Python | Numpy np.lagvander3d() method

np.lagvander3d() method is used to returns the Vandermonde matrix of degree deg and sample points x, y and z.

Syntax : np.lagvander3d(x, y, z, deg)
Parameters:
x, y, z :[ array_like ] Array of points. The dtype is converted to float64 or complex128 depending on whether any of the elements are complex. If x is scalar it is converted to a 1-D array.
deg :[int] Degree of the resulting matrix.

Return : Return the Vandermonde matrix.



Example #1 :
In this example we can see that by using np.lagvander3d() method, we are able to get the pseudo-vandermonde matrix using this method.

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# import numpy
import numpy as np
import numpy.polynomial.laguerre as geek
  
# using np.lagvander3d() method
ans = geek.lagvander3d((1, 3, 5), (2, 4, 6), (1, 2, 3), [2, 2, 2])
  
print(ans)

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Output :

[[ 1. 0. -0.5 -1. -0. 0.5 -1. -0. 0.5 0. 0.
-0. -0. -0. 0. -0. -0. 0. -0.5 -0. 0.25
0.5 0. -0.25 0.5 0. -0.25]
[ 1. -1. -1. -3. 3. 3. 1. -1. -1. -2. 2.
2. 6. -6. -6. -2. 2. 2. -0.5 0.5 0.5
1.5 -1.5 -1.5 -0.5 0.5 0.5 ]
[ 1. -2. -0.5 -5. 10. 2.5 7. -14. -3.5 -4. 8.
2. 20. -40. -10. -28. 56. 14. 3.5 -7. -1.75
-17.5 35. 8.75 24.5 -49. -12.25]]

Example #2 :

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# import numpy
import numpy as np
import numpy.polynomial.laguerre as geek
  
ans = geek.lagvander3d((1, 2), (3, 4), (5, 6), [3, 3, 3])
  
print(ans)

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Output :

[[ 1. -4. 3.5 2.66666667 -2. 8.
-7. -5.33333333 -0.5 2. -1.75 -1.33333333
1. -4. 3.5 2.66666667 0. -0.
0. 0. -0. 0. -0. -0.
-0. 0. -0. -0. 0. -0.
0. 0. -0.5 2. -1.75 -1.33333333
1. -4. 3.5 2.66666667 0.25 -1.
0.875 0.66666667 -0.5 2. -1.75 -1.33333333
-0.66666667 2.66666667 -2.33333333 -1.77777778 1.33333333
-5.33333333 4.66666667 3.55555556 0.33333333 -1.33333333
1.16666667 0.88888889 -0.66666667 2.66666667 -2.33333333
-1.77777778]
[ 1. -5. 7. 1. -3. 15.
-21. -3. 1. -5. 7. 1.
2.33333333 -11.66666667 16.33333333 2.33333333 -1. 5.
-7. -1. 3. -15. 21. 3.
-1. 5. -7. -1. -2.33333333
11.66666667 -16.33333333 -2.33333333 -1. 5. -7.
-1. 3. -15. 21. 3. -1.
5. -7. -1. -2.33333333 11.66666667
-16.33333333 -2.33333333 -0.33333333 1.66666667 -2.33333333
-0.33333333 1. -5. 7. 1. -0.33333333
1.66666667 -2.33333333 -0.33333333 -0.77777778 3.88888889
-5.44444444 -0.77777778]]



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