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

6       SPPTRF  - the Cholesky factorization of a real symmetric positive defi‐
7       nite matrix A stored in packed format
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SYNOPSIS

10       SUBROUTINE SPPTRF( UPLO, N, AP, INFO )
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12           CHARACTER      UPLO
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14           INTEGER        INFO, N
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16           REAL           AP( * )
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PURPOSE

19       SPPTRF computes the Cholesky factorization of a real symmetric positive
20       definite matrix A stored in packed format.
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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       AP      (input/output) REAL array, dimension (N*(N+1)/2)
37               On  entry,  the upper or lower triangle of the symmetric matrix
38               A, packed columnwise in a linear array.  The j-th column  of  A
39               is  stored  in  the  array AP as follows: if UPLO = 'U', AP(i +
40               (j-1)*j/2) =  A(i,j)  for  1<=i<=j;  if  UPLO  =  'L',  AP(i  +
41               (j-1)*(2n-j)/2)  =  A(i,j)  for j<=i<=n.  See below for further
42               details.
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44               On exit, if INFO = 0, the triangular factor U  or  L  from  the
45               Cholesky  factorization  A  = U**T*U or A = L*L**T, in the same
46               storage format as A.
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48       INFO    (output) INTEGER
49               = 0:  successful exit
50               < 0:  if INFO = -i, the i-th argument had an illegal value
51               > 0:  if INFO = i, the leading minor of order i is not positive
52               definite, and the factorization could not be completed.
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FURTHER DETAILS

55       The  packed storage scheme is illustrated by the following example when
56       N = 4, UPLO = 'U':
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58       Two-dimensional storage of the symmetric matrix A:
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60          a11 a12 a13 a14
61              a22 a23 a24
62                  a33 a34     (aij = aji)
63                      a44
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65       Packed storage of the upper triangle of A:
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67       AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
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72 LAPACK routine (version 3.1)    November 2006                       SPPTRF(1)
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