CeedBasis

int CeedBasisGetCollocatedGrad(CeedBasis basis, CeedScalar *collo_grad_1d)

Return collocated gradient matrix.

Backend Developer Functions

Parameters:

• basis – [in] CeedBasis

• collo_grad_1d – [out] Row-major (Q_1d * Q_1d) matrix expressing derivatives of basis functions at quadrature points

Returns:

An error code: 0 - success, otherwise - failure

int CeedBasisGetChebyshevInterp1D(CeedBasis basis, CeedScalar *chebyshev_interp_1d)

Return 1D interpolation matrix to Chebyshev polynomial coefficients on quadrature space.

Backend Developer Functions

Parameters:

• basis – [in] CeedBasis

• chebyshev_interp_1d – [out] Row-major (P_1d * Q_1d) matrix interpolating from basis nodes to Chebyshev polynomial coefficients

Returns:

An error code: 0 - success, otherwise - failure

int CeedBasisIsTensor(CeedBasis basis, bool *is_tensor)

Get tensor status for given CeedBasis

Backend Developer Functions

Parameters:

• basis – [in] CeedBasis

• is_tensor – [out] Variable to store tensor status

Returns:

An error code: 0 - success, otherwise - failure

int CeedBasisGetData(CeedBasis basis, void *data)

Get backend data of a CeedBasis

Backend Developer Functions

Parameters:

• basis – [in] CeedBasis

• data – [out] Variable to store data

Returns:

An error code: 0 - success, otherwise - failure

int CeedBasisSetData(CeedBasis basis, void *data)

Set backend data of a CeedBasis

Backend Developer Functions

Parameters:

• basis – [inout] CeedBasis

• data – [in] Data to set

Returns:

An error code: 0 - success, otherwise - failure

int CeedBasisReference(CeedBasis basis)

Increment the reference counter for a CeedBasis

Backend Developer Functions

Parameters:

• basis – [inout] CeedBasis to increment the reference counter

Returns:

An error code: 0 - success, otherwise - failure

int CeedBasisGetNumQuadratureComponents(CeedBasis basis, CeedEvalMode eval_mode, CeedInt *q_comp)

Get number of Q-vector components for given CeedBasis

Backend Developer Functions

Parameters:

• basis – [in] CeedBasis

• eval_mode – [in] CEED_EVAL_INTERP to use interpolated values, CEED_EVAL_GRAD to use gradients, CEED_EVAL_DIV to use divergence, CEED_EVAL_CURL to use curl

• q_comp – [out] Variable to store number of Q-vector components of basis

Returns:

An error code: 0 - success, otherwise - failure

int CeedBasisGetFlopsEstimate(CeedBasis basis, CeedTransposeMode t_mode, CeedEvalMode eval_mode, CeedSize *flops)

Estimate number of FLOPs required to apply CeedBasis in t_mode and eval_mode

Backend Developer Functions

Parameters:

• basis – [in] CeedBasis to estimate FLOPs for

• t_mode – [in] Apply basis or transpose

• eval_mode – [in] CeedEvalMode

• flops – [out] Address of variable to hold FLOPs estimate

int CeedBasisGetFESpace(CeedBasis basis, CeedFESpace *fe_space)

Get CeedFESpace for a CeedBasis

Backend Developer Functions

Parameters:

• basis – [in] CeedBasis

• fe_space – [out] Variable to store CeedFESpace

Returns:

An error code: 0 - success, otherwise - failure

int CeedBasisGetTopologyDimension(CeedElemTopology topo, CeedInt *dim)

Get dimension for given CeedElemTopology

Backend Developer Functions

Parameters:

• topo – [in] CeedElemTopology

• dim – [out] Variable to store dimension of topology

Returns:

An error code: 0 - success, otherwise - failure

int CeedBasisGetTensorContract(CeedBasis basis, CeedTensorContract *contract)

Get CeedTensorContract of a CeedBasis

Backend Developer Functions

Parameters:

• basis – [in] CeedBasis

• contract – [out] Variable to store CeedTensorContract

Returns:

An error code: 0 - success, otherwise - failure

int CeedBasisSetTensorContract(CeedBasis basis, CeedTensorContract contract)

Set CeedTensorContract of a CeedBasis

Backend Developer Functions

Parameters:

• basis – [inout] CeedBasis

• contract – [in] CeedTensorContract to set

Returns:

An error code: 0 - success, otherwise - failure

int CeedMatrixMatrixMultiply(Ceed ceed, const CeedScalar *mat_A, const CeedScalar *mat_B, CeedScalar *mat_C, CeedInt m, CeedInt n, CeedInt kk)

Return a reference implementation of matrix multiplication \(C = A B\).

Note: This is a reference implementation for CPU CeedScalar pointers that is not intended for high performance.

Utility Functions

Parameters:

• ceed – [in] Ceed context for error handling

• mat_A – [in] Row-major matrix A

• mat_B – [in] Row-major matrix B

• mat_C – [out] Row-major output matrix C

• m – [in] Number of rows of C

• n – [in] Number of columns of C

• kk – [in] Number of columns of A/rows of B

Returns:

An error code: 0 - success, otherwise - failure

int CeedQRFactorization(Ceed ceed, CeedScalar *mat, CeedScalar *tau, CeedInt m, CeedInt n)

Return QR Factorization of a matrix.

Utility Functions

Parameters:

• ceed – [in] Ceed context for error handling

• mat – [inout] Row-major matrix to be factorized in place

• tau – [inout] Vector of length m of scaling factors

• m – [in] Number of rows

• n – [in] Number of columns

Returns:

An error code: 0 - success, otherwise - failure

int CeedHouseholderApplyQ(CeedScalar *mat_A, const CeedScalar *mat_Q, const CeedScalar *tau, CeedTransposeMode t_mode, CeedInt m, CeedInt n, CeedInt k, CeedInt row, CeedInt col)

Apply Householder Q matrix.

Compute mat_A = mat_Q mat_A, where mat_Q is \(m \times m\) and mat_A is \(m \times n\).

Utility Functions

Parameters:

• mat_A – [inout] Matrix to apply Householder Q to, in place

• mat_Q – [in] Householder Q matrix

• tau – [in] Householder scaling factors

• t_mode – [in] Transpose mode for application

• m – [in] Number of rows in A

• n – [in] Number of columns in A

• k – [in] Number of elementary reflectors in Q, k < m

• row – [in] Row stride in A

• col – [in] Col stride in A

Returns:

An error code: 0 - success, otherwise - failure

int CeedMatrixPseudoinverse(Ceed ceed, const CeedScalar *mat, CeedInt m, CeedInt n, CeedScalar *mat_pinv)

Return pseudoinverse of a matrix.

Utility Functions

Parameters:

• ceed – [in] Ceed context for error handling

• mat – [in] Row-major matrix to compute pseudoinverse of

• m – [in] Number of rows

• n – [in] Number of columns

• mat_pinv – [out] Row-major pseudoinverse matrix

Returns:

An error code: 0 - success, otherwise - failure

int CeedSymmetricSchurDecomposition(Ceed ceed, CeedScalar *mat, CeedScalar *lambda, CeedInt n)

Return symmetric Schur decomposition of the symmetric matrix mat via symmetric QR factorization.

Utility Functions

Parameters:

• ceed – [in] Ceed context for error handling

• mat – [inout] Row-major matrix to be factorized in place

• lambda – [out] Vector of length n of eigenvalues

• n – [in] Number of rows/columns

Returns:

An error code: 0 - success, otherwise - failure

int CeedSimultaneousDiagonalization(Ceed ceed, CeedScalar *mat_A, CeedScalar *mat_B, CeedScalar *mat_X, CeedScalar *lambda, CeedInt n)

Return Simultaneous Diagonalization of two matrices.

This solves the generalized eigenvalue problem A x = lambda B x, where A and B are symmetric and B is positive definite. We generate the matrix X and vector Lambda such that X^T A X = Lambda and X^T B X = I. This is equivalent to the LAPACK routine ‘sygv’ with TYPE = 1.

Utility Functions

Parameters:

• ceed – [in] Ceed context for error handling

• mat_A – [in] Row-major matrix to be factorized with eigenvalues

• mat_B – [in] Row-major matrix to be factorized to identity

• mat_X – [out] Row-major orthogonal matrix

• lambda – [out] Vector of length n of generalized eigenvalues

• n – [in] Number of rows/columns

Returns:

An error code: 0 - success, otherwise - failure

int CeedTensorContractCreate(Ceed ceed, CeedTensorContract *contract)

Create a CeedTensorContract object for a CeedBasis

Backend Developer Functions

Parameters:

• ceed – [in] Ceed object used to create the CeedTensorContract

• contract – [out] Address of the variable where the newly created CeedTensorContract will be stored.

Returns:

An error code: 0 - success, otherwise - failure

int CeedTensorContractApply(CeedTensorContract contract, CeedInt A, CeedInt B, CeedInt C, CeedInt J, const CeedScalar *restrict t, CeedTransposeMode t_mode, const CeedInt add, const CeedScalar *restrict u, CeedScalar *restrict v)

Apply tensor contraction.

Contracts on the middle index NOTRANSPOSE: v_ajc = t_jb u_abc TRANSPOSE: v_ajc = t_bj u_abc If add != 0, = is replaced by +=

Backend Developer Functions

Parameters:

• contract – [in] CeedTensorContract to use

• A – [in] First index of u, v

• B – [in] Middle index of u, one index of t

• C – [in] Last index of u, v

• J – [in] Middle index of v, one index of t

• t – [in] Tensor array to contract against

• t_mode – [in] Transpose mode for t, CEED_NOTRANSPOSE for t_jb CEED_TRANSPOSE for t_bj

• add – [in] Add mode

• u – [in] Input array

• v – [out] Output array

Returns:

An error code: 0 - success, otherwise - failure

int CeedTensorContractStridedApply(CeedTensorContract contract, CeedInt A, CeedInt B, CeedInt C, CeedInt D, CeedInt J, const CeedScalar *restrict t, CeedTransposeMode t_mode, const CeedInt add, const CeedScalar *restrict u, CeedScalar *restrict v)

Apply tensor contraction.

Contracts on the middle index NOTRANSPOSE: v_dajc = t_djb u_abc TRANSPOSE: v_ajc = t_dbj u_dabc If add != 0, = is replaced by +=

Backend Developer Functions

Parameters:

• contract – [in] CeedTensorContract to use

• A – [in] First index of u, second index of v

• B – [in] Middle index of u, one of last two indices of t

• C – [in] Last index of u, v

• D – [in] First index of v, first index of t

• J – [in] Third index of v, one of last two indices of t

• t – [in] Tensor array to contract against

• t_mode – [in] Transpose mode for t, CEED_NOTRANSPOSE for t_djb CEED_TRANSPOSE for t_dbj

• add – [in] Add mode

• u – [in] Input array

• v – [out] Output array

Returns:

An error code: 0 - success, otherwise - failure

int CeedTensorContractGetCeed(CeedTensorContract contract, Ceed *ceed)

Get the Ceed associated with a CeedTensorContract

Backend Developer Functions

Parameters:

• contract – [in] CeedTensorContract

• ceed – [out] Variable to store Ceed

Returns:

An error code: 0 - success, otherwise - failure

Ceed CeedTensorContractReturnCeed(CeedTensorContract contract)

Return the Ceed associated with a CeedTensorContract

Backend Developer Functions

Parameters:

• contract – [in] CeedTensorContract

Returns:

Ceed associated with contract

int CeedTensorContractGetData(CeedTensorContract contract, void *data)

Get backend data of a CeedTensorContract

Backend Developer Functions

Parameters:

• contract – [in] CeedTensorContract

• data – [out] Variable to store data

Returns:

An error code: 0 - success, otherwise - failure

int CeedTensorContractSetData(CeedTensorContract contract, void *data)

Set backend data of a CeedTensorContract

Backend Developer Functions

Parameters:

• contract – [inout] CeedTensorContract

• data – [in] Data to set

Returns:

An error code: 0 - success, otherwise - failure

int CeedTensorContractReference(CeedTensorContract contract)

Increment the reference counter for a CeedTensorContract

Backend Developer Functions

Parameters:

• contract – [inout] CeedTensorContract to increment the reference counter

Returns:

An error code: 0 - success, otherwise - failure

int CeedTensorContractReferenceCopy(CeedTensorContract tensor, CeedTensorContract *tensor_copy)

Copy the pointer to a CeedTensorContract.

Both pointers should be destroyed with CeedTensorContractDestroy().

Note: If the value of *tensor_copy passed to this function is non-NULL, then it is assumed that *tensor_copy is a pointer to a CeedTensorContract. This CeedTensorContract will be destroyed if *tensor_copy is the only reference to this CeedTensorContract.

User Functions

Parameters:

• tensor – [in] CeedTensorContract to copy reference to

• tensor_copy – [inout] Variable to store copied reference

Returns:

An error code: 0 - success, otherwise - failure

int CeedTensorContractDestroy(CeedTensorContract *contract)

Destroy a CeedTensorContract

Backend Developer Functions

Parameters:

• contract – [inout] CeedTensorContract to destroy

Returns:

An error code: 0 - success, otherwise - failure