.TH CPBTRF 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME CPBTRF - the Cholesky factorization of a complex Hermitian positive definite band matrix A .SH SYNOPSIS .TP 19 SUBROUTINE CPBTRF( 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 CPBTRF computes the Cholesky factorization of a complex Hermitian positive definite band matrix A. The factorization has the form .br A = U**H * U, if UPLO = \(aqU\(aq, or .br A = L * L**H, if UPLO = \(aqL\(aq, .br where U is an upper triangular matrix and L is lower triangular. .SH ARGUMENTS .TP 8 UPLO (input) CHARACTER*1 = \(aqU\(aq: Upper triangle of A is stored; .br = \(aqL\(aq: Lower triangle of A is stored. .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 KD (input) INTEGER The number of superdiagonals of the matrix A if UPLO = \(aqU\(aq, or the number of subdiagonals 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**H*U or A = L*L**H 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 = -i, the i-th argument had an illegal value .br > 0: if INFO = i, the leading minor of order i 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 Contributed by .br Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989