Contents
zhesv - compute the solution to a complex system of linear
equations A * X = B,
SUBROUTINE ZHESV(UPLO, N, NRHS, A, LDA, IPIVOT, B, LDB, WORK, LDWORK,
INFO)
CHARACTER * 1 UPLO
DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*)
INTEGER N, NRHS, LDA, LDB, LDWORK, INFO
INTEGER IPIVOT(*)
SUBROUTINE ZHESV_64(UPLO, N, NRHS, A, LDA, IPIVOT, B, LDB, WORK,
LDWORK, INFO)
CHARACTER * 1 UPLO
DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*)
INTEGER*8 N, NRHS, LDA, LDB, LDWORK, INFO
INTEGER*8 IPIVOT(*)
F95 INTERFACE
SUBROUTINE HESV(UPLO, [N], [NRHS], A, [LDA], IPIVOT, B, [LDB], [WORK],
[LDWORK], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, B
INTEGER :: N, NRHS, LDA, LDB, LDWORK, INFO
INTEGER, DIMENSION(:) :: IPIVOT
SUBROUTINE HESV_64(UPLO, [N], [NRHS], A, [LDA], IPIVOT, B, [LDB],
[WORK], [LDWORK], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A, B
INTEGER(8) :: N, NRHS, LDA, LDB, LDWORK, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
C INTERFACE
#include <sunperf.h>
void zhesv(char uplo, int n, int nrhs, doublecomplex *a, int
lda, int *ipivot, doublecomplex *b, int ldb, int
*info);
void zhesv_64(char uplo, long n, long nrhs, doublecomplex
*a, long lda, long *ipivot, doublecomplex *b, long
ldb, long *info);
zhesv computes the solution to a complex system of linear
equations
A * X = B, where A is an N-by-N Hermitian matrix 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) triangular matrices, and D is Hermitian 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.
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)
On entry, the Hermitian matrix A. If UPLO = 'U',
the leading N-by-N upper triangular part of A con-
tains the upper triangular part of the matrix A,
and the strictly lower triangular part of A is not
referenced. If UPLO = 'L', the leading N-by-N
lower triangular part of A contains the lower tri-
angular part of the matrix A, and the strictly
upper triangular part of A is not referenced.
On exit, if INFO = 0, 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 CHETRF.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,N).
IPIVOT (output)
Details of the interchanges and the block struc-
ture of D, as determined by CHETRF. 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 diago-
nal 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)
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).
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal
LDWORK.
LDWORK (input)
The length of WORK. LDWORK >= 1, and for best
performance LDWORK >= N*NB, where NB is the
optimal blocksize for CHETRF.
If LDWORK = -1, then a workspace query is assumed;
the routine only calculates the optimal size of
the WORK array, returns this value as the first
entry of the WORK array, and no error message
related to LDWORK is issued by XERBLA.
INFO (output)
= 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.