table of contents
| ptcon(3) | LAPACK | ptcon(3) |
NAME¶
ptcon - ptcon: condition number estimate
SYNOPSIS¶
Functions¶
subroutine cptcon (n, d, e, anorm, rcond, rwork, info)
CPTCON subroutine dptcon (n, d, e, anorm, rcond, work, info)
DPTCON subroutine sptcon (n, d, e, anorm, rcond, work, info)
SPTCON subroutine zptcon (n, d, e, anorm, rcond, rwork, info)
ZPTCON
Detailed Description¶
Function Documentation¶
subroutine cptcon (integer n, real, dimension( * ) d, complex, dimension( * ) e, real anorm, real rcond, real, dimension( * ) rwork, integer info)¶
CPTCON
Purpose:
CPTCON computes the reciprocal of the condition number (in the
1-norm) of a complex Hermitian positive definite tridiagonal matrix
using the factorization A = L*D*L**H or A = U**H*D*U computed by
CPTTRF.
Norm(inv(A)) is computed by a direct method, and the reciprocal of
the condition number is computed as
RCOND = 1 / (ANORM * norm(inv(A))).
Parameters
N
N is INTEGER
The order of the matrix A. N >= 0.
D
D is REAL array, dimension (N)
The n diagonal elements of the diagonal matrix D from the
factorization of A, as computed by CPTTRF.
E
E is COMPLEX array, dimension (N-1)
The (n-1) off-diagonal elements of the unit bidiagonal factor
U or L from the factorization of A, as computed by CPTTRF.
ANORM
ANORM is REAL
The 1-norm of the original matrix A.
RCOND
RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the
1-norm of inv(A) computed in this routine.
RWORK
RWORK is REAL array, dimension (N)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
The method used is described in Nicholas J. Higham, 'Efficient
Algorithms for Computing the Condition Number of a Tridiagonal
Matrix', SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
subroutine dptcon (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer info)¶
DPTCON
Purpose:
DPTCON computes the reciprocal of the condition number (in the
1-norm) of a real symmetric positive definite tridiagonal matrix
using the factorization A = L*D*L**T or A = U**T*D*U computed by
DPTTRF.
Norm(inv(A)) is computed by a direct method, and the reciprocal of
the condition number is computed as
RCOND = 1 / (ANORM * norm(inv(A))).
Parameters
N
N is INTEGER
The order of the matrix A. N >= 0.
D
D is DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the diagonal matrix D from the
factorization of A, as computed by DPTTRF.
E
E is DOUBLE PRECISION array, dimension (N-1)
The (n-1) off-diagonal elements of the unit bidiagonal factor
U or L from the factorization of A, as computed by DPTTRF.
ANORM
ANORM is DOUBLE PRECISION
The 1-norm of the original matrix A.
RCOND
RCOND is DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the
1-norm of inv(A) computed in this routine.
WORK
WORK is DOUBLE PRECISION array, dimension (N)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
The method used is described in Nicholas J. Higham, 'Efficient
Algorithms for Computing the Condition Number of a Tridiagonal
Matrix', SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
subroutine sptcon (integer n, real, dimension( * ) d, real, dimension( * ) e, real anorm, real rcond, real, dimension( * ) work, integer info)¶
SPTCON
Purpose:
SPTCON computes the reciprocal of the condition number (in the
1-norm) of a real symmetric positive definite tridiagonal matrix
using the factorization A = L*D*L**T or A = U**T*D*U computed by
SPTTRF.
Norm(inv(A)) is computed by a direct method, and the reciprocal of
the condition number is computed as
RCOND = 1 / (ANORM * norm(inv(A))).
Parameters
N
N is INTEGER
The order of the matrix A. N >= 0.
D
D is REAL array, dimension (N)
The n diagonal elements of the diagonal matrix D from the
factorization of A, as computed by SPTTRF.
E
E is REAL array, dimension (N-1)
The (n-1) off-diagonal elements of the unit bidiagonal factor
U or L from the factorization of A, as computed by SPTTRF.
ANORM
ANORM is REAL
The 1-norm of the original matrix A.
RCOND
RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the
1-norm of inv(A) computed in this routine.
WORK
WORK is REAL array, dimension (N)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
The method used is described in Nicholas J. Higham, 'Efficient
Algorithms for Computing the Condition Number of a Tridiagonal
Matrix', SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
subroutine zptcon (integer n, double precision, dimension( * ) d, complex*16, dimension( * ) e, double precision anorm, double precision rcond, double precision, dimension( * ) rwork, integer info)¶
ZPTCON
Purpose:
ZPTCON computes the reciprocal of the condition number (in the
1-norm) of a complex Hermitian positive definite tridiagonal matrix
using the factorization A = L*D*L**H or A = U**H*D*U computed by
ZPTTRF.
Norm(inv(A)) is computed by a direct method, and the reciprocal of
the condition number is computed as
RCOND = 1 / (ANORM * norm(inv(A))).
Parameters
N
N is INTEGER
The order of the matrix A. N >= 0.
D
D is DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the diagonal matrix D from the
factorization of A, as computed by ZPTTRF.
E
E is COMPLEX*16 array, dimension (N-1)
The (n-1) off-diagonal elements of the unit bidiagonal factor
U or L from the factorization of A, as computed by ZPTTRF.
ANORM
ANORM is DOUBLE PRECISION
The 1-norm of the original matrix A.
RCOND
RCOND is DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the
1-norm of inv(A) computed in this routine.
RWORK
RWORK is DOUBLE PRECISION array, dimension (N)
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
The method used is described in Nicholas J. Higham, 'Efficient
Algorithms for Computing the Condition Number of a Tridiagonal
Matrix', SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
Author¶
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