hecon_rook - {he,sy}con_rook: condition number estimate

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subroutinechecon_rook(characteruplo,integern,complex,dimension(lda,*)a,integerlda,integer,dimension(*)ipiv,realanorm,realrcond,complex,dimension(*)work,integerinfo)CHECON_ROOKestimatesthereciprocaloftheconditionnumberfortHEmatricesusingfactorizationobtainedwithoneoftheboundeddiagonalpivotingmethods(max2interchanges)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))). ParametersUPLO 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 subroutinecsycon_rook(characteruplo,integern,complex,dimension(lda,*)a,integerlda,integer,dimension(*)ipiv,realanorm,realrcond,complex,dimension(*)work,integerinfo)CSYCON_ROOKPurpose: 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))). ParametersUPLO 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 subroutinedsycon_rook(characteruplo,integern,doubleprecision,dimension(lda,*)a,integerlda,integer,dimension(*)ipiv,doubleprecisionanorm,doubleprecisionrcond,doubleprecision,dimension(*)work,integer,dimension(*)iwork,integerinfo)DSYCON_ROOKPurpose: 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))). ParametersUPLO 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 subroutinessycon_rook(characteruplo,integern,real,dimension(lda,*)a,integerlda,integer,dimension(*)ipiv,realanorm,realrcond,real,dimension(*)work,integer,dimension(*)iwork,integerinfo)SSYCON_ROOKPurpose: 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))). ParametersUPLO 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 subroutinezhecon_rook(characteruplo,integern,complex*16,dimension(lda,*)a,integerlda,integer,dimension(*)ipiv,doubleprecisionanorm,doubleprecisionrcond,complex*16,dimension(*)work,integerinfo)ZHECON_ROOKestimatesthereciprocaloftheconditionnumberfortHEmatricesusingfactorizationobtainedwithoneoftheboundeddiagonalpivotingmethods(max2interchanges)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))). ParametersUPLO 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 subroutinezsycon_rook(characteruplo,integern,complex*16,dimension(lda,*)a,integerlda,integer,dimension(*)ipiv,doubleprecisionanorm,doubleprecisionrcond,complex*16,dimension(*)work,integerinfo)ZSYCON_ROOKPurpose: 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))). ParametersUPLO 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

hecon_rook - {he,sy}con_rook: condition number estimate

Functions subroutine checon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, info) CHECON_ROOKestimatesthereciprocaloftheconditionnumberfortHEmatricesusingfactorizationobtainedwithoneoftheboundeddiagonalpivotingmethods(max2interchanges) 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_ROOKestimatesthereciprocaloftheconditionnumberfortHEmatricesusingfactorizationobtainedwithoneoftheboundeddiagonalpivotingmethods(max2interchanges) subroutine zsycon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, info) ZSYCON_ROOK