table of contents
| pttrf(3) | LAPACK | pttrf(3) |
NAME¶
pttrf - pttrf: triangular factor
SYNOPSIS¶
Functions¶
subroutine cpttrf (n, d, e, info)
CPTTRF subroutine dpttrf (n, d, e, info)
DPTTRF subroutine spttrf (n, d, e, info)
SPTTRF subroutine zpttrf (n, d, e, info)
ZPTTRF
Detailed Description¶
Function Documentation¶
subroutine cpttrf (integer n, real, dimension( * ) d, complex, dimension( * ) e, integer info)¶
CPTTRF
Purpose:
CPTTRF computes the L*D*L**H factorization of a complex Hermitian
positive definite tridiagonal matrix A. The factorization may also
be regarded as having the form A = U**H *D*U.
Parameters
N
N is INTEGER
The order of the matrix A. N >= 0.
D
D is REAL array, dimension (N)
On entry, the n diagonal elements of the tridiagonal matrix
A. On exit, the n diagonal elements of the diagonal matrix
D from the L*D*L**H factorization of A.
E
E is COMPLEX array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix A. On exit, the (n-1) subdiagonal elements of the
unit bidiagonal factor L from the L*D*L**H factorization of A.
E can also be regarded as the superdiagonal of the unit
bidiagonal factor U from the U**H *D*U factorization of A.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
> 0: if INFO = k, the leading principal minor of order k
is not positive; if k < N, the factorization could not
be completed, while if k = N, the factorization was
completed, but D(N) <= 0.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dpttrf (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, integer info)¶
DPTTRF
Purpose:
DPTTRF computes the L*D*L**T factorization of a real symmetric
positive definite tridiagonal matrix A. The factorization may also
be regarded as having the form A = U**T*D*U.
Parameters
N
N is INTEGER
The order of the matrix A. N >= 0.
D
D is DOUBLE PRECISION array, dimension (N)
On entry, the n diagonal elements of the tridiagonal matrix
A. On exit, the n diagonal elements of the diagonal matrix
D from the L*D*L**T factorization of A.
E
E is DOUBLE PRECISION array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix A. On exit, the (n-1) subdiagonal elements of the
unit bidiagonal factor L from the L*D*L**T factorization of A.
E can also be regarded as the superdiagonal of the unit
bidiagonal factor U from the U**T*D*U factorization of A.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
> 0: if INFO = k, the leading principal minor of order k
is not positive; if k < N, the factorization could not
be completed, while if k = N, the factorization was
completed, but D(N) <= 0.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine spttrf (integer n, real, dimension( * ) d, real, dimension( * ) e, integer info)¶
SPTTRF
Purpose:
SPTTRF computes the L*D*L**T factorization of a real symmetric
positive definite tridiagonal matrix A. The factorization may also
be regarded as having the form A = U**T*D*U.
Parameters
N
N is INTEGER
The order of the matrix A. N >= 0.
D
D is REAL array, dimension (N)
On entry, the n diagonal elements of the tridiagonal matrix
A. On exit, the n diagonal elements of the diagonal matrix
D from the L*D*L**T factorization of A.
E
E is REAL array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix A. On exit, the (n-1) subdiagonal elements of the
unit bidiagonal factor L from the L*D*L**T factorization of A.
E can also be regarded as the superdiagonal of the unit
bidiagonal factor U from the U**T*D*U factorization of A.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
> 0: if INFO = k, the leading principal minor of order k
is not positive; if k < N, the factorization could not
be completed, while if k = N, the factorization was
completed, but D(N) <= 0.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zpttrf (integer n, double precision, dimension( * ) d, complex*16, dimension( * ) e, integer info)¶
ZPTTRF
Purpose:
ZPTTRF computes the L*D*L**H factorization of a complex Hermitian
positive definite tridiagonal matrix A. The factorization may also
be regarded as having the form A = U**H *D*U.
Parameters
N
N is INTEGER
The order of the matrix A. N >= 0.
D
D is DOUBLE PRECISION array, dimension (N)
On entry, the n diagonal elements of the tridiagonal matrix
A. On exit, the n diagonal elements of the diagonal matrix
D from the L*D*L**H factorization of A.
E
E is COMPLEX*16 array, dimension (N-1)
On entry, the (n-1) subdiagonal elements of the tridiagonal
matrix A. On exit, the (n-1) subdiagonal elements of the
unit bidiagonal factor L from the L*D*L**H factorization of A.
E can also be regarded as the superdiagonal of the unit
bidiagonal factor U from the U**H *D*U factorization of A.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
> 0: if INFO = k, the leading principal minor of order k
is not positive; if k < N, the factorization could not
be completed, while if k = N, the factorization was
completed, but D(N) <= 0.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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