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To evaluate a 3D Laguerre series at points (x, y, z), use the polynomial.laguerre.lagval3d() method in Python Numpy. The method returns the values of the multidimensional polynomial on points formed with triples of corresponding values from x, y, and z..If c has fewer than 3 dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape. The 1st parameter is x, y, z. The three dimensional series is evaluated at the points (x, y, z), where x, y, and z must have the same shape. If any of x, ... Read More
To evaluate a 2D Laguerre series at points x, use the polynomial.laguerre.lagval2d() method in Python Numpy. The method returns the values of the two dimensional polynomial at points formed with pairs of corresponding values from x and y.The 1st parameter is x, y. The two dimensional series is evaluated at the points (x, y), where x and y must have the same shape. If x or y is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn’t an ndarray it is treated as a scalar.The 2nd parameter, C, is ... Read More
To generate a Vandermonde matrix of the Hermite polynomial, use the chebyshev.hermvander() in Python Numpy. The method returns the pseudo-Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1, ), where The last index is the degree of the corresponding Hermite polynomial. The dtype will be the same as the converted x.The parameter, x returns an 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. The parameter, deg is the degree of the resulting ... Read More
To generate a Vandermonde matrix of the Hermite polynomial, use the hermite.hermvander() in Python Numpy. The method returns the pseudo-Vandermonde matrix. The shape of the returned matrix is x.shape + (deg + 1, ), where The last index is the degree of the corresponding Hermite polynomial. The dtype will be the same as the converted x.The parameter, x returns an 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. The parameter, deg is the degree of the resulting ... Read More
To compute the roots of a Hermite series., use the hermite.hermroots() method in Python Numpy. The method returns an array of the roots of the series. If all the roots are real, then out is also real, otherwise it is complex. The parameter, c is a 1-D array of coefficients.The root estimates are obtained as the eigenvalues of the companion matrix, Roots far from the origin of the complex plane may have large errors due to the numerical instability of the series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value of ... Read More
Suppose we have two numbers n and k. Amal and Bimal are playing a game. The rules are simple. Amal draws n sticks in a row. After that the players take turns crossing out exactly k sticks from left or right in each turn. Amal starts the game. If there are less than k sticks on the paper before some turn, the game ends. Amal wins if he makes strictly more moves than Bimal. We have to find who will be the winner.So, if the input is like n = 10; k = 4, then the output will be Bimal. ... Read More
To compute the roots of a Hermite series., use the hermite.hermroots() method in Python Numpy. The method returns an Array of the roots of the series. If all the roots are real, then out is also real, otherwise it is complex. The parameter, c is a 1-D array of coefficients.The root estimates are obtained as the eigenvalues of the companion matrix, Roots far from the origin of the complex plane may have large errors due to the numerical instability of the series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value of ... Read More
To evaluate a Laguerre series at multi-dimensional array of points x, use the polynomial.laguerre.lagval() method in Python Numpy. The 1st parameter is x. If x is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, x or its elements must support addition and multiplication with themselves and with the elements of c.The 2nd parameter, C, an array of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If c is multidimensional the remaining indices enumerate multiple polynomials. In the two ... Read More
To evaluate a Laguerre series at array of points x, use the polynomial.laguerre.lagval() method in Python Numpy. The 1st parameter is x. If x is a list or tuple, it is converted to an ndarray, otherwise it is left unchanged and treated as a scalar. In either case, x or its elements must support addition and multiplication with themselves and with the elements of c.The 2nd parameter, C, an array of coefficients ordered so that the coefficients for terms of degree n are contained in c[n]. If c is multidimensional the remaining indices enumerate multiple polynomials. In the two dimensional ... Read More
Suppose we have an array A with n elements. We can perform these operations any number of times −Select any positive integer kSelect any position in the sequence and insert k into that positionSo, the sequence is changed, we proceed with this sequence in the next operation.We have to find minimum number of operations needed to satisfy the condition: A[i]