Solving Systems of Linear Equations: LAPACK Computational Routines

This section describes the LAPACK routines for solving systems of linear equations. Before calling most of these routines, you need to factorize the matrix of your system of equations (see Routines for Matrix Factorization). However, the factorization is not necessary if your system of equations has a triangular matrix.

• ?getrs
  Solves a system of linear equations with an LU-factored square coefficient matrix, with multiple right-hand sides.
• ?gbtrs
  Solves a system of linear equations with an LU-factored band coefficient matrix, with multiple right-hand sides.
• ?gttrs
  Solves a system of linear equations with a tridiagonal coefficient matrix using the LU factorization computed by ?gttrf.
• ?dttrsb
  Solves a system of linear equations with a diagonally dominant tridiagonal coefficient matrix using the LU factorization computed by ?dttrfb.
• ?potrs
  Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrix.
• ?pftrs
  Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrix using the Rectangular Full Packed (RFP) format.
• ?pptrs
  Solves a system of linear equations with a packed Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrix.
• ?pbtrs
  Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite band coefficient matrix.
• ?pttrs
  Solves a system of linear equations with a symmetric (Hermitian) positive-definite tridiagonal coefficient matrix using the factorization computed by ?pttrf.
• ?sytrs
  Solves a system of linear equations with a UDU^T- or LDL^T-factored symmetric coefficient matrix.
• ?sytrs_aa
  Solves a system of linear equations A * X = B with a symmetric matrix.
• ?sytrs_rook
  Solves a system of linear equations with a UDU- or LDL-factored symmetric coefficient matrix.
• ?hetrs
  Solves a system of linear equations with a UDU^T- or LDL^T-factored Hermitian coefficient matrix.
• ?hetrs_aa
  BSolves a system of linear equations A*X = with a complex Hermitian matrix.
• ?hetrs_rook
  Solves a system of linear equations with a UDU- or LDL-factored Hermitian coefficient matrix.
• ?sytrs2
  Solves a system of linear equations with a UDU- or LDL-factored symmetric coefficient matrix.
• ?hetrs2
  Solves a system of linear equations with a UDU- or LDL-factored Hermitian coefficient matrix.
• ?sytrs_3
  Solves a system of linear equations A * X = B with a real or complex symmetric matrix.
• ?hetrs_3
  Solves a system of linear equations A * X = B with a complex Hermitian matrix using the factorization computed by ?hetrf_rk.
• ?sptrs
  Solves a system of linear equations with a UDU- or LDL-factored symmetric coefficient matrix using packed storage.
• ?hptrs
  Solves a system of linear equations with a UDU- or LDL-factored Hermitian coefficient matrix using packed storage.
• ?trtrs
  Solves a system of linear equations with a triangular coefficient matrix, with multiple right-hand sides.
• ?tptrs
  Solves a system of linear equations with a packed triangular coefficient matrix, with multiple right-hand sides.
• ?tbtrs
  Solves a system of linear equations with a band triangular coefficient matrix, with multiple right-hand sides.