ZTRCON(3F) ZTRCON(3F)
ZTRCON - estimate the reciprocal of the condition number of a triangular
matrix A, in either the 1-norm or the infinity-norm
SUBROUTINE ZTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK, RWORK, INFO
)
CHARACTER DIAG, NORM, UPLO
INTEGER INFO, LDA, N
DOUBLE PRECISION RCOND
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( LDA, * ), WORK( * )
ZTRCON estimates the reciprocal of the condition number of a triangular
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.
A (input) COMPLEX*16 array, dimension (LDA,N)
The triangular matrix A. If UPLO = 'U', the leading N-by-N upper
triangular part of the array A contains the upper triangular
matrix, and the strictly lower triangular part of A is not
referenced. If UPLO = 'L', the leading N-by-N lower triangular
part of the array A contains the lower triangular matrix, and the
strictly upper triangular part of A is not referenced. If DIAG =
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ZTRCON(3F) ZTRCON(3F)
'U', the diagonal elements of A are also not referenced and are
assumed to be 1.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
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
ZTRCON(3F) ZTRCON(3F)
ZTRCON - estimate the reciprocal of the condition number of a triangular
matrix A, in either the 1-norm or the infinity-norm
SUBROUTINE ZTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK, RWORK, INFO
)
CHARACTER DIAG, NORM, UPLO
INTEGER INFO, LDA, N
DOUBLE PRECISION RCOND
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( LDA, * ), WORK( * )
ZTRCON estimates the reciprocal of the condition number of a triangular
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.
A (input) COMPLEX*16 array, dimension (LDA,N)
The triangular matrix A. If UPLO = 'U', the leading N-by-N upper
triangular part of the array A contains the upper triangular
matrix, and the strictly lower triangular part of A is not
referenced. If UPLO = 'L', the leading N-by-N lower triangular
part of the array A contains the lower triangular matrix, and the
strictly upper triangular part of A is not referenced. If DIAG =
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ZTRCON(3F) ZTRCON(3F)
'U', the diagonal elements of A are also not referenced and are
assumed to be 1.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
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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