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, FILE *stream)

View an array stored in a CeedBasis

Library Developer Functions

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

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

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