Description
Calculate fixedPoint=offset/(1-multiplier) and centered=value-fixedPoint, rejecting multiplier one.
A sequence rule specifies an index origin, state order, and relation among terms. Advancing one step, mapping an index, and checking a local residual answer different questions. Supplied coefficients or periods define a model; they do not establish that observations follow it.
Calculate fixedPoint=offset/(1-multiplier) and centered=value-fixedPoint, rejecting multiplier one.
When to use this tool
Use Recurrence Affine Fixed Point Shift when you need this particular index map, recurrence step, count, or local algebraic term under supplied sequence conventions.
How to use the tool and how it works
- Enter multiplier, offset, value. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read fixedPoint, centered. Use the output convention below.
Calculate fixedPoint=offset/(1-multiplier) and centered=value-fixedPoint, rejecting multiplier one.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| multiplier | Multiplier | Required. Finite number. |
| offset | Offset | Required. Finite number. |
| value | Value | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| fixedPoint | Fixed Point | Required. Finite number. |
| centered | Centered | Required. Finite number. |
{
"input": {
"multiplier": 0.5,
"offset": 2,
"value": 7
},
"output": {
"fixedPoint": 4,
"centered": 3
}
}Limitations and assumptions
- This is one affine recurrence's algebraic fixed point, not a convergence guarantee. Multipliers near one can make the result sensitive or out of range; no trajectory is generated.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Choose exact integer arithmetic when the index or coefficient range requires it. A complete sequence analysis needs actual terms and a consistent index and state-order convention beyond one local step.
References
Similar or alternative tools
- Recurrence Delay State Shift Index
Return nextIndex=index+1 for a bounded state index except the final position, which returns minus one and dropped true.
- Recurrence Initial State Shift Step
Emit state[0] and return the nonempty state's remaining entries followed by supplied next.