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---
:name: cptcon
:md5sum: f44569b6ef35f71a7ce889e59b7f2950
:category: :subroutine
:arguments:
- n:
:type: integer
:intent: input
- d:
:type: real
:intent: input
:dims:
- n
- e:
:type: complex
:intent: input
:dims:
- n-1
- anorm:
:type: real
:intent: input
- rcond:
:type: real
:intent: output
- rwork:
:type: real
:intent: workspace
:dims:
- n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE CPTCON( N, D, E, ANORM, RCOND, RWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* CPTCON computes the reciprocal of the condition number (in the\n\
* 1-norm) of a complex Hermitian positive definite tridiagonal matrix\n\
* using the factorization A = L*D*L**H or A = U**H*D*U computed by\n\
* CPTTRF.\n\
*\n\
* Norm(inv(A)) is computed by a direct method, and the reciprocal of\n\
* the condition number is computed as\n\
* RCOND = 1 / (ANORM * norm(inv(A))).\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* D (input) REAL array, dimension (N)\n\
* The n diagonal elements of the diagonal matrix D from the\n\
* factorization of A, as computed by CPTTRF.\n\
*\n\
* E (input) COMPLEX array, dimension (N-1)\n\
* The (n-1) off-diagonal elements of the unit bidiagonal factor\n\
* U or L from the factorization of A, as computed by CPTTRF.\n\
*\n\
* ANORM (input) REAL\n\
* The 1-norm of the original matrix A.\n\
*\n\
* RCOND (output) REAL\n\
* The reciprocal of the condition number of the matrix A,\n\
* computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is the\n\
* 1-norm of inv(A) computed in this routine.\n\
*\n\
* RWORK (workspace) REAL array, dimension (N)\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* The method used is described in Nicholas J. Higham, \"Efficient\n\
* Algorithms for Computing the Condition Number of a Tridiagonal\n\
* Matrix\", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.\n\
*\n\
* =====================================================================\n\
*\n"
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