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

6       CPPSV  -  the solution to a complex system of linear equations  A * X =
7       B,
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SYNOPSIS

10       SUBROUTINE CPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
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12           CHARACTER     UPLO
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14           INTEGER       INFO, LDB, N, NRHS
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16           COMPLEX       AP( * ), B( LDB, * )
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PURPOSE

19       CPPSV computes the solution to a complex system of linear equations
20          A * X = B, where A is an N-by-N Hermitian positive  definite  matrix
21       stored in packed format and X and B are N-by-NRHS matrices.
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23       The Cholesky decomposition is used to factor A as
24          A = U**H* U,  if UPLO = 'U', or
25          A = L * L**H,  if UPLO = 'L',
26       where  U  is  an  upper  triangular  matrix and L is a lower triangular
27       matrix.  The factored form of A is then used to  solve  the  system  of
28       equations A * X = B.
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ARGUMENTS

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

71       The  packed storage scheme is illustrated by the following example when
72       N = 4, UPLO = 'U':
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74       Two-dimensional storage of the Hermitian matrix A:
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76          a11 a12 a13 a14
77              a22 a23 a24
78                  a33 a34     (aij = conjg(aji))
79                      a44
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81       Packed storage of the upper triangle of A:
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83       AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
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88 LAPACK driver routine (version 3.N1o)vember 2006                        CPPSV(1)