Contents
dsytrf - compute the factorization of a real symmetric
matrix A using the Bunch-Kaufman diagonal pivoting method
SUBROUTINE DSYTRF(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO)
CHARACTER * 1 UPLO
INTEGER N, LDA, LDWORK, INFO
INTEGER IPIVOT(*)
DOUBLE PRECISION A(LDA,*), WORK(*)
SUBROUTINE DSYTRF_64(UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO)
CHARACTER * 1 UPLO
INTEGER*8 N, LDA, LDWORK, INFO
INTEGER*8 IPIVOT(*)
DOUBLE PRECISION A(LDA,*), WORK(*)
F95 INTERFACE
SUBROUTINE SYTRF(UPLO, N, A, [LDA], IPIVOT, [WORK], [LDWORK], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER :: N, LDA, LDWORK, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: A
SUBROUTINE SYTRF_64(UPLO, N, A, [LDA], IPIVOT, [WORK], [LDWORK],
[INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, LDA, LDWORK, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void dsytrf(char uplo, int n, double *a, int lda, int
*ipivot, int *info);
void dsytrf_64(char uplo, long n, double *a, long lda, long
*ipivot, long *info);
dsytrf computes the factorization of a real symmetric matrix
A using the Bunch-Kaufman diagonal pivoting method. The
form of the factorization is
A = U*D*U**T or A = L*D*L**T
where U (or L) is a product of permutation and unit upper
(lower) triangular matrices, and D is symmetric 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 symmetric 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.
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, 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).