Solve UX = B for X when U is upper triangular matrix
Math Functions / Matrices and Linear Algebra / Linear System Solvers
dspsolvers
The Backward Substitution block solves the linear system UX = B by simple backward substitution of variables, where:
U is the upper triangular MbyM matrix input to the U port.
B is the MbyN matrix input to the B port.
The MbyN output matrix X is the solution of the equations. The block does not check the rank of the inputs.
The block uses only the elements in the upper triangle of input U and ignores the lower elements. When you select the Input U is unitupper triangular check box, the block assumes the elements on the diagonal of U are 1s. This is useful when matrix U is the result of another operation, such as an LDL decomposition, that uses the diagonal elements to represent the D matrix.
The block treats a lengthM vector input at port B as an Mby1 matrix.
The following diagram shows the data types used within the Backward Substitution block for fixedpoint signals.
You can set the product output, accumulator, and output data types in the block dialog.
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.
Main Tab
Select this check box only when all elements on the diagonal of
U have a value of 1
. When you do
so, the block optimizes its behavior by skipping an unnecessary division
operation.
Do not select this check box if there are any elements on the diagonal of
U that do not have a value of 1
.
When you clear the Input U is unitupper triangular
check box, the block always performs the necessary division
operation.
Select to optimize simulation speed when the diagonal elements of complex input U are real. This parameter is only visible when Input U is unitupper triangular is not selected.
Note
When U is a complex fixedpoint signal, you must select either Input U is unitupper triangular or Diagonal of complex input U is real. When either of these options are selected, the block ignores any imaginary part of the diagonal of U.
Data Types Tab
Note
Floatingpoint inheritance takes precedence over the data type settings defined on this pane. When inputs are floating point, the block ignores these settings, and all internal data types are floating point.
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 diagrams showing 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 first 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 product
output
.
A rule that inherits a data type, for example,
Inherit: Same as first 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 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 first 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 data type parameter.
See Control Signal Data Types (Simulink) for more information.
Specify the minimum value that the block should output. The default value
is []
(unspecified). Simulink^{®} uses this value to perform:
Simulation range checking (see Specify Signal Ranges (Simulink))
Automatic scaling of fixedpoint data types
Specify the maximum value that the block should output. The default value
is []
(unspecified). Simulink uses this value to perform:
Simulation range checking (see Specify Signal Ranges (Simulink))
Automatic scaling of fixedpoint data types
Select this parameter to prevent the fixedpoint tools from overriding the data types you specify on the block mask.
Port  Supported Data Types 

U 

B 

X 
