| 1 | = Linear Algebra Package (LAPACK) = |

| 2 | [http://www.netlib.org/lapack/ LAPACK website] [http://www.netlib.org/lapack/lapackqref.ps List of subroutine] |

| 3 | |

| 4 | Many routines for linear algebra. Typical name: XYYZZZ |

| 5 | |

| 6 | * X is precision |

| 7 | * YY is type of matrix, |

| 8 | * e.g. GE (general), GB (general banded), GT (general tridiagonal) |

| 9 | |

| 10 | * ZZZ is type of operation, |

| 11 | * e.g. SV (solve system), SVX (solve system expert), EV (eigenvalues, vectors), SVD (singularvalues, vectors) |

| 12 | |

| 13 | ==== General Dense Matrix System Solver ==== |

| 14 | Ex: DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO ) |

| 15 | |

| 16 | [[Image(Lapack_DGESV.png)]] |

| 17 | |

| 18 | DGESV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices. The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B. |

| 19 | |

| 20 | [[Example Codes]] |

| 21 | |

| 22 | ==== Tri-diagonal Matrix System Solver ==== |

| 23 | Ex:DGTSV( N, NRHS, DL, D, DU, B, LDB, INFO ) |

| 24 | |

| 25 | [[Image(Lapack_DGTSV.png)]] |

| 26 | |

| 27 | DGTSV solves the equation A*X = B, where A is an n by n tridiagonal matrix, by Gaussian elimination with partial pivoting. Note that the equation A'*X = B may be solved by interchanging the order of the arguments DU and DL. |

| 28 | |

| 29 | [[Example Codes]] |

| 30 | |

| 31 | ==== Band Matrix System Solver ==== |

| 32 | Ex: DGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO ) |

| 33 | |

| 34 | [[Image(Lapack_DGBSV.png)]] |

| 35 | |

| 36 | DGBSV computes the solution to a real system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are N-by-NRHS matrices. The LU decomposition with partial pivoting and row interchanges is used to factor A as A = L * U, where L is a product of permutation and unit lower triangular matrices with KL subdiagonals, and U is upper triangular with KL+KU superdiagonals. The factored form of A is then used to solve the system of equations A * X = B. |

| 37 | |

| 38 | [[Band Storage Scheme]] |

| 39 | |

| 40 | [[Example Codes]] |