Factor square matrix into lower and upper triangular components
Math Functions / Matrices and Linear Algebra / Matrix Factorizations
dspfactors
The LU Factorization block factors a rowpermuted version of the square input matrix
A as A_{p} =
L*U, where L is a
unitlower triangular matrix, U is an upper triangular matrix, and
A_{p} contains the rows of
A permuted as indicated by the permutation index vector
P. The block uses the pivot matrix
A_{p} instead of the exact input matrix
A because it improves the numerical accuracy of the
factorization. You can determine the singularity of the input matrix
A by enabling the optional output port S. When
A is singular, the block outputs a 1
at port
S; when A is nonsingular, it outputs a 0
.
To improve efficiency, the output of the LU Factorization block at port LU is a
composite matrix containing both the lower triangle elements of L and
the upper triangle elements of U. Thus, the output is in a different
format than the output of the MATLAB^{®}
lu
function, which returns
L and U as separate matrices. To convert the
output from the block's LU
port to separate L and
U matrices, use the following code:
L = tril(LU,1)+eye(size(LU)); U = triu(LU);
If you compare the results produced by these equations to the actual output of the
MATLAB
lu
function, you may see slightly different values. These differences
are due to rounding error, and are expected.
See the lu
function reference page in the
MATLAB documentation for more information about LU factorizations.
The following diagram shows the data types used within the LU Factorization block for fixedpoint signals.
You can set the product output, accumulator, and output data types in the block dialog as discussed below.
The output of the multiplier is in the product output data type when the input is real. When the input is complex, the result of the multiplication is in the accumulator data type. For details on the complex multiplication performed, see Multiplication Data Types.
The rowpivoted matrix A_{p} and permutation index vector P computed by the block are shown below for 3by3 input matrix A.
$$A=\left[\begin{array}{ccc}1& 8& 5\\ 9& 1& 2\\ 2& 5& 7\end{array}\right]\text{}P=\left(\begin{array}{ccc}2& 1& 3\end{array}\right)\text{}{A}_{P}=\left[\begin{array}{ccc}9& 1& 2\\ 1& 8& 5\\ 2& 5& 7\end{array}\right]$$
The LU
output is a composite matrix whose lower subtriangle forms
L and whose upper triangle forms U.
See Matrix Factorizations in the DSP System Toolbox™ User's Guide for another example using the LU Factorization block.
Main Tab
Select to output the singularity of the input at port S, which outputs Boolean data type values of 1 or 0. An output of 1 indicates that the current input is singular, and an output of 0 indicates the current input is nonsingular.
Data Types Tab
Specify the rounding mode for fixedpoint operations as one of the following:
Floor
Ceiling
Convergent
Nearest
Round
Simplest
Zero
For more details, see rounding mode.
When you select this parameter, the block saturates the result of its
fixedpoint operation. When you clear this parameter, the block wraps the
result of its fixedpoint operation. For details on
saturate
and wrap
, see overflow
mode for fixedpoint operations.
Specify the product output data type. See FixedPoint Data Types and Multiplication Data Types for illustrations depicting the use of the product output data type in this block. You can set it to:
A rule that inherits a data type, for example,
Inherit: Inherit via internal rule
.
For more information on this rule, see Inherit via Internal Rule.
A rule that inherits a data type, for example,
Inherit: Same as input
.
An expression that evaluates to a valid data type, for example,
fixdt(1,16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Product output parameter.
See Specify Data Types Using Data Type Assistant (Simulink) for more information.
Specify the accumulator data type. See FixedPoint Data Types for illustrations depicting the use of the accumulator data type in this block. You can set this parameter to:
A rule that inherits a data type, for example,
Inherit: Inherit via internal rule
.
For more information on this rule, see Inherit via Internal Rule.
A rule that inherits a data type, for example,
Inherit: Same as input
.
A rule that inherits a data type, for example,
Inherit: Same as product
output
.
An expression that evaluates to a valid data type, for example,
fixdt(1,16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Accumulator parameter.
See Specify Data Types Using Data Type Assistant (Simulink) for more information.
Specify the output data type. See FixedPoint Data Types for illustrations depicting the use of the output data type in this block. You can set it to:
A rule that inherits a data type, for example,
Inherit: Same as input
An expression that evaluates to a valid data type, for example,
fixdt(1,16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Output parameter.
See Control Signal Data Types (Simulink) for more information.
Select this parameter to prevent the fixedpoint tools from overriding the data types you specify on the block mask.
Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed. Baltimore, MD: Johns Hopkins University Press, 1996.
Port  Supported Data Types 

A 

LU 

P 

S 
