# CeedBasis

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

Compute Chebyshev polynomial values at a point.

Library Developer Functions

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.

Library Developer Functions

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 mxn matrix indexed as A[i*row + j*col]

Library Developer Functions

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 mxn matrix indexed as A[i*n + j*m]

Library Developer Functions

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.