hpcon - {hp,sp}con: condition number estimate

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Thu Aug 7 2025 17:26:25 hpcon(3)

subroutinechpcon(characteruplo,integern,complex,dimension(*)ap,integer,dimension(*)ipiv,realanorm,realrcond,complex,dimension(*)work,integerinfo)CHPCONPurpose: CHPCON estimates the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF. 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. AP AP is COMPLEX array, dimension (N*(N+1)/2) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHPTRF, stored as a packed triangular matrix. IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CHPTRF. 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. subroutinecspcon(characteruplo,integern,complex,dimension(*)ap,integer,dimension(*)ipiv,realanorm,realrcond,complex,dimension(*)work,integerinfo)CSPCONPurpose: CSPCON estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF. 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. AP AP is COMPLEX array, dimension (N*(N+1)/2) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSPTRF, stored as a packed triangular matrix. IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CSPTRF. 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. subroutinedspcon(characteruplo,integern,doubleprecision,dimension(*)ap,integer,dimension(*)ipiv,doubleprecisionanorm,doubleprecisionrcond,doubleprecision,dimension(*)work,integer,dimension(*)iwork,integerinfo)DSPCONPurpose: DSPCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF. 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. AP AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSPTRF, stored as a packed triangular matrix. IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by DSPTRF. 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. subroutinesspcon(characteruplo,integern,real,dimension(*)ap,integer,dimension(*)ipiv,realanorm,realrcond,real,dimension(*)work,integer,dimension(*)iwork,integerinfo)SSPCONPurpose: SSPCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF. 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. AP AP is REAL array, dimension (N*(N+1)/2) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by SSPTRF, stored as a packed triangular matrix. IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by SSPTRF. 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. subroutinezhpcon(characteruplo,integern,complex*16,dimension(*)ap,integer,dimension(*)ipiv,doubleprecisionanorm,doubleprecisionrcond,complex*16,dimension(*)work,integerinfo)ZHPCONPurpose: ZHPCON estimates the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF. 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. AP AP is COMPLEX*16 array, dimension (N*(N+1)/2) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZHPTRF, stored as a packed triangular matrix. IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZHPTRF. 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. subroutinezspcon(characteruplo,integern,complex*16,dimension(*)ap,integer,dimension(*)ipiv,doubleprecisionanorm,doubleprecisionrcond,complex*16,dimension(*)work,integerinfo)ZSPCONPurpose: ZSPCON estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric packed matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF. 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. AP AP is COMPLEX*16 array, dimension (N*(N+1)/2) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZSPTRF, stored as a packed triangular matrix. IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZSPTRF. 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.

hpcon - {hp,sp}con: condition number estimate

Functions subroutine chpcon (uplo, n, ap, ipiv, anorm, rcond, work, info) CHPCON subroutine cspcon (uplo, n, ap, ipiv, anorm, rcond, work, info) CSPCON subroutine dspcon (uplo, n, ap, ipiv, anorm, rcond, work, iwork, info) DSPCON subroutine sspcon (uplo, n, ap, ipiv, anorm, rcond, work, iwork, info) SSPCON subroutine zhpcon (uplo, n, ap, ipiv, anorm, rcond, work, info) ZHPCON subroutine zspcon (uplo, n, ap, ipiv, anorm, rcond, work, info) ZSPCON