# cblas_dtpsv(_:_:_:_:_:_:_:_:) Solves a packed triangular system of equations. ``` func cblas_dtpsv(_ ORDER: CBLAS_ORDER, _ UPLO: CBLAS_UPLO, _ TRANSA: CBLAS_TRANSPOSE, _ DIAG: CBLAS_DIAG, _ N: __LAPACK_int, _ AP: UnsafePointer?, _ X: UnsafeMutablePointer?, _ INCX: __LAPACK_int) ``` ## Parameters `ORDER` Specifies row-major (C) or column-major (Fortran) data ordering. `UPLO` Specifies whether to use the upper or lower triangle from the matrix. Valid values are `'U'` or `'L'`. `TRANSA` Specifies whether to use matrix A (`'N'` or `'n'`) or the transpose of A (`'T'`, `'t'`, `'C'`, or `'c'`). `DIAG` Specifies whether the matrix is unit triangular. Possible values are `'U'` (unit triangular) or `'N'` (not unit triangular). `N` Order of matrix `A`. `AP` Matrix `A` (in packed storage format). `X` Contains vector `B` on entry. Overwritten with vector `X` on return. `INCX` Stride within `X`. For example, if `incX` is 7, every 7th element is used. ## Discussion Solves the system of equations `A*X=B` or `A'*X=B`, depending on the value of `TransA`. > Important: > Apple provides the BLAS and LAPACK libraries under the Accelerate framework to be in line with LAPACK 3.9.1. Starting with iOS 26, iPadOS 26, macOS 26, tvOS 26, visionOS 26, and watchOS 26, the libraries are in line with LAPACK 3.12.0. These new interfaces provide additional functionality, as well as a new ILP64 interface. To use the new interfaces, define `ACCELERATE_NEW_LAPACK` before including the Accelerate or vecLib headers. For ILP64 interfaces, also define `ACCELERATE_LAPACK_ILP64`. For Swift projects, specify `ACCELERATE_NEW_LAPACK=1` and `ACCELERATE_LAPACK_ILP64=1` as preprocessor macros in Xcode build settings under Apple Clang - Preprocessing > Preprocessor Macros. --- 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)