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# coincidence

Coincidence algorithm

## Syntax

``x = coincidence(res,div,maxval)``
``x = coincidence(res,div,maxval,tol)``

## Description

example

````x = coincidence(res,div,maxval)` returns the scalar `x` that is less than or equal to `maxval` and is congruent to each remainder in `res` for the corresponding divisor in `div`. `x` satisfies mod(`x`,`div`) = `res`.In other words, dividing `x` by each element of `div` leaves as remainder the corresponding element of `res`.```
````x = coincidence(res,div,maxval,tol)` also specifies the tolerance. In practice, there may be no value that satisfies all constraints in `res` and `div` exactly. In that case, `coincidence` identifies a set of candidates that approximately satisfy the constraints and are within an interval of width 2 × `tol` centered at the candidates' median. The function then returns the median as `x`.```

## Examples

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Find a number smaller than `1000` that has a remainder of `2` when divided by `9`, a remainder of `3` when divided by `10.4`, and a remainder of `6.3` when divided by `11`.

There is no number that satisfies the constraints exactly, so specify a tolerance of `1`. `coincidence` identifies a set of numbers that approximately satisfy the constraints and are within $2×tol=2$ from their median. The function then outputs the median.

```tol = 1; x = coincidence([2 3 6.3],[9 10.4 11],1000,tol)```
```x = 127.8000 ```

Increase the tolerance to `2`.

```tol = 2; x = coincidence([2 3 6.3],[9 10.4 11],1000,tol)```
```x = 74 ```

Specify a tolerance of `3.3`. Any tolerance larger than this value results in the same answer.

```tol = 3.3; x = coincidence([2 3 6.3],[9 10.4 11],1000,tol)```
```x = 3 ```

In a staggered pulse repetition frequency (PRF) radar system, the first PRF corresponds to `70` range bins and the second PRF corresponds to `85` range bins. The target is detected at bin `47` for the first PRF and bin `12` for the second PRF. Assuming each range bin is `50` meters, compute the target range from these two measurements. Assume the farthest target can be `50` km away.

```idx = coincidence([47 12],[70 85],50e3/50); r = 50*idx```
```r = 30350 ```

## Input Arguments

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Remainder array, specified as a row vector of nonnegative numbers. `res` must have the same number of elements as `div`.

Data Types: `single` | `double`

Divisor array, specified as a row vector of positive integers. `div` must have the same number of elements as `res`.

Data Types: `single` | `double`

Upper bound, specified as a positive scalar.

Data Types: `single` | `double`

Tolerance, specified as a nonnegative scalar.

Data Types: `single` | `double`

## Output Arguments

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Congruent value, returned as a scalar.

## Version History

Introduced in R2021a