1DPPSV(1)              LAPACK driver routine (version 3.1)             DPPSV(1)
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NAME

6       DPPSV - the solution to a real system of linear equations  A * X = B,
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SYNOPSIS

9       SUBROUTINE DPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
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11           CHARACTER     UPLO
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13           INTEGER       INFO, LDB, N, NRHS
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15           DOUBLE        PRECISION AP( * ), B( LDB, * )
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PURPOSE

18       DPPSV computes the solution to a real system of linear equations
19          A  *  X = B, where A is an N-by-N symmetric positive definite matrix
20       stored in packed format and X and B are N-by-NRHS matrices.
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22       The Cholesky decomposition is used to factor A as
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  a  lower  triangular
26       matrix.   The  factored  form  of A is then used to solve the system of
27       equations A * X = B.
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ARGUMENTS

31       UPLO    (input) CHARACTER*1
32               = 'U':  Upper triangle of A is stored;
33               = 'L':  Lower triangle of A is stored.
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35       N       (input) INTEGER
36               The number of linear equations, i.e., the order of  the  matrix
37               A.  N >= 0.
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39       NRHS    (input) INTEGER
40               The  number of right hand sides, i.e., the number of columns of
41               the matrix B.  NRHS >= 0.
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43       AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
44               On entry, the upper or lower triangle of the  symmetric  matrix
45               A,  packed  columnwise in a linear array.  The j-th column of A
46               is stored in the array AP as follows: if UPLO  =  'U',  AP(i  +
47               (j-1)*j/2)  =  A(i,j)  for  1<=i<=j;  if  UPLO  =  'L',  AP(i +
48               (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.  See  below  for  further
49               details.
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51               On  exit, if INFO = 0, the factor U or L from the Cholesky fac‐
52               torization A = U**T*U or A = L*L**T, in the same storage format
53               as A.
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55       B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
56               On  entry, the N-by-NRHS right hand side matrix B.  On exit, if
57               INFO = 0, the N-by-NRHS solution matrix X.
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59       LDB     (input) INTEGER
60               The leading dimension of the array B.  LDB >= max(1,N).
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62       INFO    (output) INTEGER
63               = 0:  successful exit
64               < 0:  if INFO = -i, the i-th argument had an illegal value
65               > 0:  if INFO = i, the leading minor of order i  of  A  is  not
66               positive definite, so the factorization could not be completed,
67               and the solution has not been computed.
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FURTHER DETAILS

70       The packed storage scheme is illustrated by the following example  when
71       N = 4, UPLO = 'U':
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73       Two-dimensional storage of the symmetric matrix A:
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75          a11 a12 a13 a14
76              a22 a23 a24
77                  a33 a34     (aij = conjg(aji))
78                      a44
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80       Packed storage of the upper triangle of A:
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82       AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
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87 LAPACK driver routine (version 3.N1o)vember 2006                        DPPSV(1)