Contents
dsptrf - compute the factorization of a real symmetric
matrix A stored in packed format using the Bunch-Kaufman
diagonal pivoting method
SUBROUTINE DSPTRF(UPLO, N, AP, IPIVOT, INFO)
CHARACTER * 1 UPLO
INTEGER N, INFO
INTEGER IPIVOT(*)
DOUBLE PRECISION AP(*)
SUBROUTINE DSPTRF_64(UPLO, N, AP, IPIVOT, INFO)
CHARACTER * 1 UPLO
INTEGER*8 N, INFO
INTEGER*8 IPIVOT(*)
DOUBLE PRECISION AP(*)
F95 INTERFACE
SUBROUTINE SPTRF(UPLO, [N], AP, IPIVOT, [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER :: N, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:) :: AP
SUBROUTINE SPTRF_64(UPLO, [N], AP, IPIVOT, [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL(8), DIMENSION(:) :: AP
C INTERFACE
#include <sunperf.h>
void dsptrf(char uplo, int n, double *ap, int *ipivot, int
*info);
void dsptrf_64(char uplo, long n, double *ap, long *ipivot,
long *info);
dsptrf computes the factorization of a real symmetric matrix
A stored in packed format 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) triangular matrices, and D is symmetric and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.
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.
AP (input/output)
Double precision array, dimension (N*(N+1)/2) On
entry, the upper or lower triangle of the sym-
metric matrix A, packed columnwise in a linear
array. The j-th column of A is stored in the
array AP as follows: if UPLO = 'U', AP(i + (j-
1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i
+ (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
On exit, the block diagonal matrix D and the mul-
tipliers used to obtain the factor U or L, stored
as a packed triangular matrix overwriting A (see
below for further details).
IPIVOT (output)
Integer array, dimension (N) Details of the inter-
changes and the block structure 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 interchanged and
D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
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 divi-
sion 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).