chptrf - compute the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method
SUBROUTINE CHPTRF( UPLO, N, A, IPIVOT, INFO) CHARACTER * 1 UPLO COMPLEX A(*) INTEGER N, INFO INTEGER IPIVOT(*)
SUBROUTINE CHPTRF_64( UPLO, N, A, IPIVOT, INFO) CHARACTER * 1 UPLO COMPLEX A(*) INTEGER*8 N, INFO INTEGER*8 IPIVOT(*)
SUBROUTINE HPTRF( UPLO, [N], A, IPIVOT, [INFO]) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: A INTEGER :: N, INFO INTEGER, DIMENSION(:) :: IPIVOT
SUBROUTINE HPTRF_64( UPLO, [N], A, IPIVOT, [INFO]) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: A INTEGER(8) :: N, INFO INTEGER(8), DIMENSION(:) :: IPIVOT
#include <sunperf.h>
void chptrf(char uplo, int n, complex *a, int *ipivot, int *info);
void chptrf_64(char uplo, long n, complex *a, long *ipivot, long *info);
chptrf computes the factorization of a complex Hermitian packed matrix A using the Bunch-Kaufman diagonal pivoting method:
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.
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
A(i,j) for 1 < =i < =j;
if UPLO = 'L', A(i + (j-1)*(2n-j)/2) = A(i,j) for j < =i < =n.
On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L, stored as a packed triangular matrix overwriting A (see below for further details).
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.
= 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, and division by zero will occur if it is used to solve a system of equations.
5-96 - Based on modifications by J. Lewis, Boeing Computer Services Company
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).