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Using Proc IMLStatistical Computing
Spring 2014
What is IML? SAS vs R
SAS: procedures (PROCs) and datasets R: functions/operations and matrices/vectors
Proc IML IML = Interactive Matrix Language R-like programming inside of SAS Pros: more flexible Cons: programs are not validated
Applications Simulate data Matrix algebra (e.g. contrasts, algorithms) Many things you could normally only do in R Graphics
The Matrix A matrix is a collection of numbers ordered by rows
and columns. Matrices are characterized by the number of rows and
columns The elements in a matrix are referred to first by their row
then column
2221
1211
xxxx
X
Special Matrices A 1 x 1 matrix is also known as a scalar
r x 1 or 1 x c matrices are known as vectors
A diagonal matrix is a square matrix where the off-diagonal elements are zero An identity matrix is a diagonal matrix where the diagonal
elements are 1. These are also denoted by Ic, where c is the dimension of the matrix
22
11
00
xx
X
1001
2I
11xX
1211 xxX
21
11
xx
X
Creating Matrices in IMLPROC IML;A = 1; /* CREATE A SCALAR*/B = {1 2 3}; /* CREATE A ROW VECTOR OF LENGTH 3*/C = { 4,5,6}; /* CREATE A COLUMN VECTOR OF LENGTH 3*/D ={ 1 2,3 4,5 .}; /* CREATE A 3 BY 2 MATRIX WHERE THE 3,2 ELEMENT IS MISSING*/
PRINT A B C D; /* DISPLAY THE MATRICES IN THE OUTPUT*/
QUIT;*Can assign characters instead of numbers but matrix algebra won’t work
Manipulating Matrices Using brackets inside the specification allows you to request
repeats A={ [2] ‘Yes’, [2] ‘No’} is equivalent to A={‘Yes’ ‘Yes’, ‘No’ ‘No’} SAS: {[# Repeats] Value}, R: rep(value, number of times)
Select a single element A={1 2, 3 4} To select the number 3: A2=A[2,1]
Select a row or column To select the first row: A3=A[1, ] To select the first column: A4=A[ ,1]
Select a submatrix B={1 2 0 0, 3 4 00} To select the A matrix from within B:
A_new=B[1:2,1:2] or B[,{1 2} ]
Manipulating Matrices (cont.) To define row and column labels, first create a vector with the
labels PRINT B[rowname=name label vector] Can also use colname, format, and labels in this way To permanently assign use mattrib matrix rowname= colname=
This then allows you to index using the matrix attributes (e.g. A[“True”,])
Selecting elements with logical arguments Instead of listing the specific elements use a logical argument A=[1 2 3 4], B=A[loc(A>2)]=[3 4]
Replace elements Option 1: reassign specific elements
A[2]=7 will yield A=[1 7 3 4] Option 2: reassign by a rule
A[loc(A>2)]=0 will yield A=[1 2 0 0]
Manipulating Matrices in IMLPROC IML;REPEAT_O1={[2]"YES" [2] "NO"}; /*USING THE REPEAT FUNCTION TO FILL THE MATRIX*/REPEAT_O2={"YES" "YES" "NO" "NO"}; /* REPEATING ELEMENTS MANUALLY*/PRINT REPEAT_O1 REPEAT_O2;
A={1 2, 3 4}; /* DEFINE MATRIX*/A1=A[2,1]; /* SELECT THE ELEMENT IN THE 2ND ROW, FIRST COLUMN: A1 SOULD EQUAL 3 */A2=A[1,]; /* SELECT THE FIRST ROW, A2 SHOULD EQUAL A 2 X 1 VECTOR {1 2} */A3=A[,1]; /* SELECT THE FIRST COLUMN, A3 SHOULD EQUAL A 1 X 2 VECTOR {1,3} */B={1 2 0 0, 3 4 0 0}; /* DEFINE A MATRIX B, WITH TWO SUBMATRICES A AND A 2 X 2 NULL MATRIX*/A_NEW=B[1:2,1:2]; /* RECOVER THE A MATRIX FROM B */A_NEW2=B[,{1 2}]; /*RECOVER THE A MATRIX FROM B, ANOTHER WAY TO WRITE IT*/C_ROWNM={M F}; /* SET ROW NAMES FOR MATRIX C*/C_COLNM={TRUE FALSE}; /* SET COL NAMES FOR MATRIX C*/C={10 25,9 18};PRINT A A1 A2 A3 B A_NEW
C[ROWNAME=C_ROWNM COLNAME=C_COLNM FORMAT=6.1 LABEL="MY MATRIX"] /*MODIFYING PRINTED OUTPUT FOR MATRIX C*/;
Manipulating Matrices in IMLC_NEW=C; /* CREATING A DUPLICATE MATRIX*/MATTRIB C_NEW ROWNAME=C_ROWNM COLNAME=C_COLNM FORMAT=6.1 LABEL="MY MATRIX"; /* PERMANANTLY CHANGING OUTPUT FORMAT*/PRINT C C_NEW; /* COMPARING DIFFERENT APPROACHES*/
D=A[LOC(A>1)];/* SELECTING ONLY ELEMENTS THAT MEET RULE, NOTE THAT MATRIX STRUCTURE NOT RETAINED*/PRINT A D;E_TEMP=A; /* CREATING A DUPLICATE MATRIX*/E_TEMP[1,1]=25 /* CHANGING A SINGLE ELEMENT*/PRINT E_TEMP;E_TEMP[LOC(E_TEMP>5)]=.; /* SETTING ALL ELEMENTS MEETING RULE TO MISSING*/PRINT E_TEMP;QUIT;
Creating Special Matrices Identity Matrix
I(r): Identity matrix of size r Dummy Matrix
j(nrow,ncol,x) nrow= number of rows, ncol=number of columns, x =fill value
Diagonal matrix diag(vector) diag(matrix) Note you can also accomplish this by using a Kroeneker
product ( @ ) for multiplying the desired matrix by an identity matrix
Creating Special Matrices Block diagonal matrix
Block(M1, M2, …) Repeat(matrix,nrow,ncol)
repeats the specified matrix for the number of rows and columns given
Shape(vector,nrow,ncol) Repeats the given vector row-wise for the number of rows and
number of columns given. Note that the number of cells to repeat must be a multiple of the vector length
Generate a sequence Do(start,finish, by) creates a vector using the specified skip pattern.
For example do(-1,0,0.5) would return [-1 -0.5 0]. In R you can use seq(start, finish,by)
Brief Introduction to Matrix Algebra
Matrix Addition and Subtraction To add or subtract two matrices, they both must
have the same number of rows and columns. The addition or subtraction is element wise
Example:
jibarBAR ijijij ,
5954
0725
5231
Matrix Multiplication and Division Scalar by Matrix multiplication and division is an
element wise operation and commutative.
Multiplication of vectors and matrices Not commutative (AB ≠ BA) Requires that the number of columns in A equals the
number of rows in B The resulting matrix R will have dimension equal to rows of
A and columns of B
ijij abrBaaBR
crcxxr RBA ,,,
Multiplication and Division (cont.)
643326
2414128
0564251403622312
0261
,5432
r where,1
ij
BA
AB
BA
baBARx
hhjihjxxiji
Special Properties Transpose: A’= (aji)
Inverse (indicated with -1 superscript): the inverse of a number is that number which, when multiplied by the original number, gives a product of 1 Must be a square matrix
642531
',642
531
AA
IAAAA 11
IML Commands for Special Matrices
Function IML Code
Transpose `
Determinant Det(matrix)
Inverse Inv(matrix)
Trace Tr(matrix)
Matrix Algebra in IML
Matrix Operators: Arithmetic
Operation IML Code
Addition +
Subtraction -
Division, element wise /
Multiplication, element wise #
Multiplication, matrix *
Power, element wise ##
Power, Matrix **
Matrix Algebra in IMLPROC IML;
*MATRIX ADDITION;A={1 3, 2 5}; /*DEFINE MATRIX*/B={-5 2, 7 0}; /*DEFINE MATRIX*/C=A+B; /* ADD A AND B*/PRINT C;
*MATRIX MULTIPLICATION;A={2 3,4 5}; /*DEFINE MATRIX*/B={1 6,2 0}; /*DEFINE MATRIX*/AB=A*B; /*MULTIPLY A BY B*/BA=B*A; /* MULTIPLY B BY A*/PRINT A B AB BA; /* NOTE THAT MULTIPLICATION IS NOT
COMMUTATIVE, AB DOESN'T EQUAL BA*/QUIT;
Matrix Operators: Comparison Element wise comparison of matrices, result is a
matrix of 0(False) and 1 (True) Comparisons
Less than (<), less than or equal to (<=) Greater than (>), greater than or equal to (>=) Equal to (=), Not equal to (^=)
Can create compound arguments using logical functions And (&) Or ( |) Not ( ^)
Solving Systems of Equations Solve the following system of equations
When the problem is rewritten in terms of a matrix
4210394511423
zyyxzyx
42911
1030045423
zyx
Solving Systems of Equations (cont) To solve, we can
rearrangePROC IML;
A={3 2 -4, 5 -4 0, 0 3 10};B={11,9,42};
OPT1=SOLVE(A,B);OPT2=INV(A)*B;PRINT OPT1 OPT2;QUIT;
429
11
1030045423 1
1
zyx
BAXBAX
Working with SAS Datasets
Opening a SAS Dataset Before you can access a SAS dataset, you must first
submit a command to open it. To simply read from an existing data set, submit a USE
statement. USE <SAS Dataset> VAR <Variable Names> WHERE expression;
To read and write to an existing data set, use the EDIT statement. In addition to READ you can also EDIT, DELETE, and PURGE
observations from a dataset that has been opened using edit
Each dataset must only be opened once
Reading in Datasets Create matrices from a SAS dataset
Create a vector for each variable Create a matrix containing multiple variables Select all observations or a subset
To transfer data from a SAS dataset to a matrix SETIN
Specifies an open dataset as the current input dataset READ
Transforms dataset into matrix
READ <range> VAR operand <WHERE (expression)>INTO name;
READ all VAR VAR1 WHERE VAR1>80 INTO MYMAT;
Comparison OperatorsOperation IML Code
Less than <
Less than or equal to <=
Equal to =
Greater than >
Greater than or equal to >=
Not equal to ^=
Contains a given string ?
Does not contain a given string ^?
Begins with a given string =:
Sounds like or is spelled like a given string =*
Sorting SAS Datasets First close the dataset SORT dataset out=new_dataset by var_name; Can use the keyword DESCENDING to denote the
alternative sort order
Creating Datasets from Matrices When you create a dataset
Columns become variables Rows become observations
CREATE Opens a new SAS dataset for I/O
APPEND Writes to the dataset
CREATE SAS-data-set FROM matrix <[COLNAME=column-name ROWNAME=row name]>
CREATE SAS-dataset VAR variable-names; APPEND FROM matrix-name;
Data Management CommandsCommand Description Command Description
APPEND Adds observations to the end of a SAS dataset
RESET DEFLIB
Names default libname
CLOSE Closes a SAS dataset SETIN Selects an open SAS dataset for input
CREATE Creates and opens a new SAS dataset or input and output
SETOUT Selects an open SAS dataset for output
DELETE Marks observations for deletion in a SAS dataset
SHOW CONTENTS
Shows contents of the current input SAS dataset
EDIT Opens an existing SAS dataset for I/O
SHOW DATASETS
Shows SAS datasets currently open
FIND Finds observations SORT Sorts a SAS dataset
READ Reads observations into IML variables
SUMMARY Produces summary statistics for numeric variables
REPLACE Writes observations back into a SAS dataset
USE Opens an existing SAS dataset for input
Reading in SAS data with IML*CREATING A SAS DATASET TO WORK WITH;DATA MYDATA;SET SASHELP.CARS;RUN;
PROC IML;USE MYDATA VAR {MSRP MPG_CITY MPG_HIGHWAY} ; /*
OPEN DATASET*/READ ALL VAR _ALL_ WHERE (MSRP<12000) INTO
CAR_MAT; /* READ DATASET*/Z=NROW(CAR_MAT); /* FIGURE OUT HOW MANY
ROWS*/PRINT Z CAR_MAT[COLNAME={MSRP CITY HWY}]; /* LOOK
AT DATA*/QUIT;
Analyzing Data & Writing Programs
Subscript Operations Commands that can be applied
to obtain summary statistics on matrices Select a single element, row,
column, or submatrix Similar to the APPLY function in R
SUMMARY produces summary statistics on the numeric variables of a SAS data set. If you want them by subgroup use the CLASS option. SUMMARY VAR {VARIABLE LIST}
<CLASS (By Variables)> STAT (Desired stats) <OPT (SAVE)>
Reduction operators Addition + Multiplication # Mean: Sum of Squares ## Maximum <> Minimum >< Index of maximum <:> Index of minimum >:<
Additional Operators Concatenation: Horizontal ||,
Vertical // Number of rows: nrow(matrix),
Number of Columns: ncol(matrix)
Types of Statements Control Statements
Direct the flow of execution E.g. IF-THEN/ELSE statement
Functions and CALL statements Perform special tasks or user-defined operations
Command statements Perform special processing such as setting options,
displaying windows, and handling input and output
Control StatementsStatement Description
PROC IML; QUIT; Initiates and ends an IML session
DO; END; Specifies a group of statements
Iterative DO; END; Defines an iteration loop
IF-THEN;ELSE; Conditionally routes execution
START; FINISH; Defines a module
RUN; Executes a Module
IF-THEN/ELSE statements IF expression THEN
statement-one; ELSE statement-two; IML processess the
expression and uses this to decide whether statement one or statement two is executed.
You may also nest IF-THEN/ELSE Statements
PROC IML;A={12 22 33};
IF MAX(A)<20 THEN P=1; ELSE P=0; PRINT P;QUIT;
DO groups Several statements can be grouped
together into a compound statement to be executed as a unit. DO; Statements; END;
You can combine DO arguments with IF/ELSE IF (X<Y) THEN DO; Z=X+Y; END; ELSE DO; Z=X-Y; END;
The iterative DO <WHILE/UNTIL expression> repeats a set of statements over an number of times defined by the index. If DO WHILE is used, the expression is
evaluated at the beginning of each loop with iterations continuing until the expression is false. If the expression begins false the loop does not run.
If DO UNTIL is used the expression is evaluated at the end of the loop, this means that the loop will always execute at least once.
PROC IML;Y=0;DO I=1 TO 3;Y=Y+1;PRINT Y;END;
QUIT;PROC IML;COUNT=1;
DO WHILE(COUNT<3);COUNT=COUNT+1;PRINT “WHILE";END;
COUNT=1;DO UNTIL(COUNT>3);COUNT=COUNT+1;PRINT “UNTIL";END;
QUIT;
Interacting with Procs Option One
Write the data to a SAS data set by using the CREATE and APPEND statements Use the SUBMIT statement to call a SAS procedure that analyzes the data Read the results of the analysis into IML matrices using USE and READ statements
Option Two Do what can only be done in IML Write the data back out to a SAS dataset Call PROCs normally
ODS TRACE ON;/ODS TRACE OFF; Placed before and after a proc will print to the log the names of the various output. Useful for requesting/saving specific parts of the analysis.
To use PROCs SUBMIT; Statements; END SUBMIT; Like macros you can list variables already existing in IML that you would like to use in the
proc. Then inside the submit command refer to these variables using &Varname Substitutions take place before the block is processed so no macro variable is created If you use SUBMIT *, you indicate a wildcard so that any of the existing variables can be
referred Any variable inside the submit block that is referenced (&var) but not created in the IML
procedure does not get substituted. This is used for creating true macros.
Interacting with ProcsPROC IML;
Q={2 5 7 9};CREATE MYDATA VAR{Q};APPEND;CLOSE MYDATA;
*Table=“Moments”;SUBMIT;*SUBMIT table;
PROC UNIVARIATE DATA=MYDATA;VAR Q;ODS OUTPUT MOMENTS=MOMENTS;* ODS OUTPUT MOMENTS=&Table;
RUN;ENDSUBMIT;USE MOMENTS;READ ALL VAR{NVALUE1 LABEL1};CLOSE MOMENTS;LABL ="MY OUTPUT";PRINT NVALUE1[ROWNAME=LABEL1 LABEL=LABL];QUIT;
Modules Modules are used for two purposes
To create user-defined subroutine or function. To define variables that are local to the module. START MODULE-NAME OPTIONS; STATEMENTS; FINISH MODULE-NAME;
To execute the module use RUN MODULE-NAME; execute module first then subroutines CALL MODULE_NAME; execute subroutines then modules
A function is a special type of module that only returns a specific value. START MODULE; STATEMENTS; RETURN(VARIABLE); FINISH MODULE; Any variables created inside the module but not mentioned in the return
statement will not be retained for future use. Possible to store and load modules (like a macro library or SOURCE in R)
STORE MODULE= MODULE NAME; LOAD MODULE=MODULE NAME; These will retain a program after IML has exited
Creating a Permanent Module Library Permanent libraries maintain functions for multiple
users. Equivilant to datasets stored in a permanent library vs. work folderLIBNAME LIBRARY ‘PATH’;PROC IML;START FUNC1(X); RETURN(X+1); FINISH;START FUNC2(X); RETURN(X**2); FINISH;RESET STORAGE=SOURCEFILE.LIBRARY;STORE MODULE=_ALL_;QUIT;
Command StatmentsStatement Description
FREE Frees memory associated with a matrix
LOAD Loads a matrix or module from a storage library
MATTRIB Associates printing attributes with matrices
PRINT Prints a matrix or message
RESET Sets various system options
REMOVE Removes a matrix or module from library storage
SHOW Displays system information
STORE Stores a matrix or module in the storage library
Using R
Calling R from within IML Check to see if R has permission for your SAS
PROC OPTIONS OPTION=RLANG; If not, you will have to add the –RLANG option to startup
Similar to calling procs SUBMIT/R; ENDSUBMIT;
Export ExportDataSetToR: SAS dataset ->R data frame ExportMatrixtoR:IML Matrix->R Matrix
Import IMPORTDATASETFROMR: R Expression ->SAS Dataset IMPORTMATRIXFROMR : R Expression ->SAS MATRIX
R OBJECTS TEND TO BE COMPLEX SO YOU CAN ONLY TRANSFER SOMETHING THAT HAS BEEN COERCED TO DATA FRAME
SAS to R and back againproc iml;/* Comparison of matrix operations in IML and R */print "---------- SAS/IML Results -----------------";x = 1:3; /* vector of sequence 1,2,3 */m = {1 2 3, 4 5 6, 7 8 9}; /* 3 x 3 matrix */q = m * t(x); /* matrix multiplication */print q;
print "------------- R Results --------------------";submit / R;rx <- matrix( 1:3, nrow=1) # vector of sequence 1,2,3rm <- matrix( 1:9, nrow=3, byrow=TRUE) # 3 x 3
matrixrq <- rm %*% t(rx) # matrix multiplicationprint(rq)endsubmit;
submit / R;hist(p, freq=FALSE) # histogramlines(est) # kde overlayendsubmit;
proc iml;use Sashelp.Class;read all var {Weight Height};close Sashelp.Class;/* send matrices to R */call ExportMatrixToR(Weight, "w");call ExportMatrixToR(Height, "h");submit / R;Model <- lm(w ~ h, na.action="na.exclude") # aParamEst <- coef(Model) # bPred <- fitted(Model)Resid <- residuals(Model)endsubmit;call ImportMatrixFromR(pe, "ParamEst");print pe[r={"Intercept" "Height"}];ht = T( do(55, 70, 5) );A = j(nrow(ht),1,1) || ht;pred_wt = A * pe;print ht pred_wt;
YVar = "Weight";XVar = "Height";submit XVar YVar / R;Model <- lm(&YVar ~ &XVar, data=Class, na.action="na.exclude")print (Model$call)endsubmit;
MISC