# Which linear function of SciPy is used to solve Hermitian positive-definite banded matrix equation?

The linear function named scipy.linalg.solveh_banded is used to solve Hermitian positive-definite banded matrix equations. The form of this function is as follows −

scipy.linalg.solveh_banded(ab, b, overwrite_ab=False, overwrite_b=False, lower=False, check_finite=True)

This linear function will solve the equation ax = b for x where a is Hermitian positivedefinite banded matrix.

The banded matrix a is stored in ab in lower or upper diagonal ordered form as follows −

ab[u + i - j, j] == a[i,j] (if upper form; i<=j)
ab[ i - j, j] == a[i,j] (if lower form; i >= j)

The example of ab in the upper form is given as follows −

*    *    a02   a13   a24  a35
*    a01  a12   a23   a34  a45
a00 a11 a22 a33 a44    a55

Here the shape of a is (6, 6) and u =2.

The example of ab in the lower form is given as follows−

a00 a11 a22 a33 a44 a55
a10  a21 a32 a43 a54  *
a20 a31 a42 a53 *    *

Here the shape of a is (6, 6) and u =2.

## Parameters

Below are given the parameters of the function scipy.linalg.solveh_banded() −

• ab− ( u + 1, M) array_like

This parameter represents the banded matrix.

• b− (M,) or (M, K)array_like

This parameter represents the right-hand side.

• Overwrite_ab− bool, optional

This parameter is used to discard the data in banded matrix ab. It may enhance the performance of matrices.

• Overwrite_b− bool, optional

This parameter is used to discard the data in b. It may enhance the performance of matrices

• lower− bool, optional

This parameter is used to check if the banded matrix is in lower form. The default is the upper form of a banded matrix.

• check_finite− bool, optional

This parameter is used to check whether the input matrices contain only finite numbers or not. We may get some performance gain after disabling it. It may result in problems if the inputs do not contain infinites.

## Returns

• x− (M,) or (M, K) ndarray

It returns the solution of the banded matrix equation ax = b. The shape of the output will depend on the shape of b.

Updated on: 24-Nov-2021

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