## 1-D Physical System Statistics

The 1-D Physical System statistics represent the aggregate statistics of all physical networks associated with blocks from Simscape™, Simscape Driveline™, Simscape Fluids™, and Simscape Electrical™ libraries, with the exception of Specialized Power Systems blocks.

The individual statistics are:

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

• Continuous variables (retained) — 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 can be further categorized 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.

• Differential variables — 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.

• Algebraic variables — 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.

• Continuous variables (eliminated) — 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.

• Differential variables — 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.

• Algebraic variables — 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.

• Continuous variables (secondary) — Number of secondary variables associated with all 1-D physical systems in the model. Secondary variables are variables added to the system to make it solvable. Secondary variables can be categorized further as algebraic and differential variables.

• Differential variables — Number of secondary 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 added to the system to make it solvable.

• Algebraic variables — Number of secondary 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. 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 added to the system to make it solvable.

• Discrete variables — 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 can be further categorized as integer-valued and real-valued discrete variables.

• Integer-valued variables — 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.

• Real-valued variables — 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.

• Discrete variables (secondary) — Number of secondary discrete variables associated with all 1-D physical systems in the model. Discrete secondary variables represent those discrete variables in the model that have been added to the system to make it solvable.

• Number of zero-crossing signals — 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.

• Constraints — Number of primary constraint equations in the model, along with the total number of differential variables involved in each constraint. Primary constraints are the constraints identified before index reduction. These equations and variables are further handled by index reduction algorithms.

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