1DPBTRF(1)                LAPACK routine (version 3.1)                DPBTRF(1)
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NAME

6       DPBTRF  - the Cholesky factorization of a real symmetric positive defi‐
7       nite band matrix A
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SYNOPSIS

10       SUBROUTINE DPBTRF( UPLO, N, KD, AB, LDAB, INFO )
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12           CHARACTER      UPLO
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14           INTEGER        INFO, KD, LDAB, N
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16           DOUBLE         PRECISION AB( LDAB, * )
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PURPOSE

19       DPBTRF computes the Cholesky factorization of a real symmetric positive
20       definite band matrix A.
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22       The factorization has the form
23          A = U**T * U,  if UPLO = 'U', or
24          A = L  * L**T,  if UPLO = 'L',
25       where U is an upper triangular matrix and L is lower triangular.
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ARGUMENTS

29       UPLO    (input) CHARACTER*1
30               = 'U':  Upper triangle of A is stored;
31               = 'L':  Lower triangle of A is stored.
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33       N       (input) INTEGER
34               The order of the matrix A.  N >= 0.
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36       KD      (input) INTEGER
37               The  number of superdiagonals of the matrix A if UPLO = 'U', or
38               the number of subdiagonals if UPLO = 'L'.  KD >= 0.
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40       AB      (input/output) DOUBLE PRECISION array, dimension (LDAB,N)
41               On entry, the upper or lower triangle  of  the  symmetric  band
42               matrix A, stored in the first KD+1 rows of the array.  The j-th
43               column of A is stored in the j-th column of  the  array  AB  as
44               follows:  if  UPLO  = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-
45               kd)<=i<=j;  if  UPLO  =  'L',  AB(1+i-j,j)     =   A(i,j)   for
46               j<=i<=min(n,j+kd).
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48               On  exit,  if  INFO  = 0, the triangular factor U or L from the
49               Cholesky factorization A = U**T*U or A =  L*L**T  of  the  band
50               matrix A, in the same storage format as A.
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52       LDAB    (input) INTEGER
53               The leading dimension of the array AB.  LDAB >= KD+1.
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55       INFO    (output) INTEGER
56               = 0:  successful exit
57               < 0:  if INFO = -i, the i-th argument had an illegal value
58               > 0:  if INFO = i, the leading minor of order i is not positive
59               definite, and the factorization could not be completed.
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FURTHER DETAILS

62       The band storage scheme is illustrated by the following example, when N
63       = 6, KD = 2, and UPLO = 'U':
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65       On entry:                       On exit:
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67           *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
68           *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
69          a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
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71       Similarly, if UPLO = 'L' the format of A is as follows:
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73       On entry:                       On exit:
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75          a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
76          a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
77          a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
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79       Array elements marked * are not used by the routine.
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81       Contributed by
82       Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989
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87 LAPACK routine (version 3.1)    November 2006                       DPBTRF(1)
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