# Matrix and Vector Operations Perform computations with matrices and vectors. ## Topics ### Complex vector operations [`sparse_pack_vector_double_complex`](/documentation/Accelerate/sparse_pack_vector_double_complex(_:_:_:_:_:_:)) [`sparse_pack_vector_float_complex`](/documentation/Accelerate/sparse_pack_vector_float_complex(_:_:_:_:_:_:)) [`sparse_unpack_vector_double_complex`](/documentation/Accelerate/sparse_unpack_vector_double_complex(_:_:_:_:_:_:_:)) [`sparse_unpack_vector_float_complex`](/documentation/Accelerate/sparse_unpack_vector_float_complex(_:_:_:_:_:_:_:)) [`sparse_vector_norm_double_complex`](/documentation/Accelerate/sparse_vector_norm_double_complex(_:_:_:_:)) [`sparse_vector_norm_float_complex`](/documentation/Accelerate/sparse_vector_norm_float_complex(_:_:_:_:)) ### Complex matrix operations [`sparse_elementwise_norm_double_complex`](/documentation/Accelerate/sparse_elementwise_norm_double_complex(_:_:)) [`sparse_elementwise_norm_float_complex`](/documentation/Accelerate/sparse_elementwise_norm_float_complex(_:_:)) [`sparse_get_vector_nonzero_count_double_complex`](/documentation/Accelerate/sparse_get_vector_nonzero_count_double_complex(_:_:_:)) [`sparse_get_vector_nonzero_count_float_complex`](/documentation/Accelerate/sparse_get_vector_nonzero_count_float_complex(_:_:_:)) [`sparse_operator_norm_double_complex`](/documentation/Accelerate/sparse_operator_norm_double_complex(_:_:)) [`sparse_operator_norm_float_complex`](/documentation/Accelerate/sparse_operator_norm_float_complex(_:_:)) [`sparse_permute_cols_double_complex`](/documentation/Accelerate/sparse_permute_cols_double_complex(_:_:)) [`sparse_permute_cols_float_complex`](/documentation/Accelerate/sparse_permute_cols_float_complex(_:_:)) [`sparse_permute_rows_double_complex`](/documentation/Accelerate/sparse_permute_rows_double_complex(_:_:)) [`sparse_permute_rows_float_complex`](/documentation/Accelerate/sparse_permute_rows_float_complex(_:_:)) [`sparse_permute_rows_float_complex`](/documentation/Accelerate/sparse_permute_rows_float_complex(_:_:)) ### Matrix-Matrix Operations [`sparse_matrix_product_dense_double`](/documentation/Accelerate/sparse_matrix_product_dense_double(_:_:_:_:_:_:_:_:_:)) Multiplies the dense matrix *B* by the sparse matrix *A* and adds the result to the dense matrix *C*, all with double-precision values. [`sparse_matrix_product_dense_float`](/documentation/Accelerate/sparse_matrix_product_dense_float(_:_:_:_:_:_:_:_:_:)) Multiplies the dense matrix *B* by the sparse matrix *A* and adds the result to the dense matrix *C*, all with single-precision values. [`sparse_matrix_product_sparse_double`](/documentation/Accelerate/sparse_matrix_product_sparse_double(_:_:_:_:_:_:_:)) Multiplies the sparse matrix *B* by the sparse matrix *A* and adds the result to the dense matrix *C*, all with double-precision values. [`sparse_matrix_product_sparse_float`](/documentation/Accelerate/sparse_matrix_product_sparse_float(_:_:_:_:_:_:_:)) Multiplies the sparse matrix *B* by the sparse matrix *A* and adds the result to the dense matrix *C*, all with single-precision values. [`sparse_matrix_triangular_solve_dense_double`](/documentation/Accelerate/sparse_matrix_triangular_solve_dense_double(_:_:_:_:_:_:_:)) Solves the system of equations *B = alpha * T⁻¹ * B* for *B* where *B* is a dense matrix and *T* is a triangular sparse matrix, both with double-precision values. [`sparse_matrix_triangular_solve_dense_float`](/documentation/Accelerate/sparse_matrix_triangular_solve_dense_float(_:_:_:_:_:_:_:)) Solves the system of equations *B = alpha * T⁻¹ * B* for *B* where *B* is a dense matrix and *T* is a triangular sparse matrix, both with double-precision values. ### Matrix-Vector Operations [`sparse_matrix_vector_product_dense_double`](/documentation/Accelerate/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`](/documentation/Accelerate/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`](/documentation/Accelerate/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`](/documentation/Accelerate/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`](/documentation/Accelerate/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`](/documentation/Accelerate/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`](/documentation/Accelerate/sparse_permute_rows_double(_:_:)) Permutes the rows of the double-precision sparse matrix *A* based on the provided permutation array. [`sparse_permute_rows_float`](/documentation/Accelerate/sparse_permute_rows_float(_:_:)) Permutes the rows of the single-precision sparse matrix *A* based on the provided permutation array. [`sparse_permute_cols_double`](/documentation/Accelerate/sparse_permute_cols_double(_:_:)) Permutes the columns of the double-precision sparse matrix *A* based on the provided permutation array. [`sparse_permute_cols_float`](/documentation/Accelerate/sparse_permute_cols_float(_:_:)) Permutes the columns of the single-precision sparse matrix *A* based on the provided permutation array. [`sparse_elementwise_norm_double`](/documentation/Accelerate/sparse_elementwise_norm_double(_:_:)) Computes the specified element-wise norm of the double-precision sparse matrix *A*. [`sparse_elementwise_norm_float`](/documentation/Accelerate/sparse_elementwise_norm_float(_:_:)) Computes the specified element-wise norm of the single-precision sparse matrix *A*. [`sparse_operator_norm_double`](/documentation/Accelerate/sparse_operator_norm_double(_:_:)) Computes the specified operator norm of the double-precision sparse matrix *A*. [`sparse_operator_norm_float`](/documentation/Accelerate/sparse_operator_norm_float(_:_:)) Computes the specified operator norm of the single-precision sparse matrix *A*. [`sparse_matrix_trace_double`](/documentation/Accelerate/sparse_matrix_trace_double(_:_:)) Computes the sum along the specified diagonal of the double-precision sparse matrix *A*. [`sparse_matrix_trace_float`](/documentation/Accelerate/sparse_matrix_trace_float(_:_:)) Computes the sum along the specified diagonal of the single-precision sparse matrix *A*. ### Vector-Vector Operations [`sparse_inner_product_dense_double`](/documentation/Accelerate/sparse_inner_product_dense_double(_:_:_:_:_:)) Computes the inner product of sparse vector *x* with double-precision *y*, with both vectors containing double-precision values. [`sparse_inner_product_dense_float`](/documentation/Accelerate/sparse_inner_product_dense_float(_:_:_:_:_:)) Computes the inner product of sparse vector *x* with dense vector *y,* with both vectors containing single-precision values. [`sparse_inner_product_sparse_double`](/documentation/Accelerate/sparse_inner_product_sparse_double(_:_:_:_:_:_:)) Computes the inner product of sparse vector *x* with sparse vector *y,* with both vectors containing double-precision values. [`sparse_inner_product_sparse_float`](/documentation/Accelerate/sparse_inner_product_sparse_float(_:_:_:_:_:_:)) Computes the inner product of sparse vector *x* with sparse vector *y,* with both vectors containing single-precision values. [`sparse_vector_add_with_scale_dense_double`](/documentation/Accelerate/sparse_vector_add_with_scale_dense_double(_:_:_:_:_:_:)) Scales the sparse vector *x* by *alpha* and adds the result to the dense vector *y,* with both vectors containing double-precision values. [`sparse_vector_add_with_scale_dense_float`](/documentation/Accelerate/sparse_vector_add_with_scale_dense_float(_:_:_:_:_:_:)) Scales the sparse vector *x* by *alpha* and adds the result to the dense vector *y,* with both vectors containing single-precision values. [`sparse_vector_norm_double`](/documentation/Accelerate/sparse_vector_norm_double(_:_:_:_:)) Computes the specified norm of the double-precision sparse vector *x*. [`sparse_vector_norm_float`](/documentation/Accelerate/sparse_vector_norm_float(_:_:_:_:)) Computes the specified norm of the single-precision sparse vector *x*. ### Supporting Types [`sparse_matrix_double`](/documentation/Accelerate/sparse_matrix_double) Sparse matrix opaque type for double. [`sparse_matrix_float`](/documentation/Accelerate/sparse_matrix_float) Sparse matrix opaque type for float. [`sparse_status`](/documentation/Accelerate/sparse_status) The type reflecting the status of an operations. [`sparse_dimension`](/documentation/Accelerate/sparse_dimension) The dimension type. [`sparse_index`](/documentation/Accelerate/sparse_index) The index type. [`sparse_norm`](/documentation/Accelerate/sparse_norm) The norm specifier. [`sparse_stride`](/documentation/Accelerate/sparse_stride) The stride type. --- Copyright © 2026 Apple Inc. All rights reserved. | [Terms of Use](https://www.apple.com/legal/internet-services/terms/site.html) | [Privacy Policy](https://www.apple.com/privacy/privacy-policy)