Function

# 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.

## Parameters

`M`

The number of rows of x and the resulting matrix.

`N`

The number of columns of the resulting matrix. The number of nonzero values must be less than or equal to `N`.

`nz`

The number of nonzero values in the sparse vector y. Must be less than or equal to `N`.

`alpha`

Scalar multiplier of x.

`x`

Pointer to the dense vector x. Must be `M` number of elements. Negative strides are supported. Note, unlike dense BLAS routines, the pointer points to the last element when stride is negative.

`incx`

Increment between valid values in the dense vector x. Negative strides are supported.

`y`

Pointer to the dense storage for the values of the sparse vector y. The corresponding entry in `indy` holds the index of the value. Contains `nz` values.

`indy`

Pointer to the dense storage for the index values of the sparse vector y. The corresponding entry in y holds the values of the vector. Contains `nz` values.

`C`

Pointer to an uninitialized sparse matrix object. On success a newly allocated sparse matrix object is returned in this pointer. On error, this set to `NULL`.You are responsible for calling `sparse_matrix_destroy(_:)` on this matrix object.

## Return Value

On success `SPARSE_SUCCESS` is returned an `C` is valid matrix object. The caller is responsible for cleaning up the sparse matrix object with `sparse_matrix_destroy(_:)`.

Will return `SPARSE_ILLEGAL_PARAMETER` if `nz > N`, and `C` will be unchanged.

## Discussion

Compute the outer product of the dense vector x and the sparse vector y and return a new sparse matrix in the uninitialized pointer sparse matrix pointer `C`. `C = alpha * x * y'`. You are responsible for calling `sparse_matrix_destroy(_:)` on the returned matrix.The matrix object returned on success is a point wise based sparse matrix.

Indices in `indx` are always assumed to be stored in ascending order. Additionally, indices are assumed to be unique. The behavior of this function is undefined if either of these assumptions are not met.

All indices are 0 based (the first element of a pointer is `ptr`).

### Matrix-Vector Operations

`func sparse_matrix_vector_product_dense_double(CBLAS_TRANSPOSE, Double, sparse_matrix_double!, UnsafePointer<Double>!, sparse_stride, UnsafeMutablePointer<Double>!, sparse_stride) -> sparse_status`

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.

`func sparse_matrix_vector_product_dense_float(CBLAS_TRANSPOSE, Float, sparse_matrix_float!, UnsafePointer<Float>!, sparse_stride, UnsafeMutablePointer<Float>!, sparse_stride) -> sparse_status`

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.

`func sparse_vector_triangular_solve_dense_double(CBLAS_TRANSPOSE, Double, sparse_matrix_double!, UnsafeMutablePointer<Double>!, sparse_stride) -> sparse_status`

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.

`func sparse_vector_triangular_solve_dense_float(CBLAS_TRANSPOSE, Float, sparse_matrix_float!, UnsafeMutablePointer<Float>!, sparse_stride) -> sparse_status`

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.

`func sparse_permute_rows_double(sparse_matrix_double!, UnsafePointer<sparse_index>!) -> sparse_status`

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

`func sparse_permute_rows_float(sparse_matrix_float!, UnsafePointer<sparse_index>!) -> sparse_status`

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

`func sparse_permute_cols_double(sparse_matrix_double!, UnsafePointer<sparse_index>!) -> sparse_status`

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

`func sparse_permute_cols_float(sparse_matrix_float!, UnsafePointer<sparse_index>!) -> sparse_status`

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

`func sparse_elementwise_norm_double(sparse_matrix_double!, sparse_norm) -> Double`

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

`func sparse_elementwise_norm_float(sparse_matrix_float!, sparse_norm) -> Float`

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

`func sparse_operator_norm_double(sparse_matrix_double!, sparse_norm) -> Double`

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

`func sparse_operator_norm_float(sparse_matrix_float!, sparse_norm) -> Float`

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

`func sparse_matrix_trace_double(sparse_matrix_double!, sparse_index) -> Double`

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

`func sparse_matrix_trace_float(sparse_matrix_float!, sparse_index) -> Float`

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

Beta Software

This documentation contains preliminary information about an API or technology in development. This information is subject to change, and software implemented according to this documentation should be tested with final operating system software.