/IML User's Guide).
The SAS/IML language contains all of the standard mathematical functions that are available in the SAS DATA step. If you call one of these functions with a matrix argument, the function returns a matrix of values. For example, the following statement applies the SQRT function to every element of a 1 × 4 matrix:
x = {1 4 9 16};
s = sqrt(x);Table B.2 indicates a few of the many mathematical functions that are available in the SAS/IML language.
Table B.3 indicates a few of the probability functions that are available in the SAS/IML language.
Table B.3. Probability Functions and Subroutines
Function | Description |
|---|---|
CDF | Returns a value from a cumulative probability distribution |
NORMAL | Generates pseudorandom numbers from a normal distribution |
Returns a value from a probability density distribution | |
QUANTILE | Returns a quantile from a distribution |
RANDGEN | Call Generates pseudorandom numbers from a distribution |
RANDSEED | Call Specifies the sequence for the RANDGEN subroutine |
UNIFORM | Generates pseudorandom numbers from a uniform distribution |
You can use the NORMAL and UNIFORM functions for generating small samples. However, the RANDGEN subroutine implements a Mersenne-Twister random number generator that is preferred by experts in statistical computation. You should use the RANDGEN subroutine when you intend to generate millions of random numbers.
Several functions for descriptive statistics were introduced in SAS/IML 9.22: COUNTMISS, COUNTN, MEAN, PROD, QNTL, and VAR. Table B.4 lists some of the SAS/IML functions and subroutines for computing descriptive statistics.
Table B.4. Descriptive Statistical Functions and Subroutines
COUNTMISS | Returns the number of missing elements |
COUNTN | Returns the number of nonmissing elements |
CUSUM | Returns the cumulative sum of the elements |
MIN, MAX | Returns the minimum or maximum element |
MEAN | Returns various means of the elements |
PROD | Returns the product of the elements |
QNTL Call | Returns quantiles of the elements |
RANK | Returns the ranks of the elements |
RANKTIE | Returns the tied ranks of the elements |
SSQ | Returns the sum of the squares of elements |
SUM | Returns the sum of the elements |
VAR | Returns the variance of the elements |
A matrix query function gives you information about data in a matrix. What are the dimensions of the matrix? Are the data numerical or character? Are any elements nonzero? What are the locations of the nonzero elements? Table B.5 lists some of the matrix query functions.
Table B.5. Matrix Query Functions
Function | Description |
|---|---|
ALL | Returns 1 if all elements are nonzero |
ANY | Returns 1 if any element is nonzero |
CHOOSE | Returns a value based on a criterion evaluated for each observation |
LENGTH | Returns a size for each element in a character matrix. For English characters, this size corresponds to the number of characters in each element. |
LOC | Returns the indices that satisfy a criterion |
NCOL, NROW | Returns the number of columns or rows |
NLENG | Returns a scalar number that indicates the size (in bytes) of the elements of a matrix |
TYPE | Returns the type of matrix: 'C', 'N', 'U' |
Table B.6 lists functions that create, resize, or reshape a matrix. See Chapter 2, "Getting Started with the SAS/IML Matrix Programming Language," for details.
Table B.6. Functions That Create and Reshape Matrices
Description | |
|---|---|
DIAG | Creates a diagonal matrix |
DO | Creates an arithmetic sequence |
I | Creates an identity matrix |
INSERT | Inserts rows or columns into a matrix |
J | Creates a matrix with identical values |
REMOVE | Removes rows or columns from a matrix |
REPEAT | Creates a matrix with repeated values |
SHAPE | Reshapes a matrix |
T | Transposes a matrix |
VECDIAG | Returns a vector that contains the diagonal elements of a matrix |
Table B.7 lists a few functions that are useful for performing linear algebraic operations such as solving a system of linear equations. The SAS/IML language contains many other advanced functions for matrix computations.
Table B.7. Linear Algebra Functions and Subroutines
Function | Description |
|---|---|
DET | Returns the determinant |
EIGEN Call | Computes eigenvectors and eigenvalues |
GINV | Returns a generalized inverse for a matrix |
INV | Returns the inverse for a nonsingular matrix |
QR Call | Computes the QR decomposition of a matrix |
ROOT | Computes the Cholesky decomposition of a symmetric positive definite matrix |
SOLVE | Returns the solution to a linear system of equations |
SVD Call | Computes the singular value decomposition |
TRACE | Returns the sum of the diagonal elements |
Table B.8 lists functions that are useful for finding the union and intersection of sets of values. See Section 2.11 for details.
Table B.9 lists functions that are useful for formatting data and for manipulating character strings. Many of these functions are documented in the SAS Language Reference: Dictionary.
Table B.9. Formatting Functions
Function | Description |
|---|---|
CHAR | Returns the result of applying a w.d format to a numeric matrix |
NUM | Returns a numeric matrix from a character string that contain numbers |
PUTC | Returns the result of applying a format to a character matrix |
PUTN | Returns the result of applying a format to a numeric matrix |
STRIP | Removes leading and trailing blanks from a character string |
TRIM | Removes trailing blanks from a character string |
LEFT | Left-aligns a character string |
RIGHT | Right-aligns a character string |
A module is a user-defined function or subroutine. Table B.10 lists statements that are useful for defining, storing, and loading modules. The mechanism for storing and loading IMLPlus modules is different than the PROC IML mechanism, as explained in Section 5.7.
A control statement enables you to iterate and to conditionally execute certain statements. See Section 2.8 for more information. Table B.11 lists some of the important control statements.
Table B.11. Control Statements
Statement | |
|---|---|
DO | Iterates over a series of statements by incrementing a counter |
DO/UNTIL | Iterates over a series of statements until a condition is satisfied |
DO/WHILE | Iterates over a series of statements while a condition is satisfied |
IF-THEN/ELSE | Tests a condition and executes certain statements depending on whether the condition is true or false |
SUBMIT-ENDSUBMIT | Send statements to the SAS System or to R |
The SUBMIT and ENDSUBMIT statements were introduced in SAS/IML 9.22.
You can read data from a SAS data set into SAS/IML vectors. You can also read numerical (or character) data into a matrix. You can create SAS data sets from data that are in SAS/IML matrices. Table B.12 lists some of the statements that are useful for reading and writing data sets. See Chapter 3, "Programming Techniques for Data Analysis," for details.
You can print the values of one or more matrices by using the PRINT statement. You can list multiple matrices on a single print statement. If you separate the matrices with commas, each matrix is printed on a separate row. Table B.13 lists optional arguments that you can use to print matrices with headers or labels, or to format the data. See Section 2.2.1 for details.