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# tf.math.polyval

Computes the elementwise value of a polynomial.

If `x` is a tensor and `coeffs` is a list n + 1 tensors, this function returns the value of the n-th order polynomial

p(x) = coeffs[n-1] + coeffs[n-2] * x + ... + coeffs[0] * x**(n-1)

evaluated using Horner's method, i.e.

p(x) = coeffs[n-1] + x * (coeffs[n-2] + ... + x * (coeffs[1] + x * coeffs[0]))

Usage Example:

````coefficients = [1.0, 2.5, -4.2]`
`x = 5.0`
`y = tf.math.polyval(coefficients, x)`
`y`
`<tf.Tensor: shape=(), dtype=float32, numpy=33.3>`
```

#### Usage Example:

````tf.math.polyval([2, 1, 0], 3) # evaluates 2 * (3**2) + 1 * (3**1) + 0 * (3**0)`
`<tf.Tensor: shape=(), dtype=int32, numpy=21>`
```

`tf.math.polyval` can also be used in polynomial regression. Taking advantage of this function can facilitate writing a polynomial equation as compared to explicitly writing it out, especially for higher degree polynomials.

````x = tf.constant(3)`
`theta1 = tf.Variable(2)`
`theta2 = tf.Variable(1)`
`theta3 = tf.Variable(0)`
`tf.math.polyval([theta1, theta2, theta3], x)`
`<tf.Tensor: shape=(), dtype=int32, numpy=21>`
```

`coeffs` A list of `Tensor` representing the coefficients of the polynomial.
`x` A `Tensor` representing the variable of the polynomial.
`name` A name for the operation (optional).

A `tensor` of the shape as the expression p(x) with usual broadcasting rules for element-wise addition and multiplication applied.

#### Numpy Compatibility

Equivalent to numpy.polyval.

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