Function cusolverDnCsytrf 

pub unsafe extern "C" fn cusolverDnCsytrf(
    handle: cusolverDnHandle_t,
    uplo: cublasFillMode_t,
    n: c_int,
    A: *mut cuComplex,
    lda: c_int,
    ipiv: *mut c_int,
    work: *mut cuComplex,
    lwork: c_int,
    info: *mut c_int,
) -> cusolverStatus_t

These helper functions calculate the size of the needed buffers.

The S and D data types are real valued single and double precision, respectively.

The C and Z data types are complex valued single and double precision, respectively.

This function computes the factorization of a symmetric indefinite matrix using the Bunch-Kaufman diagonal pivoting.

A is a $n \times n$ symmetric matrix, only lower or upper part is meaningful. The input parameter uplo indicates which part of the matrix is used. If devIpiv is null, no pivoting is performed, which is not numerically stable.

If input parameter uplo is cublasFillMode_t::CUBLAS_FILL_MODE_LOWER, only lower triangular part of A is processed, and replaced by lower triangular factor L and block diagonal matrix D. Each block of D is either 1x1 or 2x2 block, depending on pivoting. $$ P\*A\*P^{T} = L\*D\*L^{T} $$

If input parameter uplo is cublasFillMode_t::CUBLAS_FILL_MODE_UPPER, only upper triangular part of A is processed, and replaced by upper triangular factor U and block diagonal matrix D. $$ P\*A\*P^{T} = U\*D\*U^{T} $$

The user has to provide working space which is pointed by input parameter work. The input parameter lwork is size of the working space, and it is returned by sytrf_bufferSize(). Please note that the size in bytes of the working space is equal to sizeof(<type>) * lwork. When no pivoting is performed, the other triangular part of the input matrix A is used as workspace.

If Bunch-Kaufman factorization failed, i.e. A is singular. The output parameter devInfo = i would indicate D(i,i)=0.

If output parameter devInfo = -i (less than zero), the i-th parameter is wrong (not counting handle).

The output parameter devIpiv contains pivoting sequence. If devIpiv(i) = k > 0, D(i,i) is 1x1 block, and i-th row/column of A is interchanged with k-th row/column of A. If uplo is cublasFillMode_t::CUBLAS_FILL_MODE_UPPER and devIpiv(i-1) = devIpiv(i) = -m < 0, D(i-1:i,i-1:i) is a 2x2 block, and (i-1)-th row/column is interchanged with m-th row/column. If uplo is cublasFillMode_t::CUBLAS_FILL_MODE_LOWER and devIpiv(i+1) = devIpiv(i) = -m < 0, D(i:i+1,i:i+1) is a 2x2 block, and (i+1)-th row/column is interchanged with m-th row/column.