Function

sparse_operator_norm_double

Computes the specified operator norm of the double-precision sparse matrix A.

Declaration

double sparse_operator_norm_double(sparse_matrix_double A, sparse_norm norm);

Parameters

A

The sparse matrix, A.

norm

Specify the norm to be computed. Must be one of SPARSE_NORM_ONE, SPARSE_NORM_TWO, or SPARSE_NORM_INF. See discussion for further details.

Return Value

The requested norm.

Discussion

This is the norm of the matrix treated as an linear operator, not the element-wise norm. Specify one of:

SPARSE_NORM_ONE

max over j ( sum over i ( | A[i,j] | ) )

SPARSE_NORM_TWO

Maximum singular value. This is significantly more expensive to compute than the other norms.

SPARSE_NORM_INF

max over i ( sum over j ( | A[i,j] | ) )

SPARSE_NORM_R1

Not supported, undefined.

If norm is not one of the enumerated norm types, the default value is SPARSE_NORM_INF.

See Also

Matrix-Vector Operations

sparse_matrix_vector_product_dense_double

Multiplies the dense vector x by the sparse matrix A and adds the result to the dense vector y, with all operands containing double-precision values.

sparse_matrix_vector_product_dense_float

Multiplies the dense vector x by the sparse matrix A and adds the result to the dense vector y, with all operands containing single-precision values.

sparse_vector_triangular_solve_dense_double

Solves the system of equations x = alpha * T⁻¹ * x for x where x is a dense vector and T is a triangular sparse matrix, with all operands containing double-precision values.

sparse_vector_triangular_solve_dense_float

Solves the system of equations x = alpha * T⁻¹ * x for x where x is a dense vector and T is a triangular sparse matrix, with all operands containing single-precision values.

sparse_outer_product_dense_double

Computes the outer product of the dense vector x and the sparse vector y, with both operands containing double-precision values.

sparse_outer_product_dense_float

Computes the outer product of the dense vector x and the sparse vector y, with both operands containing single-precision values.

sparse_permute_rows_double

Permutes the rows of the double-precision sparse matrix A based on the provided permutation array.

sparse_permute_rows_float

Permutes the rows of the single-precision sparse matrix A based on the provided permutation array.

sparse_permute_cols_double

Permutes the columns of the double-precision sparse matrix A based on the provided permutation array.

sparse_permute_cols_float

Permutes the columns of the single-precision sparse matrix A based on the provided permutation array.

sparse_elementwise_norm_double

Computes the specified element-wise norm of the double-precision sparse matrix A.

sparse_elementwise_norm_float

Computes the specified element-wise norm of the single-precision sparse matrix A.

sparse_operator_norm_float

Computes the specified operator norm of the single-precision sparse matrix A.

sparse_matrix_trace_double

Computes the sum along the specified diagonal of the double-precision sparse matrix A.

sparse_matrix_trace_float

Computes the sum along the specified diagonal of the single-precision sparse matrix A.

Beta Software

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