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# scipy.linalg.solveh_banded

`scipy.linalg.``solveh_banded`(ab, b, overwrite_ab=0, overwrite_b=0, lower=0)

  Solve equation a x = b. a is Hermitian positive-definite banded matrix.

  The matrix a is stored in ab either in lower diagonal or upper diagonal ordered form:

  > 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)

  Example of ab (shape of a is (6,6), u=2):

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

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

  Cells marked with * are not used.

  Parameters: | ab : array, shape (M, u + 1) Banded matrix b : array, shape (M,) or (M, K) Right-hand side overwrite_ab : boolean Discard data in ab (may enhance performance) overwrite_b : boolean Discard data in b (may enhance performance) lower : boolean Is the matrix in the lower form. (Default is upper form)
  Returns: | c : array, shape (M, u+1) Cholesky factorization of a, in the same banded format as ab x : array, shape (M,) or (M, K) The solution to the system a x = b

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