ZPBCON
Modified to call ZLACN2 in place of ZLACON, 10 Feb 03, SJH.
Purpose
ZPBCON estimates the reciprocal of the condition number (in the
1-norm) of a complex Hermitian positive definite band matrix using
the Cholesky factorization A = U**H*U or A = L*L**H computed by
ZPBTRF.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
1-norm) of a complex Hermitian positive definite band matrix using
the Cholesky factorization A = U**H*U or A = L*L**H computed by
ZPBTRF.
An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
Arguments
| UPLO |
(input) CHARACTER*1
= 'U': Upper triangular factor stored in AB;
= 'L': Lower triangular factor stored in AB. |
| N |
(input) INTEGER
The order of the matrix A. N >= 0.
|
| KD |
(input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of sub-diagonals if UPLO = 'L'. KD >= 0. |
| AB |
(input) COMPLEX*16 array, dimension (LDAB,N)
The triangular factor U or L from the Cholesky factorization
A = U**H*U or A = L*L**H of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows: if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd). |
| LDAB |
(input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
|
| ANORM |
(input) DOUBLE PRECISION
The 1-norm (or infinity-norm) of the Hermitian band matrix A.
|
| RCOND |
(output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine. |
| WORK |
(workspace) COMPLEX*16 array, dimension (2*N)
|
| RWORK |
(workspace) DOUBLE PRECISION array, dimension (N)
|
| INFO |
(output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value |