Function cusolverDnXsyevBatched 

pub unsafe extern "C" fn cusolverDnXsyevBatched(
    handle: cusolverDnHandle_t,
    params: cusolverDnParams_t,
    jobz: cusolverEigMode_t,
    uplo: cublasFillMode_t,
    n: i64,
    dataTypeA: cudaDataType,
    A: *mut c_void,
    lda: 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,
    batchSize: i64,
) -> cusolverStatus_t

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

The following routine:

computes eigenvalues and eigenvectors of a sequence of symmetric (Hermitian) $n \times n$ matrices: $$ A_j\V_j = V_j\\Lambda_j $$

where $\Lambda_j$ is a real $n \times n$ diagonal matrix. $V_j$ is an $n \times n$ unitary matrix. The diagonal elements of $\Lambda_j$ are the eigenvalues of $A_j$ in ascending order.

syevBatched performs an eigendecomposition on each matrix. It requires that all matrices are of the same size n and are packed in a contiguous way, $$ \begin{split}A = \begin{pmatrix} {A0} & {A1} & \cdots \\ \end{pmatrix}\end{split} $$

Each matrix is column-major with leading dimension lda, so the formula for random access is $A_{k}\operatorname{(i,j)} = {A\lbrack\ i\ +\ lda\*j\ +\ lda\*n\*k\rbrack}$.

The parameter W also contains the eigenvalues of each matrix in a contiguous way, $$ \begin{split}W = \begin{pmatrix} {W0} & {W1} & \cdots \\ \end{pmatrix}\end{split} $$

The formula for random access of W is $W_{k}\operatorname{(j)} = {W\lbrack\ j\ +\ n\*k\rbrack}$.

The user has to provide device and host working space which are pointed to by the input parameters bufferOnDevice and bufferOnHost. The input parameters workspaceInBytesOnDevice and workspaceInBytesOnHost denote the size in bytes of the device and host working space, and returned by cusolverDnXsyevBatched_bufferSize.

The output parameter info is an integer array of size batchSize. If the function returns cusolverStatus_t::CUSOLVER_STATUS_INVALID_VALUE, the first element info\[0\] = -i (less than zero) indicates the i-th parameter is wrong (not counting handle). Otherwise, if info\[i\] > 0, syevBatched does not converge on the i-th matrix.

If jobz = cusolverEigMode_t::CUSOLVER_EIG_MODE_VECTOR, $A_{j}$ contains the orthonormal eigenvectors of the matrix $A_{j}$.

Note that the problem size is limited by the condition nldabatchSize<=INT32_MAX primarily due to the current implementation constraints.

Algorithms supported by cusolverDnXsyevBatched

cusolverAlgMode_t::CUSOLVER_ALG_0 or NULL	Default. May switch between algorithms for best performance.
cusolverAlgMode_t::CUSOLVER_ALG_1	Uses a single algorithm for consistent accuracy over all n.

List of input arguments for cusolverDnXsyevBatched_bufferSize and cusolverDnXsyevBatched:

The generic API has three different types, dataTypeA is data type of the matrix A, dataTypeW is data type of the array W and computeType is compute type of the operation. cusolverDnXsyevBatched 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	SSYEVBATCHED
CUDA_R_64F	CUDA_R_64F	CUDA_R_64F	DSYEVBATCHED
CUDA_C_32F	CUDA_R_32F	CUDA_C_32F	CSYEVBATCHED
CUDA_C_64F	CUDA_R_64F	CUDA_C_64F	ZSYEVBATCHED

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.
• 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 * batchSize 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 Aj contains the upper triangular part of the matrix Aj. If uplo = cublasFillMode_t::CUBLAS_FILL_MODE_LOWER, the leading n-by-n lower triangular part of Aj contains the lower triangular part of the matrix Aj. On exit, if jobz = cusolverEigMode_t::CUSOLVER_EIG_MODE_VECTOR, and info\[j\] = 0, Aj contains the orthonormal eigenvectors of the matrix Aj. If jobz = cusolverEigMode_t::CUSOLVER_EIG_MODE_NOVECTOR, the contents of Aj are destroyed.
• lda: Leading dimension of two-dimensional array used to store matrix Aj.lda is not less than max(1,n).
• dataTypeW: Data type of array W.
• W: A real array of dimension n * batchSize. The eigenvalue values of Aj, in ascending order, i.e., sorted so that Wj(i) <= Wj(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 cusolverDnXsyevBatched_bufferSize.
• bufferOnHost: Host workspace. Array of type void of size workspaceInBytesOnHost bytes.
• workspaceInBytesOnHost: Size in bytes of bufferOnHost, returned by cusolverDnXsyevBatched_bufferSize.
• info: An integer array of dimension batchSize. If cusolverStatus_t::CUSOLVER_STATUS_INVALID_VALUE is returned, info\[0\] = -i (less than zero) indicates i-th parameter is wrong (not counting handle). Otherwise, if info\[i\] = 0, the operation is successful. If info\[i\] > 0, syevBatched does not converge on the i-th matrix.
• batchSize: Number of matrices. batchSize is not less than 1.

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 nldabatchSize>INT32_MAX, or lda<max(1,n), or jobz is not cusolverEigMode_t::CUSOLVER_EIG_MODE_NOVECTOR or uplo is not cublasFillMode_t::CUBLAS_FILL_MODE_LOWER or cublasFillMode_t::CUBLAS_FILL_MODE_UPPER or batchSize<0).
• cusolverStatus_t::CUSOLVER_STATUS_NOT_INITIALIZED: The library was not initialized.
• cusolverStatus_t::CUSOLVER_STATUS_SUCCESS: The operation completed successfully.