zpbcon zpbtrf zpbtrs zptcon zpttrf zpttrs

zpbtrf() void zpbtrf ( char  uplo, int  n, int  kd, int  ldab, doublecomplex  ab[], int *  info  ) Cholesky factorization of a Hermitian positive definite band matrix Purpose This routine computes the Cholesky factorization of a Hermitian positive definite band matrix A. The factorization has the form A = U^H * U, if uplo = 'U', or A = L * L^H, if uplo = 'L', where U is an upper triangular matrix and L is a lower triangular matrix. Parameters [in] uplo = 'U': Upper triangle of A is stored. = 'L': Lower triangle of A is stored. [in] n 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] 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. [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 ldab had an illegal value (ldab < kd+1) = i > 0: The leading minor of order i is not positive definite, and the factorization could not be completed. 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