If most lists have too little or too little index, then the calling det() function can overflow or underflow. This process ( slogdet() ) is much more robust than such problems because it includes a shortcut logarithm rather than the shortcut itself.

**np.linalg.slogdet()**

Numpy linalg slogdet() function is used to calculate a sign and (natural) logarithm of an array’s determinant.

**Syntax**

numpy.linalg.slogdet(array)

**Parameters**

The slogdet() function takes a single parameter,

**array**: This is a 2D array, and it has to be square.

**Return Value**

The slogdet() function returns two values,

**sign: **

A number represents the sign of the determinant. For a real matrix, this is 1, 0, or -1. For a complex matrix, this is a complex number with absolute value 1 (i.e., it is on the unit circle), or else 0.

**logdet:**

This is the natural log of the absolute value of the determinant.

If the determinant is zero, then `sign` will be 0, and `**logdet**` will be

-Inf. In all cases, the determinant is equal to “sign * np.exp(logdet)“.

**Programming example**

**Program to calculate the determinant of one 2D array**

# Program to calculate determinant of one 2D array import numpy as np # creating a 2D array arr = np.array([[3, 4, 5], [7, 8, 6], [10, 11, 2]]) # printing the array print(arr) # calculating the slogdet (sign, logdet) = np.linalg.slogdet(arr) # Printing those values print("Sign is : ", sign) print("Logdet is :", logdet)

**Output**

[[ 3 4 5] [ 7 8 6] [10 11 2]] Sign is : 1.0 Logdet is : 2.944438979166441

**Explanation**

In this program, we have created a square matrix of size 3×3, and then we have printed it.

Then we have called slogdet() to get the sign and logdet of the array.

We can see that we got sign 1.

**Program to compute log-determinants for a stack of matrices.**

See the following code.

# Computing log-determinants for a stack of matrices import numpy as np # creating the stack matrices arr = np.array([[[2, 1], [3, 4]], [[3, 4], [5, 6]], [[7, 8], [9, 10]]]) # printing the values print("The array is:\n", arr) print("Shape of the array is: ", arr.shape) # Calculating the slogdet (sign, logdet) = np.linalg.slogdet(arr) # Printing those values print("Sign is : ", sign) print("Logdet is :", logdet)

**Output**

The array is: [[[ 2 1] [ 3 4]] [[ 3 4] [ 5 6]] [[ 7 8] [ 9 10]]] Shape of the array is: (3, 2, 2) Sign is : [ 1. -1. -1.] Logdet is : [1.60943791 0.69314718 0.69314718]

**Explanation**

In this program, we have created a square matrix of size 3×2, and then we have printed it.

Then we have called the **slogdet()** function to get the **sign** and **logdet** of the array.

We can see that we got a sign [ 1. -1. -1 ].