WDpbsv WDposv WDptsv WDsysv

WDpbsv() Function WDpbsv ( Uplo As  String, N As  Long, Kd As  Long, Ab As  Variant, B As  Variant, Optional Nrhs As  Long = 1  ) Solution to system of linear equations AX = B for a symmetric positive definite band matrix Purpose WDpbsv computes the solution to a real system of linear equations A * X = B, where A is an N x N symmetric positive definite band matrix, and X and B are N x Nrhs matrices. The Cholesky decomposition is used to factor A as A = U^T*U, if Uplo = "U", or A = L*L^T, if Uplo = "L", where U is an upper triangular band matrix, and L is a lower triangular band matrix, with the same number of super-diagonals or sub-diagonals as A. The factored form of A is then used to solve the system of equations A * X = B. Returns N+2 x Nrhs Column 1 Column 2 . . . Column Nrhs Rows 1 to N Solution matrix X Row N+1 Reciprocal condition number 0 . . . 0 Row N+2 Return code 0 . . . 0 Return code. = 0: Successful exit. = i > 0: The leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed. Parameters [in] Uplo = "U": Upper triangle of A is stored. = "L": Lower triangle of A is stored. [in] N Number of linear equations, i.e., order of the matrix A. (N >= 1) [in] Kd Number of superdiagonals or subdiagonals of the matrix A. (Kd >= 0) [in] Ab (Kd+1 x N) N x N coefficient matrix A. (Symmetric band matrix form. See below for details) [in] B (N x Nrhs) N x Nrhs right hand side matrix B. [in] Nrhs (Optional) Number of columns of right hand side matrix B. (Nrhs >= 1) (default = 1) Further Details The symmetric band matrix form is illustrated by the following example, when n = 6, kd = 2, and uplo = "U": * * a13 a24 a35 a46 * a12 a23 a34 a45 a56 a11 a22 a33 a44 a55 a66 Similarly, if uplo = "L" the format of A is as follows: a11 a22 a33 a44 a55 a66 a21 a32 a43 a54 a65 * a31 a42 a53 a64 * * Array elements marked * are not used by the routine. Reference LAPACK Example Solve the system of linear equations Ax = B and estimate the reciprocal of the condition number (RCond) of A, where A is symmetric and ( 2.2 -0.11 -0.32 ) ( -1.5660 ) A = ( -0.11 2.93 0.81 ), B = ( -2.8425 ) ( -0.32 0.81 -2.37 ) ( -1.1765 )