CeedBasis

static int CeedChebyshevPolynomialsAtPoint(CeedScalar x, CeedInt n, CeedScalar *chebyshev_x)

Compute Chebyshev polynomial values at a point.

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Parameters:

• x – [in] Coordinate to evaluate Chebyshev polynomials at

• n – [in] Number of Chebyshev polynomials to evaluate, n >= 2

• chebyshev_x – [out] Array of Chebyshev polynomial values

Returns:

An error code: 0 - success, otherwise - failure

static int CeedChebyshevDerivativeAtPoint(CeedScalar x, CeedInt n, CeedScalar *chebyshev_dx)

Compute values of the derivative of Chebyshev polynomials at a point.

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Parameters:

• x – [in] Coordinate to evaluate derivative of Chebyshev polynomials at

• n – [in] Number of Chebyshev polynomials to evaluate, n >= 2

• chebyshev_dx – [out] Array of Chebyshev polynomial derivative values

Returns:

An error code: 0 - success, otherwise - failure

static int CeedHouseholderReflect(CeedScalar *A, const CeedScalar *v, CeedScalar b, CeedInt m, CeedInt n, CeedInt row, CeedInt col)

Compute Householder reflection.

Computes \(A = (I - b v v^T) A\), where \(A\) is an \(m \times n\) matrix indexed as A[i*row + j*col].

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Parameters:

• A – [inout] Matrix to apply Householder reflection to, in place

• v – [in] Householder vector

• b – [in] Scaling factor

• m – [in] Number of rows in A

• n – [in] Number of columns in A

• row – [in] Row stride

• col – [in] Col stride

Returns:

An error code: 0 - success, otherwise - failure

static int CeedGivensRotation(CeedScalar *A, CeedScalar c, CeedScalar s, CeedTransposeMode t_mode, CeedInt i, CeedInt k, CeedInt m, CeedInt n)

Compute Givens rotation.

Computes \(A = G A\) (or \(G^T A\) in transpose mode), where \(A\) is an \(m \times n\) matrix indexed as A[i*n + j*m].

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Parameters:

• A – [inout] Row major matrix to apply Givens rotation to, in place

• c – [in] Cosine factor

• s – [in] Sine factor

• t_mode – [in] CEED_NOTRANSPOSE to rotate the basis counter-clockwise, which has the effect of rotating columns of A clockwise; CEED_TRANSPOSE for the opposite rotation

• i – [in] First row/column to apply rotation

• k – [in] Second row/column to apply rotation

• m – [in] Number of rows in A

• n – [in] Number of columns in A

Returns:

An error code: 0 - success, otherwise - failure

static int CeedScalarView(const char *name, const char *fp_fmt, CeedInt m, CeedInt n, const CeedScalar *a, const char *tabs, FILE *stream)

View an array stored in a CeedBasis

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Parameters:

• name – [in] Name of array

• fp_fmt – [in] Printing format

• m – [in] Number of rows in array

• n – [in] Number of columns in array

• a – [in] Array to be viewed

• tabs – [in] Tabs to append before each new line

• stream – [in] Stream to view to, e.g., stdout

Returns:

An error code: 0 - success, otherwise - failure

static int CeedBasisView_Object(CeedObject basis, FILE *stream)

View a CeedBasis passed as a CeedObject

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Parameters:

• basis – [in] CeedBasis to view

• stream – [in] Filestream to write to

Returns:

An error code: 0 - success, otherwise - failure

static int CeedBasisDestroy_Object(CeedObject *basis)

Destroy a CeedBasis passed as a CeedObject

Library Developer Functions

Parameters:

• basis – [inout] Address of CeedBasis to destroy

Returns:

An error code: 0 - success, otherwise - failure

static int CeedBasisCreateProjectionMatrices(CeedBasis basis_from, CeedBasis basis_to, CeedScalar **interp_project, CeedScalar **grad_project)

Create the interpolation and gradient matrices for projection from the nodes of basis_from to the nodes of basis_to.

The interpolation is given by interp_project = interp_to^+ * interp_from, where the pseudoinverse interp_to^+ is given by QR factorization. The gradient is given by grad_project = interp_to^+ * grad_from, and is only computed for \(H^1\) spaces otherwise it should not be used.

Note: basis_from and basis_to must have compatible quadrature spaces.

Library Developer Functions

Parameters:

• basis_from – [in] CeedBasis to project from

• basis_to – [in] CeedBasis to project to

• interp_project – [out] Address of the variable where the newly created interpolation matrix will be stored

• grad_project – [out] Address of the variable where the newly created gradient matrix will be stored

Returns:

An error code: 0 - success, otherwise - failure

static int CeedBasisApplyCheckDims(CeedBasis basis, CeedInt num_elem, CeedTransposeMode t_mode, CeedEvalMode eval_mode, CeedVector u, CeedVector v)

Check input vector dimensions for CeedBasisApply[Add].

Library Developer Functions

Parameters:

• basis – [in] CeedBasis to evaluate

• num_elem – [in] The number of elements to apply the basis evaluation to; the backend will specify the ordering in CeedElemRestrictionCreate()

• t_mode – [in] CEED_NOTRANSPOSE to evaluate from nodes to quadrature points; CEED_TRANSPOSE to apply the transpose, mapping from quadrature points to nodes

• eval_mode – [in] CEED_EVAL_NONE to use values directly, 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, CEED_EVAL_WEIGHT to use quadrature weights

• u – [in] Input CeedVector

• v – [out] Output CeedVector

Returns:

An error code: 0 - success, otherwise - failure

static int CeedBasisApplyAtPointsCheckDims(CeedBasis basis, CeedInt num_elem, const CeedInt *num_points, CeedTransposeMode t_mode, CeedEvalMode eval_mode, CeedVector x_ref, CeedVector u, CeedVector v)

Check input vector dimensions for CeedBasisApply[Add]AtPoints.

Library Developer Functions

Parameters:

• basis – [in] CeedBasis to evaluate

• num_elem – [in] The number of elements to apply the basis evaluation to; the backend will specify the ordering in CeedElemRestrictionCreate()

• num_points – [in] Array of the number of points to apply the basis evaluation to in each element, size num_elem

• t_mode – [in] CEED_NOTRANSPOSE to evaluate from nodes to points; CEED_TRANSPOSE to apply the transpose, mapping from points to nodes

• eval_mode – [in] CEED_EVAL_INTERP to use interpolated values, CEED_EVAL_GRAD to use gradients, CEED_EVAL_WEIGHT to use quadrature weights

• x_ref – [in] CeedVector holding reference coordinates of each point

• u – [in] Input CeedVector, of length num_nodes * num_comp for CEED_NOTRANSPOSE

• v – [out] Output CeedVector, of length num_points * num_q_comp for CEED_NOTRANSPOSE with CEED_EVAL_INTERP

Returns:

An error code: 0 - success, otherwise - failure

static int CeedBasisApplyAtPoints_Core(CeedBasis basis, bool apply_add, CeedInt num_elem, const CeedInt *num_points, CeedTransposeMode t_mode, CeedEvalMode eval_mode, CeedVector x_ref, CeedVector u, CeedVector v)

Default implimentation to apply basis evaluation from nodes to arbitrary points.

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Parameters:

• basis – [in] CeedBasis to evaluate

• apply_add – [in] Sum result into target vector or overwrite

• num_elem – [in] The number of elements to apply the basis evaluation to; the backend will specify the ordering in CeedElemRestrictionCreate()

• num_points – [in] Array of the number of points to apply the basis evaluation to in each element, size num_elem

• t_mode – [in] CEED_NOTRANSPOSE to evaluate from nodes to points; CEED_TRANSPOSE to apply the transpose, mapping from points to nodes

• eval_mode – [in] CEED_EVAL_INTERP to use interpolated values, CEED_EVAL_GRAD to use gradients, CEED_EVAL_WEIGHT to use quadrature weights

• x_ref – [in] CeedVector holding reference coordinates of each point

• u – [in] Input CeedVector, of length num_nodes * num_comp for CEED_NOTRANSPOSE

• v – [out] Output CeedVector, of length num_points * num_q_comp for CEED_NOTRANSPOSE with CEED_EVAL_INTERP

Returns:

An error code: 0 - success, otherwise - failure