## 1-D Physical System Statistics

This node represents aggregate statistics generated from all physical networks that are associated with blocks from Simscape™, Simscape Driveline™, Simscape Fluids™, and Simscape Electrical™ libraries, with the exception of Specialized Power Systems blocks.

Each statistic is generated separately from each topologically distinct physical network of these blocks and then aggregated to appear as a single statistic.

The individual statistics are:

• Number of variables — This statistic represents the number of variables associated with all 1-D physical systems in the model. Variables are categorized further as continuous, eliminated, and discrete variables.

• Number of continuous variables (retained) — This statistic represents the number of continuous variables associated with all 1-D physical systems in the model. Continuous variables are those variables whose values vary continuously with time, although some continuous variables can change values discontinuously after events. Continuous variables are categorized further as algebraic and differential variables.

This statistic represents the number of continuous variables in the system after variable elimination. If a system is truly input-output with no dynamics, it is possible to completely eliminate all variables and, in that case, the number of variables is zero.

• Number of differential variables — This statistic represents the number of differential variables associated with all 1-D physical systems in the model. Differential variables are continuous variables whose time derivative appears in one or more system equations. These variables add dynamics to the system and require the solver to use numerical integration to compute their values.

This statistic represents the number of differential variables in the model after variable elimination.

• Number of algebraic variables — This statistic represents the number of algebraic variables associated with all 1-D physical systems in the model. Algebraic variables are continuous system variables whose time derivative does not appear in any system equations. These variables appear in algebraic equations but add no dynamics, and this typically occurs in physical systems due to conservation laws, such as conservation of mass and energy.

This statistic represents the number of algebraic variables in the model after variable elimination.

• Number of continuous variables (eliminated) — This statistic represents the number of eliminated variables associated with all 1-D physical systems in the model. Eliminated variables are continuous variables that are eliminated by the software and are not used in solving the system. Eliminated variables are categorized further as algebraic and differential variables.

• Number of differential variables — This statistic represents the number of eliminated differential variables associated with all 1-D physical systems in the model. Differential variables are continuous variables whose time derivative appears in one or more system equations. These variables add dynamics to the system and require the solver to use numerical integration to compute their values.

This statistic represents the number of differential variables in the model that have been eliminated.

• Number of algebraic variables — This statistic represents the number of eliminated algebraic variables associated with all 1-D physical systems in the model. Algebraic variables are continuous system variables whose time derivative does not appear in any system equations. These variables appear in algebraic equations but add no dynamics, and this typically occurs in physical systems due to conservation laws, such as conservation of mass and energy.

This statistic represents the number of algebraic variables in the model that have been eliminated.

• Number of discrete variables — This statistic represents the number of discrete, or event, variables associated with all 1-D physical systems in the model. Discrete variables are those variables whose values can change only at specific events. Discrete variables are categorized further as integer-valued and real-valued discrete variables.

• Number of integer-valued variables — This statistic represents the number of integer-valued discrete variables associated with all 1-D physical systems in the model. Integer-valued discrete variables are system variables that take on integer values only and can change their values only at specific events, such as sample time hits. These variables are typically generated from blocks that are sampled and run at specified sample times.

• Number of real-valued variables — This statistic represents the number of real-valued discrete variables associated with all 1-D physical systems in the model. Real-valued discrete variables are system variables that take on real values and can change their values only at specific events.

If you select a local solver in the Solver Configuration block, then all continuous variables associated with that system are discretized and represented as real-valued discrete variables.

• Number of zero-crossing signals — This statistic represents the number of scalar signals that are monitored by the Simulink® zero-crossing detection algorithm. Zero-crossing signals are scalar functions of states, inputs, and time whose crossing zero indicates discontinuity in the system. These signals are typically generated from operators and functions that contain discontinuities, such as comparison operators, `abs`, `sqrt` functions, and so on. Times when these signals cross zero are reported as zero-crossing events. During simulation it is possible for none of these signals to produce a zero-crossing event or for one or more of these signals to have multiple zero-crossing events.

• Number of dynamic variable constraints — This statistic represents the number of constraints involving only dynamic variables and inputs. Such constraints result in high-index differential algebraic equations (DAEs) and therefore can cause numerical difficulties or slow down your simulation. These are the state constraints that exist at run time, they do not include state constraints that have been eliminated by the compile-time index reduction.

If you select a statistic with a nonzero value, the Sources section lists all the variables that fall under this statistic. For each variable:

• The Source column contains the full path to the variable, starting from the top-level model, with a link to the relevant block. If you click the link in the Source column, the corresponding block is highlighted in the block diagram.

If your model contains blocks with underlying arrays of components, the full path to the variable in the Source column contains the numbered name of the array member. For more information, see Model Statistics for Component Arrays.

• The Value column contains the name of the variable, as it would appear in the Variables tab of the block dialog box.

If your model uses a Partitioning local solver, the Statistics Viewer contains additional statistics specific to this solver type. For more information, see Model Statistics Available when Using the Partitioning Solver.