## numpy.isclose¶

Returns a boolean array where two arrays are element-wise equal within a tolerance.

The tolerance values are positive, typically very small numbers. The relative difference (*rtol* * abs(*b*)) and the absolute difference *atol* are added together to compare against the absolute difference between *a* and *b*.

**a, b** : array_like

Input arrays to compare.

**rtol** : float

The relative tolerance parameter (see Notes).

**atol** : float

The absolute tolerance parameter (see Notes).

**equal_nan** : bool

Whether to compare NaN’s as equal. If True, NaN’s in *a* will be considered equal to NaN’s in *b* in the output array.

**y** : array_like

Returns a boolean array of where *a* and *b* are equal within the given tolerance. If both *a* and *b* are scalars, returns a single boolean value.

New in version 1.7.0.

For finite values, isclose uses the following equation to test whether two floating point values are equivalent.

The above equation is not symmetric in *a* and *b*, so that *isclose(a, b)* might be different from *isclose(b, a)* in some rare cases.

## numpy.isclose

Returns a boolean array where two arrays are element-wise equal within a tolerance.

The tolerance values are positive, typically very small numbers. The relative difference ( rtol * abs( b )) and the absolute difference atol are added together to compare against the absolute difference between a and b .

**a, b** : array_like

Input arrays to compare.

**rtol** : float

The relative tolerance parameter (see Notes).

**atol** : float

The absolute tolerance parameter (see Notes).

**equal_nan** : bool

Whether to compare NaN’s as equal. If True, NaN’s in a will be considered equal to NaN’s in b in the output array.

**y** : array_like

Returns a boolean array of where a and b are equal within the given tolerance. If both a and b are scalars, returns a single boolean value.

##### Notes

New in version 1.7.0.

For finite values, isclose uses the following equation to test whether two floating point values are equivalent.

absolute( a — b ) <= ( atol + rtol * absolute( b ))

The above equation is not symmetric in a and b , so that isclose(a, b) might be different from isclose(b, a) in some rare cases.

## isclose function in numpy is different from math

I have some code that performs a gradient check. Recently, I changed

the comparison function from math.isclose to numpy.isclose to more consistently use numpy, and to my surprise, some of my assertions started to fail.

I have reduced the example to the following code

Apparently math.isclose and numpy.isclose are really different.

Which one should I use, and why?

Python: 3.6.3, Numpy: 1.13.3.

It has been discussed just recently on GitHub.

The formulas used in math and

numpy are indeed different:

As you can see, numpy version is asymmetric (and it’s clearly stated in the doc).

On top of that, atol may interfere with the rtol , causing the false equality, like in your case.

## Numpy – Check If a Matrix is Invertible

In this tutorial, we will look at how to check if a numpy matrix (a 2d numpy array) is invertible or not with the help of some examples.

#### When is a matrix invertible?

A square matrix, for example, M is said to be invertible, if there exists a matrix N such that, MN = NM = I where I is an identity matrix. The following image shows an invertible matrix.

Alternatively, we can say that N is equal to the inverse of the matrix M . That is, a matrix is invertible if you can take its inverse.

A square matrix that is not invertible is called a singular matrix.

### How to check if a matrix is invertible in Numpy?

To check if a matrix is invertible or not in Numpy, check if it has a non-zero determinant.

If a matrix has a non-zero determinant (the determinant is not zero), we can say that the matrix is invertible. Use the numpy.linalg.det() function to compute the determinant of a matrix. The following is the syntax –

Let’s now look at the above method with the help of some examples. First, we will create two matrices that we will use throughout this tutorial, one invertible and the other non-invertible.

Here, the matrix ar1 is invertible and the matrix ar2 is non-invertible.

#### Example – Check if the determinant is non-zero

In this method, we calculate the determinant of the matrix using the numpy.linalg.det() function and check whether it is non-zero or not. If the determinant is non-zero, we say the matrix is invertible.

Let’s apply this method to the matrices created above.

We get True for both matrices, which is **not the correct answer**. The matrix ar1 is invertible, so the first True is okay, but the matrix ar2 is singular and this method should give False but we get True .

Why is this happening? Let’s print out the determinant for ar2 .

We get a very small value which is not exactly zero.

To work around this, you can use the numpy.isclose() function which lets you define a tolerance to determine how close two values need to be to be considered equal. By default, the tolerance is set to 1e-05, which means that two values are considered equal if they are within 0.00001 of each other. You can adjust this tolerance by passing a different value to the rtol (relative tolerance) or atol (absolute tolerance) parameters of numpy.isclose() .

Using the numpy.isclose() function to compare the results from numpy.linalg.det() to zero helps resolve the above issue.

We now get the correct answer. In the above example, we first check whether the determinant is zero (very close to zero) or not, if it isn’t, we say that the matric is invertible.

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