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Calculating the singular values of one or more matrices using NumPy

Overview:

  • The function linalg.svdvals() calculates the singular values of one or more matrices and returns the results as an ndarray.
  • The returned ndarray excludes the orthogonal matrices U, V obtained from the factorization the array A using Singular Value Decomposition.

Example:

# Example Python program that finds the singular values of
# multiple matrices in one go using the function linalg.svdvals()
import numpy

# Create an upper triangular matrix
elems     = numpy.arange(1, 18, 2)
upperTriangular  = elems.reshape(3, 3)

upperTriangular[1][0] = 0
upperTriangular[2][0] = 0
upperTriangular[2][1] = 0

print("Matrix 1:")
print(upperTriangular)

# Create a lower triangular matrix
elems     = numpy.arange(2, 19, 2)
lowerTriangular  = elems.reshape(3, 3)

lowerTriangular[0][1] = 0
lowerTriangular[0][2] = 0
lowerTriangular[1][2] = 0

print("Matrix 2:")
print(lowerTriangular)

svdValues = numpy.linalg.svdvals([upperTriangular, lowerTriangular])

print("Singular values of matrix 1:")
print(svdValues[0])

print("Singular values of matrix 2:")
print(svdValues[1])

Output:

Matrix 1:
[[ 1  3  5]
 [ 0  9 11]
 [ 0  0 17]]
Matrix 2:
[[ 2  0  0]
 [ 8 10  0]
 [14 16 18]]
Singular values of matrix 1:
[21.66412661  7.46801882  0.94568139]
Singular values of matrix 2:
[29.67443546  7.81125888  1.55309851]

 


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