When learning a new language, it is important to learn to interpret error messages that come from the language's parser or compiler. Three years ago I blogged about how to interpret SAS/IML error messages. However, many questions have been posted to the SAS/IML Support Community that indicate that some people are confused about a common error message. The message is:

ERROR: (execution) Matrices do not conform to the operation.

Matrices that conform to operations

Recall that when you add, subtract, or multiply matrices, the dimensions of the matrices must satisfy certain conditions. Otherwise, the matrix operation is not defined. Let A and B be matrices.

• For addition and subtraction, the operations A+B and A–B are defined only if the number of rows of A equals the number of rows of B, and the number of columns of A equals the number of columns of B. For example, if A is a 5 x 3 matrix, then B must have the same dimensions.
• For the matrix multiplication A*B to make sense, the number of columns of A must be the same as the number of rows of B. For example, if A is a 5 x 3 matrix, then B must have three rows.
• The horizontal concatenation operation A || B makes sense only when the number of rows of A equals the number of rows of B.
• The vertical concatenation operation A // B makes sense only when the number of columns of A equals the number of columns of B.

When the matrices have dimensions that permit them to be added, we say that the matrices conform to the addition operation. When the matrices can be multiplied, we say that the matrices conform to the rules of matrix multiplication, and similarly for other operations.

Matrices that do not conform to an operation

If you try to operate on two matrices whose dimensions are not compatible, the SAS/IML language issues an error. If you look in the SAS Log, you will see the error message, followed by a message that provides the operation that caused the error and the dimensions of the matrices involved. For example, the following example tries to add a 1 x 3 matrix and a 2 x 2 matrix, which causes an error:

proc iml;
A = {1 2 3};
B = {4 5,
     6 7};
C = A + B;    /* causes an error */

The SAS Log contains the following information:

1    proc iml;
NOTE: IML Ready
2    A = {1 2 3};
3    B = {4 5,
4         6 7};
5    C = A + B;
ERROR: (execution) Matrices do not conform to the operation.
 
 operation : + at line 5 column 7
 operands  : A, B
 
A      1 row       3 cols    (numeric)
 
         1         2         3
 
B      2 rows      2 cols    (numeric)
 
         4         5
         6         7
 
 statement : ASSIGN at line 5 column 1

The Log contains information about the error:

• The ERROR occurred during execution. There are matrices that do not conform to some operation.
• The operation that generated the error is the addition operator (+), which is located on line 5 and column 7 of the SAS Log.
• The two matrices involved (the operands) are named A and B.
• The matrix A is a 1 x 3 matrix. For small matrices, the matrix values are displayed in the Log.
• The matrix B is a 2 x 3 matrix.

From that information and from your knowledge of the rules of matrix addition, you can conclude that the expression A + B is not well-defined for these matrices because then have different dimensions.

By understanding this example, you ought to be able to track down the source of other errors that result from attempting matrix operations on nonconforming matrices. However, be aware that the SAS/IML language accepts a "shorthand notation" for row and column operations that arise often in practice, even though the matrices are not conformable in a strict mathematical sense.