zpbsv zpbsvx zptsv zptsvx

zpbsv() void zpbsv ( char  uplo, int  n, int  kd, int  nrhs, int  ldab, doublecomplex  ab[], int  ldb, doublecomplex  b[], int *  info  ) (Simple driver) Solution to system of linear equations AX = B for a Hermitian positive definite band matrix Purpose This routine computes the solution to a complex system of linear equations A * X = B, where A is an n x n Hermitian positive definite band matrix, and X and B are n x nrhs matrices. The Cholesky decomposition is used to factor A as A = U^H * U, if uplo = 'U', or A = L * L^H, 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. 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 >= 0) (If n = 0, returns without computation) [in] kd Number of super-diagonals of the matrix A if uplo = 'U', or number of sub-diagonals if uplo = 'L'. (kd >= 0) [in] nrhs Number of right hand sides, i.e., number of columns of the matrix B. (nrhs >= 0) (If nrhs = 0, returns without computation) [in] ldab Leading dimension of the two dimensional array ab[][]. (ldab >= kd + 1) [in,out] ab[][] Array ab[lab][ldab] (lab >= n) [in] n x n Hermitian positive definite band matrix A in kd+1 x n symmetric band matrix form. Upper or lower part is to be stored in accordance with uplo. See below for further details. [out] If info = 0, the triangular factor U or L from the Cholesky factorization A = U^H*U or A = L*L^H of the band matrix A, in the same storage format as A. [in] ldb Leading dimension of the two dimensional array b[][]. (ldb >= max(1, n)) [in,out] b[][] Array b[lb][ldab] (lb >= nrhs) [in] n x nrhs right hand side matrix B. [out] If info = 0, n x nrhs solution matrix X. [out] info = 0: Successful exit = -1: The argument uplo had an illegal value (uplo != 'U' nor 'L') = -2: The argument n had an illegal value (n < 0) = -3: The argument kd had an illegal value (kd < 0) = -4: The argument nrhs had an illegal value (nrhs < 0) = -5: The argument ldab had an illegal value (ldab < kd+1) = -7: The argument ldb had an illegal value (ldb < max(1, n)) = 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 Further Details The symmetric band matrix form is illustrated by the following example, when n = 6, kd = 2, and uplo = "U": On entry: * * a13 a24 a35 a46 * a12 a23 a34 a45 a56 a11 a22 a33 a44 a55 a66 On exit: * * u13 u24 u35 u46 * u12 u23 u34 u45 u56 u11 u22 u33 u44 u55 u66 Similarly, if uplo = "L" the format of A is as follows: On entry: a11 a22 a33 a44 a55 a66 a21 a32 a43 a54 a65 * a31 a42 a53 a64 * * On exit: l11 l22 l33 l44 l55 l66 l21 l32 l43 l54 l65 * l31 l42 l53 l64 * * Array elements marked * are not used by the routine. Reference LAPACK