DSPSV(l) ) DSPSV(l)
DSPSV - compute the solution to a real system of linear equations A * X = B,
SUBROUTINE DSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
INTEGER INFO, LDB, N, NRHS
INTEGER IPIV( * )
DOUBLE PRECISION AP( * ), B( LDB, * )
DSPSV 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 matrices.
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 factored form
of A is then used to solve the system of equations A * X = B.
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
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, the block diagonal matrix D and the multipliers used to obtain the factor
U or L from the factorization A = U*D*U**T or A = L*D*L**T as computed by DSPTRF,
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 structure of D, as determined by DSPTRF.
If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, 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 interchanged 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 interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
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, 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
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)
Packed storage of the upper triangle of A:
AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
LAPACK version 3.0 15 June 2000 DSPSV(l)