Provided by: liblapack-doc_3.3.1-1_all NAME

LAPACK-3 - computes the solution to a real system of linear equations  A * X = B,

SYNOPSIS

SUBROUTINE DPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )

CHARACTER     UPLO

INTEGER       INFO, LDB, N, NRHS

DOUBLE        PRECISION AP( * ), B( LDB, * )

PURPOSE

DPPSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric positive definite matrix stored in
packed format and X and B are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**T* U,  if UPLO = 'U', or
A = L * L**T,  if UPLO = 'L',
where U is an upper triangular matrix and L is a lower triangular
matrix.  The factored form of A is then used to solve the system of
equations A * X = B.

ARGUMENTS

UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

N       (input) INTEGER
The number of linear equations, i.e., the order of the
matrix A.  N >= 0.

NRHS    (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B.  NRHS >= 0.

AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array.  The j-th column of A
is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.
On exit, if INFO = 0, the factor U or L from the Cholesky
factorization A = U**T*U or A = L*L**T, in the same storage
format as A.

B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution matrix X.

LDB     (input) INTEGER
The leading dimension of the array B.  LDB >= max(1,N).

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i, the leading minor of order i of A is not
positive definite, so the factorization could not be
completed, and the solution has not been computed.

FURTHERDETAILS

The packed storage scheme is illustrated by the following example
when N = 4, UPLO = 'U':
Two-dimensional storage of the symmetric matrix A:
a11 a12 a13 a14
a22 a23 a24
a33 a34     (aij = conjg(aji))
a44
Packed storage of the upper triangle of A:
AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

LAPACK driver routine (version 3.3.1)      April 2011                             DPPSV(3lapack)