Forced Matrix Viral Calculator

Enter Matrix Values

Use a 3 by 3 influence matrix, an initial vector, and a force vector. The model repeats for the selected number of steps.

Example Data Table

Formula Used

The calculator uses a forced linear recurrence model:

x(t + 1) = d × M × x(t) + f

Here, M is the 3 by 3 influence matrix. The vector x(t) is the current segment state. The value d is the decay factor. The vector f is the outside force added at each step.

The final viral score is:

Final Viral Score = Segment A + Segment B + Segment C

The growth multiple is:

Growth Multiple = Final Total ÷ Initial Total

The spectral radius is estimated with power iteration. It helps judge whether repeated matrix action is damped or expanding.

How to Use This Calculator

1. Enter the nine matrix values. These values control segment influence.
2. Enter the initial vector values for Segment A, B, and C.
3. Enter the force vector. These values are added during each step.
4. Set the decay factor. Use values below one for damped systems.
5. Choose the number of steps and the viral threshold.
6. Press the calculate button. Results appear below the header and above the form.
7. Review the chart, table, stability estimate, and dominant segment.
8. Use CSV or PDF buttons to save the results.

Understanding Forced Matrix Viral Modeling

A forced matrix viral calculator studies how a value spreads through connected points. In this page, each matrix cell describes how one segment influences another segment. The initial vector shows the starting activity. The force vector adds outside pressure during every step. This makes the model useful for learning controlled growth, feedback, decay, and stability.

Why the Matrix Matters

The matrix is the engine of the calculation. Large diagonal values mean a segment keeps much of its own activity. Large off diagonal values mean one segment transfers activity to another segment. Decay reduces the result after each multiplication. A decay above one can exaggerate growth. A low decay can dampen the system quickly.

Reading the Viral Score

The viral score is the sum of the final vector values. It is not a medical term here. It is a mathematical spread score. A larger score means the model produced more total activity. The growth multiple compares final total activity with the starting total. The spectral radius estimates the strongest repeating effect inside the weighted matrix. When it is below one, the model usually tends toward stable behavior.

Practical Analysis

Use the calculator to compare scenarios. You can test a calm system, an aggressive system, or a system with strong outside forcing. Change one input at a time when possible. This helps you understand which factor changes the outcome. The chart shows each segment across time. The total line shows combined activity.

Advanced Use

For deeper analysis, try several force vectors. Try high force on only one segment. Then compare it with balanced force across all segments. Review row sums to see outgoing pressure. Review column sums to see incoming pressure. The determinant helps describe matrix behavior. The trace summarizes the diagonal. These values support fast comparison, but they do not replace a full proof. Always confirm critical math with a separate method.

Common Limits

The model is simplified. It assumes the same matrix repeats at every step. Real systems may change over time. Inputs may also contain noise. Use the results as a careful planning guide. Save each scenario with the export buttons for later review.