--- name: "hecon_rook" section: "3" platform: "linux" package: "lapack-doc" version: "3.12.1-2" release: "Arch Linux 2026-11-01" platforms: ["linux"] url: "https://new.carta.tech/hecon_rook" --- # hecon\_rook(3) {he,sy}con\_rook: condition number estimate ## 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.