ptcon(3) Library Functions Manual 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. Definition at line 118 of file cptcon.f. 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. Definition at line 117 of file dptcon.f. 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. Definition at line 117 of file sptcon.f. 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. Definition at line 118 of file zptcon.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 ptcon(3)