1SPBTF2(1)                LAPACK routine (version 3.1)                SPBTF2(1)
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NAME

6       SPBTF2  - the Cholesky factorization of a real symmetric positive defi‐
7       nite band matrix A
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SYNOPSIS

10       SUBROUTINE SPBTF2( 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           REAL           AB( LDAB, * )
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PURPOSE

19       SPBTF2 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' * U ,  if UPLO = 'U', or
24          A = L  * L',  if UPLO = 'L',
25       where  U is an upper triangular matrix, U' is the transpose of U, and L
26       is lower triangular.
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28       This is the unblocked version of the algorithm, calling Level 2 BLAS.
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ARGUMENTS

32       UPLO    (input) CHARACTER*1
33               Specifies whether the upper or lower  triangular  part  of  the
34               symmetric matrix A is stored:
35               = 'U':  Upper triangular
36               = 'L':  Lower triangular
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38       N       (input) INTEGER
39               The order of the matrix A.  N >= 0.
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41       KD      (input) INTEGER
42               The number of super-diagonals of the matrix A if UPLO = 'U', or
43               the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
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45       AB      (input/output) REAL array, dimension (LDAB,N)
46               On entry, the upper or lower triangle  of  the  symmetric  band
47               matrix A, stored in the first KD+1 rows of the array.  The j-th
48               column of A is stored in the j-th column of  the  array  AB  as
49               follows:  if  UPLO  = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-
50               kd)<=i<=j;  if  UPLO  =  'L',  AB(1+i-j,j)     =   A(i,j)   for
51               j<=i<=min(n,j+kd).
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53               On  exit,  if  INFO  = 0, the triangular factor U or L from the
54               Cholesky factorization A = U'*U or A = L*L' of the band  matrix
55               A, in the same storage format as A.
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57       LDAB    (input) INTEGER
58               The leading dimension of the array AB.  LDAB >= KD+1.
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60       INFO    (output) INTEGER
61               = 0: successful exit
62               < 0: if INFO = -k, the k-th argument had an illegal value
63               >  0: if INFO = k, the leading minor of order k is not positive
64               definite, and the factorization could not be completed.
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FURTHER DETAILS

67       The band storage scheme is illustrated by the following example, when N
68       = 6, KD = 2, and UPLO = 'U':
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70       On entry:                       On exit:
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72           *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
73           *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
74          a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
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76       Similarly, if UPLO = 'L' the format of A is as follows:
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78       On entry:                       On exit:
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80          a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
81          a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
82          a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
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84       Array elements marked * are not used by the routine.
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89 LAPACK routine (version 3.1)    November 2006                       SPBTF2(1)