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---
:name: zpbcon
:md5sum: dbeb25aefa4d76514d1bf4c3290a6939
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- kd:
:type: integer
:intent: input
- ab:
:type: doublecomplex
:intent: input
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- anorm:
:type: doublereal
:intent: input
- rcond:
:type: doublereal
:intent: output
- work:
:type: doublecomplex
:intent: workspace
:dims:
- 2*n
- rwork:
:type: doublereal
:intent: workspace
:dims:
- n
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE ZPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, RWORK, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZPBCON estimates the reciprocal of the condition number (in the\n\
* 1-norm) of a complex Hermitian positive definite band matrix using\n\
* the Cholesky factorization A = U**H*U or A = L*L**H computed by\n\
* ZPBTRF.\n\
*\n\
* An estimate is obtained for norm(inv(A)), and the reciprocal of the\n\
* condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* = 'U': Upper triangular factor stored in AB;\n\
* = 'L': Lower triangular factor stored in AB.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* KD (input) INTEGER\n\
* The number of superdiagonals of the matrix A if UPLO = 'U',\n\
* or the number of sub-diagonals if UPLO = 'L'. KD >= 0.\n\
*\n\
* AB (input) COMPLEX*16 array, dimension (LDAB,N)\n\
* The triangular factor U or L from the Cholesky factorization\n\
* A = U**H*U or A = L*L**H of the band matrix A, stored in the\n\
* first KD+1 rows of the array. The j-th column of U or L is\n\
* stored in the j-th column of the array AB as follows:\n\
* if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;\n\
* if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array AB. LDAB >= KD+1.\n\
*\n\
* ANORM (input) DOUBLE PRECISION\n\
* The 1-norm (or infinity-norm) of the Hermitian band matrix A.\n\
*\n\
* RCOND (output) DOUBLE PRECISION\n\
* The reciprocal of the condition number of the matrix A,\n\
* computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an\n\
* estimate of the 1-norm of inv(A) computed in this routine.\n\
*\n\
* WORK (workspace) COMPLEX*16 array, dimension (2*N)\n\
*\n\
* RWORK (workspace) DOUBLE PRECISION 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\
* =====================================================================\n\
*\n"
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