CALL CHOL Routine
Calculates the Cholesky decomposition for a given
symmetric matrix.
| Category: |
Matrix Operations |
| Alias: |
CHOLESKY_DECOMP |
| Requirement: |
Both input and output matrices must be square and have
the same dimensions. X must be symmetric positive-definite, and Y
will be a lower triangle matrix.
|
Syntax
CALL CHOL(X, Y <, validate>);
Required Arguments
- X
-
specifies a symmetric
positive-definite input matrix with dimensions m x m (that
is, X[m, m]).
- Y
-
specifies an output
matrix with dimensions m x m (that
is, Y[m, m]).
This variable contains the Cholesky decomposition, such that
where Y is a lower
triangular matrix with strictly positive diagonal entries and Y* denotes
the conjugate transpose of Y.
Note: If X is not symmetric positive-definite,
then Y will be filled with missing values.
Optional Argument
- validate
-
specifies an optional
argument that can increase the processing speed by avoiding error
checking. The argument can take the following values:
| 0 |
the matrix X will be checked for symmetry. This
is the default if the validate argument
is omitted.
|
| 1 |
the matrix is assumed to be symmetric. |
Example
The following example
uses the CHOL CALL routine:
proc fcmp;
array xx[3,3] 2 2 3 2 4 2 3 2 6;
array yy[3,3];
call chol(xx, yy, 0);
do i = 1 to 3;
put yy[i, 1] yy[i, 2] yy[i, 3];
end;
run;SAS produces the following
output:
Output from PROC FCMP and the CHOL CALL Routine
The SAS System 1
The FCMP Procedure
1.4142135624 0 0
1.4142135624 1.4142135624 0
2.1213203436 -0.707106781 1
