Multiply matrix elements along rows, columns, or entire input
Math Functions / Matrices and Linear Algebra / Matrix Operations
dspmtrx3
The Matrix Product block multiplies the elements of an MbyN input matrix u along its rows, its columns, or over all its elements.
When the Multiply over parameter is set
to Rows
, the block multiplies across the
elements of each row and outputs the resulting Mby1
matrix. The block treats lengthN unoriented vector
input as a 1byN matrix.
$$\left[\begin{array}{ccc}{u}_{11}& {u}_{12}& {u}_{13}\\ {u}_{21}& {u}_{22}& {u}_{23}\\ {u}_{31}& {u}_{32}& {u}_{33}\end{array}\right]\Rightarrow \left[\begin{array}{c}{y}_{1}\\ {y}_{2}\\ {y}_{3}\end{array}\right]=\left[\begin{array}{c}\left({\displaystyle \prod _{j=1}^{3}{u}_{1j}}\right)\\ \left({\displaystyle \prod _{j=1}^{3}{u}_{2j}}\right)\\ \left({\displaystyle \prod _{j=1}^{3}{u}_{3j}}\right)\end{array}\right]$$
When the Multiply over parameter is set
to Columns
, the block multiplies down the
elements of each column and outputs the resulting 1byN matrix.
The block treats lengthM unoriented vector input
as an Mby1 matrix.
$$\begin{array}{ccc}\left[\begin{array}{ccc}{u}_{11}& {u}_{12}& {u}_{13}\\ {u}_{21}& {u}_{22}& {u}_{23}\\ {u}_{31}& {u}_{32}& {u}_{33}\end{array}\right]& & \\ \Downarrow & & \\ \left[\begin{array}{ccc}{y}_{1}& {y}_{2}& {y}_{3}\end{array}\right]& =& \left[\begin{array}{ccc}\left({\displaystyle \prod _{i=1}^{3}{u}_{i1}}\right)& \left({\displaystyle \prod _{i=1}^{3}{u}_{i2}}\right)& \left({\displaystyle \prod _{i=1}^{3}{u}_{i3}}\right)\end{array}\right]\end{array}$$
When the Multiply over parameter is set
to Entire input
, the block multiplies all
the elements of the input together and outputs the resulting scalar.
$$\left[\begin{array}{ccc}{u}_{11}& {u}_{12}& {u}_{13}\\ {u}_{21}& {u}_{22}& {u}_{23}\\ {u}_{31}& {u}_{32}& {u}_{33}\end{array}\right]\Rightarrow y=({\displaystyle \prod _{i=1}^{3}{\displaystyle \prod _{j=1}^{3}{u}_{ij}}})$$
The following diagram shows the data types used within the Matrix Product block for fixedpoint signals.
The output of the multiplier is in the product output data type when at least one of the inputs to the multiplier is real. When both of the inputs to the multiplier are complex, the result of the multiplication is in the accumulator data type. For details on the complex multiplication performed, see Multiplication Data Types. You can set the accumulator, product output, intermediate product, and output data types in the block dialog as discussed in Dialog Box below.
The Main pane of the Matrix Product block dialog appears as follows.
Indicate whether to multiply together the elements of each row, each column, or the entire input.
The Data Types pane of the Matrix Product block dialog appears as follows.
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. 
Select the rounding mode for fixedpoint operations.
Select the overflow mode for fixedpoint operations.
Specify the intermediate product data type. As shown in FixedPoint Data Types, the output of the multiplier is cast to the intermediate product data type before the next element of the input is multiplied into it. 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([],16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Product output data type parameter.
See Specify Data Types Using Data Type Assistant for more information.
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
An expression that evaluates to a valid data type,
for example, fixdt([],16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Product output data type parameter.
See Specify Data Types Using Data Type Assistant 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
An expression that evaluates to a valid data type,
for example, fixdt([],16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Accumulator data type parameter.
See Specify Data Types Using Data Type Assistant 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 product output
An expression that evaluates to a valid data type,
for example, fixdt([],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 Specify Block Output Data Types for more information.
Specify the minimum value that the block should output. The
default value is []
(unspecified). Simulink^{®} software
uses this value to perform:
Simulation range checking (see Signal Ranges)
Automatic scaling of fixedpoint data types
Specify the maximum value that the block should output. The
default value is []
(unspecified). Simulink software
uses this value to perform:
Simulation range checking (see Signal Ranges)
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 

Input 

Output 

ArrayVector Multiply  DSP System Toolbox 
Matrix Square  DSP System Toolbox 
Matrix Sum  DSP System Toolbox 
prod  MATLAB 