*Last updated: 2023-03-16.*
# tf_quant_finance.math.pde.grids.log_uniform_grid_with_extra_point
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Creates a grid for a uniform grid in a log-space with an extra grid point.
```python
tf_quant_finance.math.pde.grids.log_uniform_grid_with_extra_point(
minimums, maximums, sizes, extra_grid_point, dtype=None, validate_args=False,
name=None
)
```
A log-uniform grid is characterized by having a constant gap between
neighboring points along each axis in the log-space, i.e., the logarithm of
output grid is the uniform grid. An extra grid point is useful, for example,
when computing sensitivities for a value through a grid pricing method.
Note that the shape of all three parameters must be fully defined and equal
to each other. The shape is used to determine the dimension of the grid.
Note that all the parameters are supplied and returned for the original space
and not the log-space.
#### Examples
```python
dtype = np.float64
extra_locations = tf.constant([[0.5, 2], [2, 3]], dtype=dtype)
min_x, max_x, sizes = [[0.1, 0.1], [0.01, 0.1]], [[10, 5], [100, 5]], [3, 2]
# Here min_x and max_x are in the original space and *not* in the log-space.
grid = log_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, 0.5, 1.0, 10.0], [0.01, 1.0, 2.0, 100.0]]
print(grid.locations[1])
# [[0.1, 2, 5], [0.1, 3, 5]]
```
#### 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).
* `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) `minimums` > 0.0 (c) `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.