hecon_rook(3) Library Functions Manual hecon_rook(3) NAME hecon_rook - {he,sy}con_rook: condition number estimate SYNOPSIS Functions subroutine checon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, info) CHECON_ROOK estimates the reciprocal of the condition number fort HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges) subroutine csycon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, info) CSYCON_ROOK subroutine dsycon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, iwork, info) DSYCON_ROOK subroutine ssycon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, iwork, info) SSYCON_ROOK subroutine zhecon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, info) ZHECON_ROOK estimates the reciprocal of the condition number fort HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges) subroutine zsycon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, info) ZSYCON_ROOK Detailed Description Function Documentation subroutine checon_rook (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real anorm, real rcond, complex, dimension( * ) work, integer info) CHECON_ROOK estimates the reciprocal of the condition number fort HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges) Purpose: !> !> CHECON_ROOK estimates the reciprocal of the condition number of a complex !> Hermitian matrix A using the factorization A = U*D*U**H or !> A = L*D*L**H computed by CHETRF_ROOK. !> !> An estimate is obtained for norm(inv(A)), and the reciprocal of the !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). !> Parameters UPLO !> UPLO is CHARACTER*1 !> Specifies whether the details of the factorization are stored !> as an upper or lower triangular matrix. !> = 'U': Upper triangular, form is A = U*D*U**H; !> = 'L': Lower triangular, form is A = L*D*L**H. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> A !> A is COMPLEX array, dimension (LDA,N) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by CHETRF_ROOK. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by CHETRF_ROOK. !> ANORM !> ANORM is REAL !> The 1-norm of the original matrix A. !> RCOND !> RCOND is REAL !> 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 !> WORK is COMPLEX array, dimension (2*N) !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: !> !> December 2016, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> !> Definition at line 137 of file checon_rook.f. subroutine csycon_rook (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real anorm, real rcond, complex, dimension( * ) work, integer info) CSYCON_ROOK Purpose: !> !> CSYCON_ROOK estimates the reciprocal of the condition number (in the !> 1-norm) of a complex symmetric matrix A using the factorization !> A = U*D*U**T or A = L*D*L**T computed by CSYTRF_ROOK. !> !> An estimate is obtained for norm(inv(A)), and the reciprocal of the !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). !> Parameters UPLO !> UPLO is CHARACTER*1 !> Specifies whether the details of the factorization are stored !> as an upper or lower triangular matrix. !> = 'U': Upper triangular, form is A = U*D*U**T; !> = 'L': Lower triangular, form is A = L*D*L**T. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> A !> A is COMPLEX array, dimension (LDA,N) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by CSYTRF_ROOK. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by CSYTRF_ROOK. !> ANORM !> ANORM is REAL !> The 1-norm of the original matrix A. !> RCOND !> RCOND is REAL !> 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 !> WORK is COMPLEX array, dimension (2*N) !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: !> !> April 2012, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> !> Definition at line 137 of file csycon_rook.f. subroutine dsycon_rook (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info) DSYCON_ROOK Purpose: !> !> DSYCON_ROOK estimates the reciprocal of the condition number (in the !> 1-norm) of a real symmetric matrix A using the factorization !> A = U*D*U**T or A = L*D*L**T computed by DSYTRF_ROOK. !> !> An estimate is obtained for norm(inv(A)), and the reciprocal of the !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). !> Parameters UPLO !> UPLO is CHARACTER*1 !> Specifies whether the details of the factorization are stored !> as an upper or lower triangular matrix. !> = 'U': Upper triangular, form is A = U*D*U**T; !> = 'L': Lower triangular, form is A = L*D*L**T. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> A !> A is DOUBLE PRECISION array, dimension (LDA,N) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by DSYTRF_ROOK. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by DSYTRF_ROOK. !> ANORM !> ANORM is DOUBLE PRECISION !> The 1-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/(ANORM * AINVNM), where AINVNM is an !> estimate of the 1-norm of inv(A) computed in this routine. !> WORK !> WORK is DOUBLE PRECISION array, dimension (2*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 !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: !> !> April 2012, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> !> Definition at line 142 of file dsycon_rook.f. subroutine ssycon_rook (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real anorm, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info) SSYCON_ROOK Purpose: !> !> SSYCON_ROOK estimates the reciprocal of the condition number (in the !> 1-norm) of a real symmetric matrix A using the factorization !> A = U*D*U**T or A = L*D*L**T computed by SSYTRF_ROOK. !> !> An estimate is obtained for norm(inv(A)), and the reciprocal of the !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). !> Parameters UPLO !> UPLO is CHARACTER*1 !> Specifies whether the details of the factorization are stored !> as an upper or lower triangular matrix. !> = 'U': Upper triangular, form is A = U*D*U**T; !> = 'L': Lower triangular, form is A = L*D*L**T. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> A !> A is REAL array, dimension (LDA,N) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by SSYTRF_ROOK. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by SSYTRF_ROOK. !> ANORM !> ANORM is REAL !> The 1-norm of the original matrix A. !> RCOND !> RCOND is REAL !> 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 !> WORK is REAL array, dimension (2*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 !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: !> !> December 2016, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> !> Definition at line 142 of file ssycon_rook.f. subroutine zhecon_rook (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex*16, dimension( * ) work, integer info) ZHECON_ROOK estimates the reciprocal of the condition number fort HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges) Purpose: !> !> ZHECON_ROOK estimates the reciprocal of the condition number of a complex !> Hermitian matrix A using the factorization A = U*D*U**H or !> A = L*D*L**H computed by CHETRF_ROOK. !> !> An estimate is obtained for norm(inv(A)), and the reciprocal of the !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). !> Parameters UPLO !> UPLO is CHARACTER*1 !> Specifies whether the details of the factorization are stored !> as an upper or lower triangular matrix. !> = 'U': Upper triangular, form is A = U*D*U**H; !> = 'L': Lower triangular, form is A = L*D*L**H. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> A !> A is COMPLEX*16 array, dimension (LDA,N) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by CHETRF_ROOK. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by CHETRF_ROOK. !> ANORM !> ANORM is DOUBLE PRECISION !> The 1-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/(ANORM * AINVNM), where AINVNM is an !> estimate of the 1-norm of inv(A) computed in this routine. !> WORK !> WORK is COMPLEX*16 array, dimension (2*N) !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: !> !> June 2017, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> !> Definition at line 137 of file zhecon_rook.f. subroutine zsycon_rook (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex*16, dimension( * ) work, integer info) ZSYCON_ROOK Purpose: !> !> ZSYCON_ROOK estimates the reciprocal of the condition number (in the !> 1-norm) of a complex symmetric matrix A using the factorization !> A = U*D*U**T or A = L*D*L**T computed by ZSYTRF_ROOK. !> !> An estimate is obtained for norm(inv(A)), and the reciprocal of the !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). !> Parameters UPLO !> UPLO is CHARACTER*1 !> Specifies whether the details of the factorization are stored !> as an upper or lower triangular matrix. !> = 'U': Upper triangular, form is A = U*D*U**T; !> = 'L': Lower triangular, form is A = L*D*L**T. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> A !> A is COMPLEX*16 array, dimension (LDA,N) !> The block diagonal matrix D and the multipliers used to !> obtain the factor U or L as computed by ZSYTRF_ROOK. !> LDA !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> IPIV !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D !> as determined by ZSYTRF_ROOK. !> ANORM !> ANORM is DOUBLE PRECISION !> The 1-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/(ANORM * AINVNM), where AINVNM is an !> estimate of the 1-norm of inv(A) computed in this routine. !> WORK !> WORK is COMPLEX*16 array, dimension (2*N) !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Contributors: !> !> December 2016, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> !> Definition at line 137 of file zsycon_rook.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 hecon_rook(3)