Repository: Project-MONAI/MONAI

I have access to a python code repository in the directory /testbed . You can explore and modify files using the available tools. Consider the following issue description:

<issue_description>
RandBiasField missing np.exp
**Describe the bug**
The bias field generated by `RandBiasField._generate_random_field` ([link](https://github.com/Project-MONAI/MONAI/blob/0ad9e73639e30f4f1af5a1f4a45da9cb09930179/monai/transforms/intensity/array.py#L434)) should be exponentiated, as done so in [NiftyNet's implementation](https://github.com/NifTK/NiftyNet/blob/935bf4334cd00fa9f9d50f6a95ddcbfdde4031e0/niftynet/layer/rand_bias_field.py#L99).

**To Reproduce**
```
import matplotlib.pyplot as plt
import numpy as np
from monai.transforms import RandBiasField

rand_bias_field = RandBiasField()
arr = np.ones((1,100,100))

bias_field = rand_bias_field(arr)

plt.figure(figsize=(12,6))
plt.subplot(121)
plt.imshow(bias_field[0])

plt.subplot(122)
plt.hist(bias_field.flatten())
plt.show()
```
![image](https://user-images.githubusercontent.com/20669652/126690750-2d55cbcc-42ee-44bf-828d-7b2738a5b2dd.png)

As shown on the histogram on the right, the values generated by the bias field are around 0 and can also be negative. This is not a proper bias field and multiplying an image by this bias field may invert values.

**Expected behavior**
The bias field should have values around 1. This is usually done by exponentiating the bias field since the bias field generated from the polynomial basis function is actually the log-transformed bias field (Refer to [last equation in section 3.1.1](https://www.sciencedirect.com/science/article/pii/S1361841517300257?via%3Dihub) and the NiftyNet implementation of RandBiasField (linked above). 

```
import matplotlib.pyplot as plt
import numpy as np
from monai.transforms import RandBiasField

rand_bias_field = RandBiasField()
arr = np.ones((1,100,100))

bias_field = np.exp(rand_bias_field(arr))

plt.figure(figsize=(12,6))
plt.subplot(121)
plt.imshow(bias_field[0])

plt.subplot(122)
plt.hist(bias_field.flatten())
plt.show()
```

![image](https://user-images.githubusercontent.com/20669652/126691848-dd9838a2-eb0f-4dca-8960-a13ef55113fc.png)

**Additional comments**
Are there any plans to make a batched Tensor-compatible implementation of RandBiasField so that this transform can theoretically be done on the GPU after batching? At the moment, the only critical numpy dependencies are the calls to `np.polynomial.legendre.leggrid2d` and `np.polynomial.legendre.leggrid3d`, but these can be easily implemented using PyTorch.
</issue_description>

Can you help me implement the necessary changes to the repository so that the requirements specified in the <issue_description> are met?
I've already taken care of all changes to any of the test files described in the <issue_description>. This means you DON'T have to modify the testing logic or any of the tests in any way!
Also the development Python environment is already set up for you (i.e., all dependencies already installed), so you don't need to install other packages.
Your task is to make the minimal changes to non-test files in the /testbed directory to ensure the <issue_description> is satisfied.

Follow these phases to resolve the issue:

Phase 1. READING: read the problem and reword it in clearer terms
   1.1 If there are code or config snippets. Express in words any best practices or conventions in them.
   1.2 Hightlight message errors, method names, variables, file names, stack traces, and technical details.
   1.3 Explain the problem in clear terms.
   1.4 Enumerate the steps to reproduce the problem.
   1.5 Hightlight any best practices to take into account when testing and fixing the issue

Phase 2. RUNNING: install and run the tests on the repository
   2.1 Activate the environment by running  
       ./opt/miniconda3/etc/profile.d/conda.sh ; conda activate testbed
   2.2 Follow the readme
   2.3 Install the environment and anything needed
   2.4 Iterate and figure out how to run the tests

Phase 3. EXPLORATION: find the files that are related to the problem and possible solutions
   3.1 Use `grep` to search for relevant methods, classes, keywords and error messages.
   3.2 Identify all files related to the problem statement.
   3.3 Propose the methods and files to fix the issue and explain why.
   3.4 From the possible file locations, select the most likely location to fix the issue.

Phase 4. TEST CREATION: before implementing any fix, create a script to reproduce and verify the issue.
   4.1 Look at existing test files in the repository to understand the test format/structure.
   4.2 Create a minimal reproduction script that reproduces the located issue.
   4.3 Run the reproduction script to confirm you are reproducing the issue.
   4.4 Adjust the reproduction script as necessary.

Phase 5. FIX ANALYSIS: state clearly the problem and how to fix it
   5.1 State clearly what the problem is.
   5.2 State clearly where the problem is located.
   5.3 State clearly how the test reproduces the issue.
   5.4 State clearly the best practices to take into account in the fix.
   5.5 State clearly how to fix the problem.

Phase 6. FIX IMPLEMENTATION: Edit the source code to implement your chosen solution.
   6.1 Make minimal, focused changes to fix the issue.

Phase 7. VERIFICATION: Test your implementation thoroughly.
   7.1 Run your reproduction script to verify the fix works.
   7.2 Add edge cases to your test script to ensure comprehensive coverage.
   7.3 Run existing tests related to the modified code to ensure you haven't broken anything.

8. FINAL REVIEW: Carefully re-read the problem description and compare your changes with the base commit 027947bf91ff0dfac94f472ed1855cd49e3feb8d.
   8.1 Ensure you've fully addressed all requirements.
   8.2 Run any tests in the repository related to:
     8.2.1 The issue you are fixing
     8.2.2 The files you modified
     8.2.3 The functions you changed
   8.3 If any tests fail, revise your implementation until all tests pass

Be thorough in your exploration, testing, and reasoning. It's fine if your thinking process is lengthy - quality and completeness are more important than brevity.

Gold patch:
diff --git a/monai/transforms/intensity/array.py b/monai/transforms/intensity/array.py
--- a/monai/transforms/intensity/array.py
+++ b/monai/transforms/intensity/array.py
@@ -431,22 +431,19 @@ def __init__(
         self.coeff_range = coeff_range
         self.dtype = dtype
 
-    def _generate_random_field(
-        self,
-        spatial_shape: Tuple[int, ...],
-        rank: int,
-        degree: int,
-        coeff: Tuple[int, ...],
-    ):
+        self._coeff = [1.0]
+
+    def _generate_random_field(self, spatial_shape: Sequence[int], degree: int, coeff: Sequence[float]):
         """
         products of polynomials as bias field estimations
         """
+        rank = len(spatial_shape)
         coeff_mat = np.zeros((degree + 1,) * rank)
         coords = [np.linspace(-1.0, 1.0, dim, dtype=np.float32) for dim in spatial_shape]
         if rank == 2:
             coeff_mat[np.tril_indices(degree + 1)] = coeff
-            field = np.polynomial.legendre.leggrid2d(coords[0], coords[1], coeff_mat)
-        elif rank == 3:
+            return np.polynomial.legendre.leggrid2d(coords[0], coords[1], coeff_mat)
+        if rank == 3:
             pts: List[List[int]] = [[0, 0, 0]]
             for i in range(degree + 1):
                 for j in range(degree + 1 - i):
@@ -456,16 +453,12 @@ def _generate_random_field(
                 pts = pts[1:]
             np_pts = np.stack(pts)
             coeff_mat[np_pts[:, 0], np_pts[:, 1], np_pts[:, 2]] = coeff
-            field = np.polynomial.legendre.leggrid3d(coords[0], coords[1], coords[2], coeff_mat)
-        else:
-            raise NotImplementedError("only supports 2D or 3D fields")
-        return field
+            return np.polynomial.legendre.leggrid3d(coords[0], coords[1], coords[2], coeff_mat)
+        raise NotImplementedError("only supports 2D or 3D fields")
 
     def randomize(self, data: np.ndarray) -> None:
         super().randomize(None)
-        self.spatial_shape = data.shape[1:]
-        self.rank = len(self.spatial_shape)
-        n_coeff = int(np.prod([(self.degree + k) / k for k in range(1, self.rank + 1)]))
+        n_coeff = int(np.prod([(self.degree + k) / k for k in range(1, len(data.shape[1:]) + 1)]))
         self._coeff = self.R.uniform(*self.coeff_range, n_coeff).tolist()
 
     def __call__(self, img: np.ndarray):
@@ -475,17 +468,15 @@ def __call__(self, img: np.ndarray):
         self.randomize(data=img)
         if not self._do_transform:
             return img
-        num_channels = img.shape[0]
+        num_channels, *spatial_shape = img.shape
         _bias_fields = np.stack(
             [
-                self._generate_random_field(
-                    spatial_shape=self.spatial_shape, rank=self.rank, degree=self.degree, coeff=self._coeff
-                )
+                self._generate_random_field(spatial_shape=spatial_shape, degree=self.degree, coeff=self._coeff)
                 for _ in range(num_channels)
             ],
             axis=0,
         )
-        return (img * _bias_fields).astype(self.dtype)
+        return (img * np.exp(_bias_fields)).astype(self.dtype)
 
 
 class NormalizeIntensity(Transform):


Test patch:
diff --git a/tests/test_random_bias_field.py b/tests/test_random_bias_field.py
--- a/tests/test_random_bias_field.py
+++ b/tests/test_random_bias_field.py
@@ -18,17 +18,12 @@
 
 TEST_CASES_2D = [{}, (3, 32, 32)]
 TEST_CASES_3D = [{}, (3, 32, 32, 32)]
-TEST_CASES_2D_ZERO_RANGE = [{"coeff_range": (0.0, 0.0)}, (3, 32, 32)]
-TEST_CASES_2D_ONES = [{"coeff_range": (1.0, 1.0)}, np.asarray([[[2, -2], [2, 10]]])]
+TEST_CASES_2D_ZERO_RANGE = [{"coeff_range": (0.0, 0.0)}, (2, 3, 3)]
+TEST_CASES_2D_ONES = [{"coeff_range": (1.0, 1.0)}, np.asarray([[[7.389056, 0.1353353], [7.389056, 22026.46]]])]
 
 
 class TestRandBiasField(unittest.TestCase):
-    @parameterized.expand(
-        [
-            TEST_CASES_2D,
-            TEST_CASES_3D,
-        ]
-    )
+    @parameterized.expand([TEST_CASES_2D, TEST_CASES_3D])
     def test_output_shape(self, class_args, img_shape):
         for degree in [1, 2, 3]:
             bias_field = RandBiasField(degree=degree, **class_args)
@@ -44,16 +39,16 @@ def test_output_shape(self, class_args, img_shape):
     @parameterized.expand([TEST_CASES_2D_ZERO_RANGE])
     def test_zero_range(self, class_args, img_shape):
         bias_field = RandBiasField(**class_args)
-        img = np.random.rand(*img_shape)
+        img = np.ones(img_shape)
         output = bias_field(img)
-        np.testing.assert_equal(output, np.zeros(img_shape))
+        np.testing.assert_allclose(output, np.ones(img_shape), rtol=1e-3)
 
     @parameterized.expand([TEST_CASES_2D_ONES])
     def test_one_range_input(self, class_args, expected):
         bias_field = RandBiasField(**class_args)
         img = np.ones([1, 2, 2])
         output = bias_field(img)
-        np.testing.assert_equal(output, expected.astype(bias_field.dtype))
+        np.testing.assert_allclose(output, expected.astype(bias_field.dtype), rtol=1e-3)
 
     def test_zero_prob(self):
         bias_field = RandBiasField(prob=0.0)
diff --git a/tests/test_random_bias_fieldd.py b/tests/test_random_bias_fieldd.py
--- a/tests/test_random_bias_fieldd.py
+++ b/tests/test_random_bias_fieldd.py
@@ -19,16 +19,14 @@
 TEST_CASES_2D = [{}, (3, 32, 32)]
 TEST_CASES_3D = [{}, (3, 32, 32, 32)]
 TEST_CASES_2D_ZERO_RANGE = [{"coeff_range": (0.0, 0.0)}, (3, 32, 32)]
-TEST_CASES_2D_ONES = [{"coeff_range": (1.0, 1.0)}, np.asarray([[[2, -2], [2, 10]]])]
+TEST_CASES_2D_ONES = [
+    {"coeff_range": (1.0, 1.0)},
+    np.asarray([[[7.3890562e00, 1.3533528e-01], [7.3890562e00, 2.2026465e04]]]),
+]
 
 
 class TestRandBiasFieldd(unittest.TestCase):
-    @parameterized.expand(
-        [
-            TEST_CASES_2D,
-            TEST_CASES_3D,
-        ]
-    )
+    @parameterized.expand([TEST_CASES_2D, TEST_CASES_3D])
     def test_output_shape(self, class_args, img_shape):
         key = "img"
         bias_field = RandBiasFieldd(keys=[key], **class_args)
@@ -41,9 +39,9 @@ def test_output_shape(self, class_args, img_shape):
     def test_zero_range(self, class_args, img_shape):
         key = "img"
         bias_field = RandBiasFieldd(keys=[key], **class_args)
-        img = np.random.rand(*img_shape)
+        img = np.ones(img_shape)
         output = bias_field({key: img})
-        np.testing.assert_equal(output[key], np.zeros(img_shape))
+        np.testing.assert_allclose(output[key], np.ones(img_shape))
 
     @parameterized.expand([TEST_CASES_2D_ONES])
     def test_one_range_input(self, class_args, expected):
@@ -51,7 +49,7 @@ def test_one_range_input(self, class_args, expected):
         bias_field = RandBiasFieldd(keys=[key], **class_args)
         img = np.ones([1, 2, 2])
         output = bias_field({key: img})
-        np.testing.assert_equal(output[key], expected.astype(bias_field.rand_bias_field.dtype))
+        np.testing.assert_allclose(output[key], expected.astype(bias_field.rand_bias_field.dtype), rtol=1e-3)
 
     def test_zero_prob(self):
         key = "img"