Function cusolverDnXsygvd 

pub unsafe extern "C" fn cusolverDnXsygvd(
    handle: cusolverDnHandle_t,
    params: cusolverDnParams_t,
    itype: cusolverEigType_t,
    jobz: cusolverEigMode_t,
    uplo: cublasFillMode_t,
    n: i64,
    dataTypeA: cudaDataType,
    d_A: *mut c_void,
    lda: i64,
    dataTypeB: cudaDataType,
    d_B: *mut c_void,
    ldb: i64,
    dataTypeW: cudaDataType,
    d_W: *mut c_void,
    computeType: cudaDataType,
    bufferOnDevice: *mut c_void,
    workspaceInBytesOnDevice: size_t,
    bufferOnHost: *mut c_void,
    workspaceInBytesOnHost: size_t,
    d_info: *mut c_int,
) -> cusolverStatus_t

The helper functions below can calculate the sizes needed for pre-allocated buffer.

The following routine computes all the eigenvalues, and optionally, the eigenvectors of a generalized symmetric (Hermitian) definite eigenproblem.

The generalized symmetric (Hermitian) definite eigenvalue problem is: $$ \operatorname{eig}(A,B) = \begin{cases} A * V = B * V * \Lambda & \text{if } itype = \text{CUSOLVER_EIG_TYPE_1} \ A * B * V = V * \Lambda & \text{if } itype = \text{CUSOLVER_EIG_TYPE_2} \ B * A * V = V * \Lambda & \text{if } itype = \text{CUSOLVER_EIG_TYPE_3} \end{cases} $$

where the matrix A and B are $n \times n$; A is symmetric/Hermitian and B is symmetric/Hermitian positive definite. The eigenvalues of (A, B) are computed and stored in the W vector in ascending order. V is an $n \times n$ orthogonal matrix. The eigenvectors are normalized as follows:v: $$ \begin{cases} V^H * B * V = I & \text{if } itype = \text{CUSOLVER_EIG_TYPE_1 or CUSOLVER_EIG_TYPE_2} \ V^H * \operatorname{inv}(B) * V = I & \text{if } itype = \text{CUSOLVER_EIG_TYPE_3} \end{cases} $$

The user has to provide device and host working spaces which are pointed by input parameters bufferOnDevice and bufferOnHost. The input parameters workspaceInBytesOnDevice (and workspaceInBytesOnHost) is size in bytes of the device (and host) working space, and it is returned by cusolverDnXsygvd_bufferSize.

If output parameter info = -i (less than zero), the i-th parameter is wrong (not counting handle). If info = i (i > 0 and i<=n) and jobz = cusolverEigMode_t::CUSOLVER_EIG_MODE_NOVECTOR, i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. If info = n + i (i > 0), then the leading minor of order i of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.

If jobz = cusolverEigMode_t::CUSOLVER_EIG_MODE_VECTOR, A contains the orthonormal eigenvectors of the matrix A. The eigenvectors are computed by a divide and conquer algorithm.

Currently, cusolverDnXsygvd supports only the default algorithm.

Algorithms supported by cusolverDnXsygvd

cusolverAlgMode_t::CUSOLVER_ALG_0 or NULL	Default algorithm.

List of input arguments for cusolverDnXsygvd_bufferSize and cusolverDnXsygvd:

The generic API has four different data types, dataTypeA is data type of the matrix A, dataTypeB is data type of the matrix B, dataTypeW is data type of the matrix W and computeType is compute type of the operation. cusolverDnXsygvd only supports the following four combinations.

Valid combination of data type and compute type

DataTypeA	DataTypeB	DataTypeW	ComputeType	Meaning
CUDA_R_32F	CUDA_R_32F	CUDA_R_32F	CUDA_R_32F	SSYGVD
CUDA_R_64F	CUDA_R_64F	CUDA_R_64F	CUDA_R_64F	DSYGVD
CUDA_C_32F	CUDA_C_32F	CUDA_R_32F	CUDA_C_32F	CHEGVD
CUDA_C_64F	CUDA_C_64F	CUDA_R_64F	CUDA_C_64F	ZHEGVD

Parameters

• handle: Handle to the cuSolverDN library context.
• params: Structure with information collected by cusolverDnSetAdvOptions.
• itype: Specifies the problem type to be solved: * itype=cusolverEigType_t::CUSOLVER_EIG_TYPE_1: A*x = (lambda)*B*x. * itype=cusolverEigType_t::CUSOLVER_EIG_TYPE_2: A*B*x = (lambda)*x. * itype=cusolverEigType_t::CUSOLVER_EIG_TYPE_3: B*A*x = (lambda)*x.
• jobz: Specifies options to either compute eigenvalue only or compute eigen-pair: jobz = cusolverEigMode_t::CUSOLVER_EIG_MODE_NOVECTOR: Compute eigenvalues only; jobz = cusolverEigMode_t::CUSOLVER_EIG_MODE_VECTOR: Compute eigenvalues and eigenvectors.
• uplo: Specifies which part of A is stored. uplo = cublasFillMode_t::CUBLAS_FILL_MODE_LOWER: Lower triangle of A is stored. uplo = cublasFillMode_t::CUBLAS_FILL_MODE_UPPER: Upper triangle of A is stored.
• n: Number of rows (or columns) of matrix A.
• dataTypeA: Data type of array A.
• lda: Leading dimension of two-dimensional array used to store matrix A.
• dataTypeB: Data type of array B.
• ldb: Leading dimension of two-dimensional array used to store matrix B.
• dataTypeW: Data type of array W.
• computeType: Data type of computation.
• bufferOnDevice: Device workspace. Array of type void of size workspaceInBytesOnDevice bytes.
• workspaceInBytesOnDevice: Size in bytes of bufferOnDevice, returned by cusolverDnXsygvd_bufferSize.
• bufferOnHost: Host workspace. Array of type void of size workspaceInBytesOnHost bytes.
• workspaceInBytesOnHost: Size in bytes of bufferOnHost, returned by cusolverDnXsygvd_bufferSize.

Return value

• cusolverStatus_t::CUSOLVER_STATUS_INTERNAL_ERROR: An internal operation failed.
• cusolverStatus_t::CUSOLVER_STATUS_INVALID_VALUE: Invalid parameters were passed (n<0, or lda<max(1,n), or ldb<max(1,n), or itype is not 1, 2 or 3, or jobz is not cusolverEigMode_t::CUSOLVER_EIG_MODE_NOVECTOR or cusolverEigMode_t::CUSOLVER_EIG_MODE_VECTOR, or uplo is not cublasFillMode_t::CUBLAS_FILL_MODE_LOWER or cublasFillMode_t::CUBLAS_FILL_MODE_UPPER), or the combination of dataType{A,B,C} and computeType are not supported.
• cusolverStatus_t::CUSOLVER_STATUS_NOT_INITIALIZED: The library was not initialized.
• cusolverStatus_t::CUSOLVER_STATUS_SUCCESS: The operation completed successfully.