*Last updated: 2023-03-16.*
# tf_quant_finance.math.pde.grids.uniform_grid_with_extra_point
View source
Creates a grid spec for a uniform grid with an extra grid point.
```python
tf_quant_finance.math.pde.grids.uniform_grid_with_extra_point(
minimums, maximums, sizes, extra_grid_point, dtype=None, validate_args=False,
name=None
)
```
A uniform grid is characterized by having a constant gap between neighboring
points along each axis. An extra grid point is useful, for example, when
computing sensitivities for a value through a grid pricing method
#### Examples
```python
dtype = np.float64
extra_locations = tf.constant([[1, 2], [2, 3]], dtype=dtype)
min_x, max_x, sizes = [[0, 0], [0, 0]], [[10, 5], [100, 5]], [3, 2]
# Here min_x and max_x are in the original space and *not* in the log-space.
grid = uniform_grid_with_extra_point(
min_x, max_x, sizes,
extra_grid_point=extra_locations, dtype=dtype)
with tf.Session() as sess:
grid = sess.run(grid)
# Note that the minimum and maximum grid locations are the same as min_x and
# max_x.
print(grid.locations[0])
# [[0, 1, 5, 10], [0, 2, 50, 100]]
print(grid.locations[1])
# [[0, 2, 5], [0, 3, 5]]
```
Note that the shape of all four parameters must be fully defined and equal
to each other. The shape is used to determine the dimension of the grid.
#### Args:
* `minimums`: Real `Tensor` of rank 1 or 2 containing the lower end points of
the grid. Must have the same shape as those of `maximums`. When rank is 2
the first dimension is the batch dimension.
* `maximums`: `Tensor` of the same dtype and shape as `minimums`. The upper
endpoints of the grid.
* `sizes`: Integer rank 1 `Tensor` of the same shape as `minimums`. The size of
the grid in each axis. Each entry must be greater than or equal to 2 (i.e.
the sizes include the end points). For example, if minimums = [0.] and
maximums = [1.] and sizes = [3], the grid will have three points at [0.0,
0.5, 1.0].
* `extra_grid_point`: A `Tensor` of the same `dtype` as `minimums` and of shape
`[batch_size, n]`, where `batch_shape` is a positive integer and `n` is
the number of points along a dimension. These are the extra points added
to the grid, so that the output grid `locations` have shape `[batch_shape,
n+1]`.
* `dtype`: Optional tf.dtype. The default dtype to use for the grid.
* `validate_args`: Python boolean indicating whether to validate the supplied
arguments. The validation checks performed are (a) `maximums` > `minimums`
(b) `sizes` >= 2.
* `name`: Python str. The name prefixed to the ops created by this function. If
not supplied, the default name 'uniform_grid_spec' is used.
#### Returns:
The grid locations as projected along each axis. One `Tensor` of shape
`[..., n]`, where `n` is the number of points along that axis. The first
dimensions are the batch shape. The grid itself can be seen as a cartesian
product of the locations array.
#### Raises:
ValueError if the shape of maximums, minimums and sizes are not fully
defined or they are not identical to each other or they are not rank 1.