gecon(3) Library Functions Manual gecon(3) NAME gecon - gecon: condition number estimate SYNOPSIS Functions subroutine cgecon (norm, n, a, lda, anorm, rcond, work, rwork, info) CGECON subroutine dgecon (norm, n, a, lda, anorm, rcond, work, iwork, info) DGECON subroutine sgecon (norm, n, a, lda, anorm, rcond, work, iwork, info) SGECON subroutine zgecon (norm, n, a, lda, anorm, rcond, work, rwork, info) ZGECON Detailed Description Function Documentation subroutine cgecon (character norm, integer n, complex, dimension( lda, * ) a, integer lda, real anorm, real rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer info) CGECON Purpose: CGECON estimates the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by CGETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). Parameters NORM NORM is CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm. N N is INTEGER The order of the matrix A. N >= 0. A A is COMPLEX array, dimension (LDA,N) The factors L and U from the factorization A = P*L*U as computed by CGETRF. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). ANORM ANORM is REAL If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A. RCOND RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK WORK is COMPLEX array, dimension (2*N) RWORK RWORK is REAL array, dimension (2*N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. NaNs are illegal values for ANORM, and they propagate to the output parameter RCOND. Infinity is illegal for ANORM, and it propagates to the output parameter RCOND as 0. = 1: if RCOND = NaN, or RCOND = Inf, or the computed norm of the inverse of A is 0. In the latter, RCOND = 0 is returned. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 130 of file cgecon.f. subroutine dgecon (character norm, integer n, double precision, dimension( lda, * ) a, integer lda, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info) DGECON Purpose: DGECON estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by DGETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). Parameters NORM NORM is CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm. N N is INTEGER The order of the matrix A. N >= 0. A A is DOUBLE PRECISION array, dimension (LDA,N) The factors L and U from the factorization A = P*L*U as computed by DGETRF. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). ANORM ANORM is DOUBLE PRECISION If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A. RCOND RCOND is DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK WORK is DOUBLE PRECISION array, dimension (4*N) IWORK IWORK is INTEGER array, dimension (N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. NaNs are illegal values for ANORM, and they propagate to the output parameter RCOND. Infinity is illegal for ANORM, and it propagates to the output parameter RCOND as 0. = 1: if RCOND = NaN, or RCOND = Inf, or the computed norm of the inverse of A is 0. In the latter, RCOND = 0 is returned. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 130 of file dgecon.f. subroutine sgecon (character norm, integer n, real, dimension( lda, * ) a, integer lda, real anorm, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info) SGECON Purpose: SGECON estimates the reciprocal of the condition number of a general real matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). Parameters NORM NORM is CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm. N N is INTEGER The order of the matrix A. N >= 0. A A is REAL array, dimension (LDA,N) The factors L and U from the factorization A = P*L*U as computed by SGETRF. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). ANORM ANORM is REAL If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A. RCOND RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK WORK is REAL array, dimension (4*N) IWORK IWORK is INTEGER array, dimension (N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. NaNs are illegal values for ANORM, and they propagate to the output parameter RCOND. Infinity is illegal for ANORM, and it propagates to the output parameter RCOND as 0. = 1: if RCOND = NaN, or RCOND = Inf, or the computed norm of the inverse of A is 0. In the latter, RCOND = 0 is returned. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 130 of file sgecon.f. subroutine zgecon (character norm, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision anorm, double precision rcond, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info) ZGECON Purpose: ZGECON estimates the reciprocal of the condition number of a general complex matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGETRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). Parameters NORM NORM is CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm. N N is INTEGER The order of the matrix A. N >= 0. A A is COMPLEX*16 array, dimension (LDA,N) The factors L and U from the factorization A = P*L*U as computed by ZGETRF. LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). ANORM ANORM is DOUBLE PRECISION If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A. RCOND RCOND is DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). WORK WORK is COMPLEX*16 array, dimension (2*N) RWORK RWORK is DOUBLE PRECISION array, dimension (2*N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. NaNs are illegal values for ANORM, and they propagate to the output parameter RCOND. Infinity is illegal for ANORM, and it propagates to the output parameter RCOND as 0. = 1: if RCOND = NaN, or RCOND = Inf, or the computed norm of the inverse of A is 0. In the latter, RCOND = 0 is returned. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 130 of file zgecon.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 gecon(3)