ssytrf - compute the factorization of a real symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
SUBROUTINE SSYTRF( UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO) CHARACTER * 1 UPLO INTEGER N, LDA, LDWORK, INFO INTEGER IPIVOT(*) REAL A(LDA,*), WORK(*)
SUBROUTINE SSYTRF_64( UPLO, N, A, LDA, IPIVOT, WORK, LDWORK, INFO) CHARACTER * 1 UPLO INTEGER*8 N, LDA, LDWORK, INFO INTEGER*8 IPIVOT(*) REAL A(LDA,*), WORK(*)
SUBROUTINE SYTRF( UPLO, [N], A, [LDA], IPIVOT, [WORK], [LDWORK], * [INFO]) CHARACTER(LEN=1) :: UPLO INTEGER :: N, LDA, LDWORK, INFO INTEGER, DIMENSION(:) :: IPIVOT REAL, DIMENSION(:) :: WORK REAL, 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, DIMENSION(:) :: WORK REAL, DIMENSION(:,:) :: A
#include <sunperf.h>
void ssytrf(char uplo, int n, float *a, int lda, int *ipivot, int *info);
void ssytrf_64(char uplo, long n, float *a, long lda, long *ipivot, long *info);
ssytrf 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.
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L (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.
WORK(1) returns the optimal LDWORK.
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.
= 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.
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).