.TH CPBTF2 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME CPBTF2 - the Cholesky factorization of a complex Hermitian positive definite band matrix A .SH SYNOPSIS .TP 19 SUBROUTINE CPBTF2( UPLO, N, KD, AB, LDAB, INFO ) .TP 19 .ti +4 CHARACTER UPLO .TP 19 .ti +4 INTEGER INFO, KD, LDAB, N .TP 19 .ti +4 COMPLEX AB( LDAB, * ) .SH PURPOSE CPBTF2 computes the Cholesky factorization of a complex Hermitian positive definite band matrix A. The factorization has the form .br A = U\(aq * U , if UPLO = \(aqU\(aq, or .br A = L * L\(aq, if UPLO = \(aqL\(aq, .br where U is an upper triangular matrix, U\(aq is the conjugate transpose of U, and L is lower triangular. .br This is the unblocked version of the algorithm, calling Level 2 BLAS. .SH ARGUMENTS .TP 8 UPLO (input) CHARACTER*1 Specifies whether the upper or lower triangular part of the Hermitian matrix A is stored: .br = \(aqU\(aq: Upper triangular .br = \(aqL\(aq: Lower triangular .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 KD (input) INTEGER The number of super-diagonals of the matrix A if UPLO = \(aqU\(aq, or the number of sub-diagonals if UPLO = \(aqL\(aq. KD >= 0. .TP 8 AB (input/output) COMPLEX array, dimension (LDAB,N) On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = \(aqU\(aq, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = \(aqL\(aq, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U\(aq*U or A = L*L\(aq of the band matrix A, in the same storage format as A. .TP 8 LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KD+1. .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -k, the k-th argument had an illegal value .br > 0: if INFO = k, the leading minor of order k is not positive definite, and the factorization could not be completed. .SH FURTHER DETAILS The band storage scheme is illustrated by the following example, when N = 6, KD = 2, and UPLO = \(aqU\(aq: .br On entry: On exit: .br * * a13 a24 a35 a46 * * u13 u24 u35 u46 * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 Similarly, if UPLO = \(aqL\(aq the format of A is as follows: .br On entry: On exit: .br a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66 a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 * a31 a42 a53 a64 * * l31 l42 l53 l64 * * Array elements marked * are not used by the routine. .br