Contents
sppsv - compute the solution to a real system of linear
equations A * X = B,
SUBROUTINE SPPSV(UPLO, N, NRHS, A, B, LDB, INFO)
CHARACTER * 1 UPLO
INTEGER N, NRHS, LDB, INFO
REAL A(*), B(LDB,*)
SUBROUTINE SPPSV_64(UPLO, N, NRHS, A, B, LDB, INFO)
CHARACTER * 1 UPLO
INTEGER*8 N, NRHS, LDB, INFO
REAL A(*), B(LDB,*)
F95 INTERFACE
SUBROUTINE PPSV(UPLO, [N], [NRHS], A, B, [LDB], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER :: N, NRHS, LDB, INFO
REAL, DIMENSION(:) :: A
REAL, DIMENSION(:,:) :: B
SUBROUTINE PPSV_64(UPLO, [N], [NRHS], A, B, [LDB], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, NRHS, LDB, INFO
REAL, DIMENSION(:) :: A
REAL, DIMENSION(:,:) :: B
C INTERFACE
#include <sunperf.h>
void sppsv(char uplo, int n, int nrhs, float *a, float *b,
int ldb, int *info);
void sppsv_64(char uplo, long n, long nrhs, float *a, float
*b, long ldb, long *info);
sppsv computes the solution to a real system of linear equa-
tions
A * X = B, where A is an N-by-N symmetric positive defin-
ite 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 tri-
angular matrix. The factored form of A is then used to
solve the system of equations A * X = B.
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The number of linear equations, i.e., the order of
the matrix A. N >= 0.
NRHS (input)
The number of right hand sides, i.e., the number
of columns of the matrix B. NRHS >= 0.
A (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 A as follows: if UPLO = 'U', A(i + (j-
1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', A(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) 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)
The leading dimension of the array B. LDB >=
max(1,N).
INFO (output)
= 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.
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:
A = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]