dspsv(3P) Sun Performance Library dspsv(3P)NAMEdspsv - compute the solution to a real system of linear equations A *
X = B,
SYNOPSIS
SUBROUTINE DSPSV(UPLO, N, NRHS, AP, IPIVOT, B, LDB, INFO)
CHARACTER * 1 UPLO
INTEGER N, NRHS, LDB, INFO
INTEGER IPIVOT(*)
DOUBLE PRECISION A(*), B(LDB,*)
SUBROUTINE DSPSV_64(UPLO, N, NRHS, AP, IPIVOT, B, LDB, INFO)
CHARACTER * 1 UPLO
INTEGER*8 N, NRHS, LDB, INFO
INTEGER*8 IPIVOT(*)
DOUBLE PRECISION A(*), B(LDB,*)
F95 INTERFACE
SUBROUTINE SPSV(UPLO, [N], [NRHS], AP, IPIVOT, B, [LDB], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER :: N, NRHS, LDB, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:) :: AP
REAL(8), DIMENSION(:,:) :: B
SUBROUTINE SPSV_64(UPLO, [N], [NRHS], AP, IPIVOT, B, [LDB], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, NRHS, LDB, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:) :: AP
REAL(8), DIMENSION(:,:) :: B
C INTERFACE
#include <sunperf.h>
void dspsv(char uplo, int n, int nrhs, double *a, int *ipivot, double
*b, int ldb, int *info);
void dspsv_64(char uplo, long n, long nrhs, double *a, long *ipivot,
double *b, long ldb, long *info);
PURPOSEdspsv 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) tri‐
angular 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.
ARGUMENTS
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.
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 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, 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.
IPIVOT (output)
Integer array, dimension (N) Details of the interchanges and
the block structure of D, as determined by DSPTRF. If
IPIVOT(k) > 0, then rows and columns k and IPIVOT(k) were
interchanged, and D(k,k) is a 1-by-1 diagonal block. If UPLO
= 'U' and IPIVOT(k) = IPIVOT(k-1) < 0, then rows and columns
k-1 and -IPIVOT(k) were interchanged and D(k-1:k,k-1:k) is a
2-by-2 diagonal block. If UPLO = 'L' and IPIVOT(k) =
IPIVOT(k+1) < 0, then rows and columns k+1 and -IPIVOT(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)
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 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 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:
A = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
6 Mar 2009 dspsv(3P)
