Computes the BunchKaufman factorization of a complex Hermitian matrix using packed storage.
Syntax

lapack_int LAPACKE_chptrf (int matrix_layout , char uplo , lapack_int n , lapack_complex_float * ap , lapack_int * ipiv );
lapack_int LAPACKE_zhptrf (int matrix_layout , char uplo , lapack_int n , lapack_complex_double * ap , lapack_int * ipiv );
Include Files
 mkl.h
Description
The routine computes the factorization of a complex Hermitian packed matrix A using the BunchKaufman diagonal pivoting method:

if uplo='U', A = U*D*U^{H}

if uplo='L', A = L*D*L^{H},
where A is the input matrix, U and L are products of permutation and triangular matrices with unit diagonal (upper triangular for U and lower triangular for L), and D is a Hermitian blockdiagonal matrix with 1by1 and 2by2 diagonal blocks. U and L have 2by2 unit diagonal blocks corresponding to the 2by2 blocks of D.
Note
This routine supports the Progress Routine feature. See Progress Function for details.
Input Parameters
matrix_layout 
Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR). 
uplo 
Must be 'U' or 'L'. Indicates whether the upper or lower triangular part of A is packed and how A is factored: If uplo = 'U', the array ap stores the upper triangular part of the matrix A, and A is factored as U*D*U^{H}. If uplo = 'L', the array ap stores the lower triangular part of the matrix A, and A is factored as L*D*L^{H}. 
n 
The order of matrix A; n≥ 0. 
ap 
Array, size at least max(1, n(n+1)/2). The array ap contains the upper or the lower triangular part of the matrix A (as specified by uplo) in packed storage (see Matrix Storage Schemes). 
Output Parameters
ap 
The upper or lower triangle of A (as specified by uplo) is overwritten by details of the blockdiagonal matrix D and the multipliers used to obtain the factor U (or L). 
ipiv 
Array, size at least max(1, n). Contains details of the interchanges and the block structure of D. If ipiv[i1] = k >0, then d_{ii} is a 1by1 block, and the ith row and column of A was interchanged with the kth row and column. If uplo = 'U' and ipiv[i] =ipiv[i1] = m < 0, then D has a 2by2 block in rows/columns i and i+1, and ith row and column of A was interchanged with the mth row and column. If uplo = 'L' and ipiv[i] =ipiv[i1] = m < 0, then D has a 2by2 block in rows/columns i and i+1, and (i+1)th row and column of A was interchanged with the mth row and column. 
Return Values
This function returns a value info.
If info = 0, the execution is successful.
If info = i, parameter i had an illegal value.
If info = i, d_{ii} is 0. The factorization has been completed, but D is exactly singular. Division by 0 will occur if you use D for solving a system of linear equations.
Application Notes
The 2by2 unit diagonal blocks and the unit diagonal elements of U and L are not stored. The remaining elements of U and L are stored in the array ap, but additional row interchanges are required to recover U or L explicitly (which is seldom necessary).
If ipiv[i1] = i for all i = 1...n, then all offdiagonal elements of U (L) are stored explicitly in the corresponding elements of the array a.
If uplo = 'U', the computed factors U and D are the exact factors of a perturbed matrix A + E, where
E ≤ c(n)ε PUDU^{T}P^{T}
c(n) is a modest linear function of n, and ε is the machine precision.
A similar estimate holds for the computed L and D when uplo = 'L'.
The total number of floatingpoint operations is approximately (4/3)n^{3}.
After calling this routine, you can call the following routines:
to solve A*X = B 

to estimate the condition number of A 

to compute the inverse of A. 