chpsv(3P) Sun Performance Library chpsv(3P)NAMEchpsv - compute the solution to a complex system of linear equations A
* X = B,
SYNOPSIS
SUBROUTINE CHPSV(UPLO, N, NRHS, A, IPIVOT, B, LDB, INFO)
CHARACTER * 1 UPLO
COMPLEX A(*), B(LDB,*)
INTEGER N, NRHS, LDB, INFO
INTEGER IPIVOT(*)
SUBROUTINE CHPSV_64(UPLO, N, NRHS, A, IPIVOT, B, LDB, INFO)
CHARACTER * 1 UPLO
COMPLEX A(*), B(LDB,*)
INTEGER*8 N, NRHS, LDB, INFO
INTEGER*8 IPIVOT(*)
F95 INTERFACE
SUBROUTINE HPSV(UPLO, [N], [NRHS], A, IPIVOT, B, [LDB], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: A
COMPLEX, DIMENSION(:,:) :: B
INTEGER :: N, NRHS, LDB, INFO
INTEGER, DIMENSION(:) :: IPIVOT
SUBROUTINE HPSV_64(UPLO, [N], [NRHS], A, IPIVOT, B, [LDB], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: A
COMPLEX, DIMENSION(:,:) :: B
INTEGER(8) :: N, NRHS, LDB, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
C INTERFACE
#include <sunperf.h>
void chpsv(char uplo, int n, int nrhs, complex *a, int *ipivot, complex
*b, int ldb, int *info);
void chpsv_64(char uplo, long n, long nrhs, complex *a, long *ipivot,
complex *b, long ldb, long *info);
PURPOSEchpsv computes the solution to a complex system of linear equations
A * X = B, where A is an N-by-N Hermitian 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**H, if UPLO = 'U', or
A = L * D * L**H, if UPLO = 'L',
where U (or L) is a product of permutation and unit upper (lower) tri‐
angular matrices, D is Hermitian 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.
A (input/output) COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian 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**H or A = L*D*L**H as computed by CHPTRF, 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 CHPTRF. If IPIVOT(k) > 0, then rows and col‐
umns 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) COMPLEX 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 Hermitian 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 ]
6 Mar 2009 chpsv(3P)
