Contents
zhetrf - compute the factorization of a complex Hermitian
matrix A using the Bunch-Kaufman diagonal pivoting method
SUBROUTINE ZHETRF(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO)
CHARACTER * 1 UPLO
DOUBLE COMPLEX A(LDA,*), WORK(*)
INTEGER N, LDA, LDWORK, INFO
INTEGER IPIVOT(*)
SUBROUTINE ZHETRF_64(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO)
CHARACTER * 1 UPLO
DOUBLE COMPLEX A(LDA,*), WORK(*)
INTEGER*8 N, LDA, LDWORK, INFO
INTEGER*8 IPIVOT(*)
F95 INTERFACE
SUBROUTINE HETRF(UPLO, [N], A, [LDA], IPIVOT, [WORK], [LDWORK], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER :: N, LDA, LDWORK, INFO
INTEGER, DIMENSION(:) :: IPIVOT
SUBROUTINE HETRF_64(UPLO, [N], A, [LDA], IPIVOT, [WORK], [LDWORK],
[INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER(8) :: N, LDA, LDWORK, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
C INTERFACE
#include <sunperf.h>
void zhetrf(char uplo, int n, doublecomplex *a, int lda, int
*ipivot, int *info);
void zhetrf_64(char uplo, long n, doublecomplex *a, long
lda, long *ipivot, long *info);
zhetrf computes the factorization of a complex Hermitian
matrix A using the Bunch-Kaufman diagonal pivoting method.
The form of the factorization is
A = U*D*U**H or A = L*D*L**H
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.
This is the blocked version of the algorithm, calling Level
3 BLAS.
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The order of the matrix A. N >= 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, the block diagonal matrix D and the mul-
tipliers used to obtain the factor U or L (see
below for further details).
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. 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 inter-
changed and D(k:k+1,k:k+1) is a 2-by-2 diagonal
block.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal
LDWORK.
LDWORK (input)
The length of WORK. LDWORK >=1. For best perfor-
mance LDWORK >= N*NB, where NB is the block size
returned by ILAENV.
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, and divi-
sion by zero will occur if it is used to solve a
system of equations.
If UPLO = 'U', then A = U*D*U', where
U = P(n)*U(n)* ... *P(k)U(k)* ...,
i.e., U is a product of terms P(k)*U(k), where k decreases
from n to 1 in steps of 1 or 2, and D is a block diagonal
matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is
a permutation matrix as defined by IPIVOT(k), and U(k) is a
unit upper triangular matrix, such that if the diagonal
block D(k) is of order s (s = 1 or 2), then
( I v 0 ) k-s
U(k) = ( 0 I 0 ) s
( 0 0 I ) n-k
k-s s n-k
If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-
1,k). If s = 2, the upper triangle of D(k) overwrites A(k-
1,k-1), A(k-1,k), and A(k,k), and v overwrites A(1:k-2,k-
1:k).
If UPLO = 'L', then A = L*D*L', where
L = P(1)*L(1)* ... *P(k)*L(k)* ...,
i.e., L is a product of terms P(k)*L(k), where k increases
from 1 to n in steps of 1 or 2, and D is a block diagonal
matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is
a permutation matrix as defined by IPIVOT(k), and L(k) is a
unit lower triangular matrix, such that if the diagonal
block D(k) is of order s (s = 1 or 2), then
( I 0 0 ) k-1
L(k) = ( 0 I 0 ) s
( 0 v I ) n-k-s+1
k-1 s n-k-s+1
If s = 1, D(k) overwrites A(k,k), and v overwrites
A(k+1:n,k). If s = 2, the lower triangle of D(k) overwrites
A(k,k), A(k+1,k), and A(k+1,k+1), and v overwrites
A(k+2:n,k:k+1).