ZTBCON(3F) ZTBCON(3F)
ZTBCON - estimate the reciprocal of the condition number of a triangular
band matrix A, in either the 1-norm or the infinity-norm
SUBROUTINE ZTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, RWORK,
INFO )
CHARACTER DIAG, NORM, UPLO
INTEGER INFO, KD, LDAB, N
DOUBLE PRECISION RCOND
DOUBLE PRECISION RWORK( * )
COMPLEX*16 AB( LDAB, * ), WORK( * )
ZTBCON estimates the reciprocal of the condition number of a triangular
band matrix A, in either the 1-norm or the infinity-norm.
The norm of A is computed and an estimate is obtained for norm(inv(A)),
then the reciprocal of the condition number is computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).
NORM (input) CHARACTER*1
Specifies whether the 1-norm condition number or the infinitynorm
condition number is required:
= '1' or 'O': 1-norm;
= 'I': Infinity-norm.
UPLO (input) CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
DIAG (input) CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N (input) INTEGER
The order of the matrix A. N >= 0.
KD (input) INTEGER
The number of superdiagonals or subdiagonals of the triangular
band matrix A. KD >= 0.
AB (input) COMPLEX*16 array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the first
kd+1 rows of the array. The j-th column of A is stored in the j
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ZTBCON(3F) ZTBCON(3F)
th column of the array AB as follows: if UPLO = 'U', AB(kd+1+ij,j)
= A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j)
= A(i,j) for j<=i<=min(n,j+kd). If DIAG = 'U', the diagonal
elements of A are not referenced and are assumed to be 1.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
RCOND (output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix A, computed
as RCOND = 1/(norm(A) * norm(inv(A))).
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
ZTBCON(3F) ZTBCON(3F)
ZTBCON - estimate the reciprocal of the condition number of a triangular
band matrix A, in either the 1-norm or the infinity-norm
SUBROUTINE ZTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, RWORK,
INFO )
CHARACTER DIAG, NORM, UPLO
INTEGER INFO, KD, LDAB, N
DOUBLE PRECISION RCOND
DOUBLE PRECISION RWORK( * )
COMPLEX*16 AB( LDAB, * ), WORK( * )
ZTBCON estimates the reciprocal of the condition number of a triangular
band matrix A, in either the 1-norm or the infinity-norm.
The norm of A is computed and an estimate is obtained for norm(inv(A)),
then the reciprocal of the condition number is computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).
NORM (input) CHARACTER*1
Specifies whether the 1-norm condition number or the infinitynorm
condition number is required:
= '1' or 'O': 1-norm;
= 'I': Infinity-norm.
UPLO (input) CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
DIAG (input) CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
N (input) INTEGER
The order of the matrix A. N >= 0.
KD (input) INTEGER
The number of superdiagonals or subdiagonals of the triangular
band matrix A. KD >= 0.
AB (input) COMPLEX*16 array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the first
kd+1 rows of the array. The j-th column of A is stored in the j
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ZTBCON(3F) ZTBCON(3F)
th column of the array AB as follows: if UPLO = 'U', AB(kd+1+ij,j)
= A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j)
= A(i,j) for j<=i<=min(n,j+kd). If DIAG = 'U', the diagonal
elements of A are not referenced and are assumed to be 1.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
RCOND (output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix A, computed
as RCOND = 1/(norm(A) * norm(inv(A))).
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
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