SSPSV - compute the solution to a real system of linear
equations A * X = B,
SYNOPSIS
SUBROUTINE SSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
CHARACTER UPLO
INTEGER INFO, LDB, N, NRHS
INTEGER IPIV( * )
REAL AP( * ), B( LDB, * )
PURPOSE
SSPSV computes the solution to a real system of linear
equations A * X = B, where A is an N-by-N symmetric matrix
stored in packed format and X and B are N-by-NRHS matri
ces.
The diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = 'U', or
A = L * D * L**T, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper
(lower) triangular matrices, D is symmetric and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks. The fac
tored form of A is then used to solve the system of equa
tions 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) REAL 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, the block diagonal matrix D and the
the factorization A = U*D*U**T or A = L*D*L**T as
computed by SSPTRF, stored as a packed triangular
matrix in the same storage format as A.
IPIV (output) INTEGER array, dimension (N)
Details of the interchanges and the block struc
ture of D, as determined by SSPTRF. If IPIV(k) >
0, then rows and columns k and IPIV(k) were inter
changed, and D(k,k) is a 1-by-1 diagonal block.
If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then
rows and columns k-1 and -IPIV(k) were inter
changed and D(k-1:k,k-1:k) is a 2-by-2 diagonal
block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0,
then rows and columns k+1 and -IPIV(k) were inter
changed and D(k:k+1,k:k+1) is a 2-by-2 diagonal
block.
B (input/output) REAL 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 ille
gal value
> 0: if INFO = i, D(i,i) is exactly zero. The
factorization has been completed, but the block
diagonal matrix D is exactly singular, so the
solution could not be 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 = 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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