ZTPCON(3F) ZTPCON(3F)
ZTPCON - estimate the reciprocal of the condition number of a packed
triangular matrix A, in either the 1-norm or the infinity-norm
SUBROUTINE ZTPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, RWORK, INFO )
CHARACTER DIAG, NORM, UPLO
INTEGER INFO, N
DOUBLE PRECISION RCOND
DOUBLE PRECISION RWORK( * )
COMPLEX*16 AP( * ), WORK( * )
ZTPCON estimates the reciprocal of the condition number of a packed
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.
AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in a
linear array. The j-th column of A is stored in the array AP as
follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. If
DIAG = 'U', the diagonal elements of A are not referenced and are
assumed to be 1.
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ZTPCON(3F) ZTPCON(3F)
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
ZTPCON(3F) ZTPCON(3F)
ZTPCON - estimate the reciprocal of the condition number of a packed
triangular matrix A, in either the 1-norm or the infinity-norm
SUBROUTINE ZTPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, RWORK, INFO )
CHARACTER DIAG, NORM, UPLO
INTEGER INFO, N
DOUBLE PRECISION RCOND
DOUBLE PRECISION RWORK( * )
COMPLEX*16 AP( * ), WORK( * )
ZTPCON estimates the reciprocal of the condition number of a packed
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.
AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in a
linear array. The j-th column of A is stored in the array AP as
follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. If
DIAG = 'U', the diagonal elements of A are not referenced and are
assumed to be 1.
Page 1
ZTPCON(3F) ZTPCON(3F)
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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