DPPTRF(3F) DPPTRF(3F)
DPPTRF - compute the Cholesky factorization of a real symmetric positive
definite matrix A stored in packed format
SUBROUTINE DPPTRF( UPLO, N, AP, INFO )
CHARACTER UPLO
INTEGER INFO, N
DOUBLE PRECISION AP( * )
DPPTRF computes the Cholesky factorization of a real symmetric positive
definite matrix A stored in packed format.
The factorization has the form
A = U**T * U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
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 symmetric 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 + (j1)*j/2)
= A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2nj)/2)
= A(i,j) for j<=i<=n. See below for further details.
On exit, if INFO = 0, the triangular factor U or L from the
Cholesky factorization A = U**T*U or A = L*L**T, in the same
storage format as A.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not positive
definite, and the factorization could not be completed.
FURTHER DETAILS
The packed storage scheme is illustrated by the following example when N
= 4, UPLO = 'U':
Page 1
DPPTRF(3F) DPPTRF(3F)
Two-dimensional storage of the symmetric matrix A:
a11 a12 a13 a14
a22 a23 a24
a33 a34 (aij = aji)
a44
Packed storage of the upper triangle of A:
AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
DPPTRF(3F) DPPTRF(3F)
DPPTRF - compute the Cholesky factorization of a real symmetric positive
definite matrix A stored in packed format
SUBROUTINE DPPTRF( UPLO, N, AP, INFO )
CHARACTER UPLO
INTEGER INFO, N
DOUBLE PRECISION AP( * )
DPPTRF computes the Cholesky factorization of a real symmetric positive
definite matrix A stored in packed format.
The factorization has the form
A = U**T * U, if UPLO = 'U', or
A = L * L**T, if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
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 symmetric 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 + (j1)*j/2)
= A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2nj)/2)
= A(i,j) for j<=i<=n. See below for further details.
On exit, if INFO = 0, the triangular factor U or L from the
Cholesky factorization A = U**T*U or A = L*L**T, in the same
storage format as A.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the leading minor of order i is not positive
definite, and the factorization could not be completed.
FURTHER DETAILS
The packed storage scheme is illustrated by the following example when N
= 4, UPLO = 'U':
Page 1
DPPTRF(3F) DPPTRF(3F)
Two-dimensional storage of the symmetric matrix A:
a11 a12 a13 a14
a22 a23 a24
a33 a34 (aij = aji)
a44
Packed storage of the upper triangle of A:
AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
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