Function cusolverDnXsyevdx 

pub unsafe extern "C" fn cusolverDnXsyevdx(
    handle: cusolverDnHandle_t,
    params: cusolverDnParams_t,
    jobz: cusolverEigMode_t,
    range: cusolverEigRange_t,
    uplo: cublasFillMode_t,
    n: i64,
    dataTypeA: cudaDataType,
    A: *mut c_void,
    lda: i64,
    vl: *mut c_void,
    vu: *mut c_void,
    il: i64,
    iu: i64,
    meig64: *mut i64,
    dataTypeW: cudaDataType,
    W: *mut c_void,
    computeType: cudaDataType,
    bufferOnDevice: *mut c_void,
    workspaceInBytesOnDevice: size_t,
    bufferOnHost: *mut c_void,
    workspaceInBytesOnHost: size_t,
    info: *mut c_int,
) -> cusolverStatus_t

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

The following routine:

computes all or selection of the eigenvalues and optionally eigenvectors of a symmetric (Hermitian) $n \times n$ matrix A using the generic API interface. The standard symmetric eigenvalue problem is: $$ A\V = V\\Lambda $$

where Λ is a real n×h_meig diagonal matrix. V is an n×h_meig unitary matrix. h_meig is the number of eigenvalues/eigenvectors computed by the routine, h_meig is equal to n when the whole spectrum (e.g., range = cusolverEigRange_t::CUSOLVER_EIG_RANGE_ALL) is requested. The diagonal elements of Λ are the eigenvalues of A in ascending order.

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 cusolverDnXsyevdx_bufferSize.

If output parameter info = -i (less than zero), the i-th parameter is wrong (not counting handle). If info = i (greater than zero), i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.

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, cusolverDnXsyevdx supports only the default algorithm.

Please visit cuSOLVER Library Samples - Xsyevdx for a code example.

Algorithms supported by cusolverDnXsyevdx

cusolverAlgMode_t::CUSOLVER_ALG_0 or NULL	Default algorithm.

List of input arguments for cusolverDnXsyevdx_bufferSize and cusolverDnXsyevdx:

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

Valid combination of data type and compute type

DataTypeA	DataTypeW	ComputeType	Meaning
CUDA_R_32F	CUDA_R_32F	CUDA_R_32F	SSYEVDX
CUDA_R_64F	CUDA_R_64F	CUDA_R_64F	DSYEVDX
CUDA_C_32F	CUDA_R_32F	CUDA_C_32F	CHEEVDX
CUDA_C_64F	CUDA_R_64F	CUDA_C_64F	ZHEEVDX

Parameters

• handle: Handle to the cuSolverDN library context.
• params: Structure with information collected by cusolverDnSetAdvOptions.
• 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.
• range: Specifies options to which selection of eigenvalues and optionally eigenvectors that need to be computed: range = cusolverEigRange_t::CUSOLVER_EIG_RANGE_ALL: all eigenvalues/eigenvectors will be found, will becomes the classical syevd/heevd routine; range = cusolverEigRange_t::CUSOLVER_EIG_RANGE_V: all eigenvalues/eigenvectors in the half-open interval (vl,vu] will be found; range = cusolverEigRange_t::CUSOLVER_EIG_RANGE_I: the il-th through iu-th eigenvalues/eigenvectors will be found;.
• 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.
• A: Array of dimension lda * n with lda is not less than max(1,n). If uplo = cublasFillMode_t::CUBLAS_FILL_MODE_UPPER, the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A. If uplo = cublasFillMode_t::CUBLAS_FILL_MODE_LOWER, the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A. On exit, if jobz = cusolverEigMode_t::CUSOLVER_EIG_MODE_VECTOR, and info = 0, A contains the orthonormal eigenvectors of the matrix A. If jobz = cusolverEigMode_t::CUSOLVER_EIG_MODE_NOVECTOR, the contents of A are destroyed.
• lda: Leading dimension of two-dimensional array used to store matrix A.lda is not less than max(1,n).
• dataTypeW: Data type of array W.
• W: A real array of dimension n. The eigenvalue values of A, in ascending order, i.e., sorted so that W(i) <= W(i+1).
• computeType: Data type of computation.
• bufferOnDevice: Device workspace. Array of type void of size workspaceInBytesOnDevice bytes.
• workspaceInBytesOnDevice: Size in bytes of bufferOnDevice, returned by cusolverDnXsyevdx_bufferSize.
• bufferOnHost: Host workspace. Array of type void of size workspaceInBytesOnHost bytes.
• workspaceInBytesOnHost: Size in bytes of bufferOnHost, returned by cusolverDnXsyevdx_bufferSize.
• info: If info = 0, the operation is successful. if info = -i, the i-th parameter is wrong (not counting handle). If info = i (> 0), info indicates i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.

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 jobz is not cusolverEigMode_t::CUSOLVER_EIG_MODE_NOVECTOR or cusolverEigMode_t::CUSOLVER_EIG_MODE_VECTOR, or range is not cusolverEigRange_t::CUSOLVER_EIG_RANGE_ALL or cusolverEigRange_t::CUSOLVER_EIG_RANGE_V or cusolverEigRange_t::CUSOLVER_EIG_RANGE_I, or uplo is not cublasFillMode_t::CUBLAS_FILL_MODE_LOWER or cublasFillMode_t::CUBLAS_FILL_MODE_UPPER).
• cusolverStatus_t::CUSOLVER_STATUS_NOT_INITIALIZED: The library was not initialized.
• cusolverStatus_t::CUSOLVER_STATUS_SUCCESS: The operation completed successfully.