dsytrf_rook - compute the factorization of a real symmetric matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm)
SUBROUTINE DSYTRF_ROOK(UPLO, N, A, LDA, IPIV, WORK, LDWORK, INFO) CHARACTER*1 UPLO INTEGER N, LDA, LDWORK, INFO INTEGER IPIV(*) DOUBLE PRECISION A(LDA,*), WORK(*) SUBROUTINE DSYTRF_ROOK_64(UPLO, N, A, LDA, IPIV, WORK, LDWORK, INFO) CHARACTER*1 UPLO INTEGER*8 N, LDA, LDWORK, INFO INTEGER*8 IPIV(*) DOUBLE PRECISION A(LDA,*), WORK(*) F95 INTERFACE SUBROUTINE SYTRF_ROOK(UPLO, N, A, LDA, IPIV, WORK, LDWORK, INFO) CHARACTER(LEN=1) :: UPLO INTEGER :: N, LDA, LDWORK, INFO INTEGER, DIMENSION(:) :: IPIV REAL(8), DIMENSION(:) :: WORK REAL(8), DIMENSION(:,:) :: A SUBROUTINE SYTRF_ROOK_64(UPLO, N, A, LDA, IPIV, WORK, LDWORK, INFO) CHARACTER(LEN=1) :: UPLO INTEGER(8) :: N, LDA, LDWORK, INFO INTEGER(8), DIMENSION(:) :: IPIV REAL(8), DIMENSION(:) :: WORK REAL(8), DIMENSION(:,:) :: A C INTERFACE #include <sunperf.h> void dsytrf_rook(char uplo, int n, double *a, int lda, int *ipiv, int *info); void dsytrf_rook_64(char uplo, long n, double *a, long lda, long *ipiv, long *info);
Oracle Solaris Studio Performance Library dsytrf_rook(3P)
NAME
dsytrf_rook - compute the factorization of a real symmetric matrix
using the bounded Bunch-Kaufman ("rook") diagonal pivoting method
(blocked algorithm)
SYNOPSIS
SUBROUTINE DSYTRF_ROOK(UPLO, N, A, LDA, IPIV, WORK, LDWORK, INFO)
CHARACTER*1 UPLO
INTEGER N, LDA, LDWORK, INFO
INTEGER IPIV(*)
DOUBLE PRECISION A(LDA,*), WORK(*)
SUBROUTINE DSYTRF_ROOK_64(UPLO, N, A, LDA, IPIV, WORK, LDWORK, INFO)
CHARACTER*1 UPLO
INTEGER*8 N, LDA, LDWORK, INFO
INTEGER*8 IPIV(*)
DOUBLE PRECISION A(LDA,*), WORK(*)
F95 INTERFACE
SUBROUTINE SYTRF_ROOK(UPLO, N, A, LDA, IPIV, WORK, LDWORK, INFO)
CHARACTER(LEN=1) :: UPLO
INTEGER :: N, LDA, LDWORK, INFO
INTEGER, DIMENSION(:) :: IPIV
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: A
SUBROUTINE SYTRF_ROOK_64(UPLO, N, A, LDA, IPIV, WORK, LDWORK,
INFO)
CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, LDA, LDWORK, INFO
INTEGER(8), DIMENSION(:) :: IPIV
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: A
C INTERFACE
#include <sunperf.h>
void dsytrf_rook(char uplo, int n, double *a, int lda, int *ipiv, int
*info);
void dsytrf_rook_64(char uplo, long n, double *a, long lda, long *ipiv,
long *info);
PURPOSE
dsytrf_rook computes the factorization of a real symmetric matrix A
using the bounded Bunch-Kaufman ("rook") 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) tri-
angular 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.
ARGUMENTS
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 contains the upper triangu-
lar 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)
The leading dimension of the array A. LDA >= max(1,N).
IPIV (output)
Details of the interchanges and the block structure of D. If
IPIV(k) > 0, then rows and columns k and IPIV(k) were inter-
changed and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U'
and 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' and 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.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.
LDWORK (input)
The length of WORK. LDWORK >=1. For best performance LDWORK
>= N*NB, where NB is the block size returned by ILAENV.
If LDWORK = -1, then a workspace query is assumed; the rou-
tine 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 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.
FURTHER DETAILS
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 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', 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 dsytrf_rook(3P)