DPPSV - compute 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 posi
tive 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 sym
metric 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.
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 ille
gal 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.
FURTHER DETAILS
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 ]
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