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SPBTF2(l)) SPBTF2(l)NAMESPBTF2 - compute the Cholesky factorization of a real symmetric positive definite band matrix ASYNOPSISSUBROUTINE SPBTF2( UPLO, N, KD, AB, LDAB, INFO ) CHARACTER UPLO INTEGER INFO, KD, LDAB, N REAL AB( LDAB, * )PURPOSESPBTF2 computes the Cholesky factorization of a real symmetric positive definite band matrix A. The factorization has the form A = U' * U , if UPLO = 'U', or A = L * L', if UPLO = 'L', where U is an upper triangular matrix, U' is the transpose of U, and L is lower triangu- lar. This is the unblocked version of the algorithm, calling Level 2 BLAS.ARGUMENTSUPLO (input) CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is stored: = 'U': Upper triangular = 'L': Lower triangular N (input) INTEGER The order of the matrix A. N >= 0. KD (input) INTEGER The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub- diagonals if UPLO = 'L'. KD >= 0. AB (input/output) REAL array, dimension (LDAB,N) On entry, the upper or lower triangle of the symmetric 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 col- umn of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', 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'*U or A = L*L' of the band matrix A, in the same storage format as A. LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KD+1. INFO (output) INTEGER = 0: successful exit < 0: if INFO =, the k-th argument had an illegal value > 0: if INFO = k, the leading minor of order k is not positive definite, and the factorization could not be completed.-kFURTHER DETAILSThe band storage scheme is illustrated by the following example, when N = 6, KD = 2, and UPLO = 'U': On entry: On exit: * * 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 = 'L' the format of A is as follows: On entry: On exit: 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.LAPACK version 3.015 June 2000 SPBTF2(l)

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