dsytf2 - compute the factorization of a real symmetric indefinite matrix, using the diagonal pivoting method (unblocked algorithm)
SUBROUTINE DSYTF2(UPLO, N, A, LDA, IPIV, INFO) CHARACTER*1 UPLO INTEGER INFO, LDA, N INTEGER IPIV(*) DOUBLE PRECISION A(LDA,*) SUBROUTINE DSYTF2_64(UPLO, N, A, LDA, IPIV, INFO) CHARACTER*1 UPLO INTEGER*8 INFO, LDA, N INTEGER*8 IPIV(*) DOUBLE PRECISION A(LDA,*) F95 INTERFACE SUBROUTINE SYTF2(UPLO, N, A, LDA, IPIV, INFO) INTEGER :: N, LDA, INFO CHARACTER(LEN=1) :: UPLO INTEGER, DIMENSION(:) :: IPIV REAL(8), DIMENSION(:,:) :: A SUBROUTINE SYTF2_64(UPLO, N, A, LDA, IPIV, INFO) INTEGER(8) :: N, LDA, INFO CHARACTER(LEN=1) :: UPLO INTEGER(8), DIMENSION(:) :: IPIV REAL(8), DIMENSION(:,:) :: A C INTERFACE #include <sunperf.h> void dsytf2 (char uplo, int n, double *a, int lda, int *ipiv, int *info); void dsytf2_64 (char uplo, long n, double *a, long lda, long *ipiv, long *info);
Oracle Solaris Studio Performance Library dsytf2(3P)
NAME
dsytf2 - compute the factorization of a real symmetric indefinite
matrix, using the diagonal pivoting method (unblocked algorithm)
SYNOPSIS
SUBROUTINE DSYTF2(UPLO, N, A, LDA, IPIV, INFO)
CHARACTER*1 UPLO
INTEGER INFO, LDA, N
INTEGER IPIV(*)
DOUBLE PRECISION A(LDA,*)
SUBROUTINE DSYTF2_64(UPLO, N, A, LDA, IPIV, INFO)
CHARACTER*1 UPLO
INTEGER*8 INFO, LDA, N
INTEGER*8 IPIV(*)
DOUBLE PRECISION A(LDA,*)
F95 INTERFACE
SUBROUTINE SYTF2(UPLO, N, A, LDA, IPIV, INFO)
INTEGER :: N, LDA, INFO
CHARACTER(LEN=1) :: UPLO
INTEGER, DIMENSION(:) :: IPIV
REAL(8), DIMENSION(:,:) :: A
SUBROUTINE SYTF2_64(UPLO, N, A, LDA, IPIV, INFO)
INTEGER(8) :: N, LDA, INFO
CHARACTER(LEN=1) :: UPLO
INTEGER(8), DIMENSION(:) :: IPIV
REAL(8), DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void dsytf2 (char uplo, int n, double *a, int lda, int *ipiv, int
*info);
void dsytf2_64 (char uplo, long n, double *a, long lda, long *ipiv,
long *info);
PURPOSE
dsytf2 computes the factorization of a real symmetric matrix A using
the Bunch-Kaufman diagonal pivoting method:
A = U*D*U**T or A = L*D*L**T
where U (or L) is a product of permutation and unit upper (lower) tri-
angular matrices, U**T is the transpose of U, and D is symmetric and
block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
This is the unblocked version of the algorithm, calling Level 2 BLAS.
ARGUMENTS
UPLO (input)
UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= 'U': Upper triangular;
= 'L': Lower triangular.
N (input)
N is INTEGER
The order of the matrix A. N >= 0.
A (input/output)
A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the symmetric matrix A.
If UPLO = 'U', the leading n-by-n upper triangular part of A
contains 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 triangular 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 multipliers used
to obtain the factor U or L (see below for further details).
LDA (input)
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
IPIV (output)
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D.
If UPLO = 'U':
If IPIV(k) > 0, then rows and columns k and IPIV(k) were
interchanged and D(k,k) is a 1-by-1 diagonal block.
If IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and
-IPIV(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2
diagonal block.
If UPLO = 'L':
If IPIV(k) > 0, then rows and columns k and IPIV(k) were
interchanged and D(k,k) is a 1-by-1 diagonal block.
If IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
-IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
diagonal block.
INFO (output)
INFO is INTEGER
= 0: successful exit;
< 0: if INFO = -k, the k-th argument had an illegal value;
> 0: if INFO = k, D(k,k) 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.
FURTHER DETAILS
If UPLO = 'U', then A = U*D*U**T, 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 IPIV(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**T, 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 IPIV(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).
7 Nov 2015 dsytf2(3P)