hpcon(3)

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version 3.12.1 · 9 versions
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💅 hpcon — Library Functions Manual, but make it cute 💅

okay so bestie, this is the hpcon(3) page from the Library Functions Manual, and it's literally the whole {hp,sp}con family — condition number estimation, six flavours, one vibe. It's long so we're splitting it, and this is part one. Buckle up 🎀

✨ NAME ✨

hpcon — {hp,sp}con: condition number estimate. that's it, that's the name, and yes they're all bundled together, iykyk 💖

✨ SYNOPSIS ✨

🌸 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

six little icons, one per precision/type taste test 💅 note the two extra iwork besties on dspcon and sspcon — they're the only ones who need an integer workspace, and we love them for it.

🦋 Detailed Description 🦋

bestie there is literally nothing under this heading in the original. heading only. no text. it's giving minimalism, it's giving "the void stared back" 💀 so we move on, no cap.

🌈 Function Documentation 🌈

💜 chpcon 💜

subroutine chpcon (character uplo, integer n, complex, dimension( * ) ap,
    integer, dimension( * ) ipiv, real anorm, real rcond, complex,
    dimension( * ) work, integer info)

CHPCON

Purpose

okay so 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))). math but make it fashion ✨

Parameters

  • UPLO — 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 — INTEGER. the order of the matrix A. N >= 0.
  • AP — 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 — INTEGER array, dimension (N). details of the interchanges and the block structure of D as determined by CHPTRF.
  • ANORM — REAL. the 1-norm of the original matrix A.
  • RCOND — 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 — COMPLEX array, dimension (2*N).
  • INFO — 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.

Definition at line 117 of file chpcon.f.

💖 cspcon 💖

subroutine cspcon (character uplo, integer n, complex, dimension( * ) ap,
    integer, dimension( * ) ipiv, real anorm, real rcond, complex,
    dimension( * ) work, integer info)

CSPCON

Purpose

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))). same energy, different transpose flag 🫶

⚠️ notice: **T, not **H — this is the symmetric one, bestie, don't mix her up with chpcon.

Parameters

  • UPLO — 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 — INTEGER. the order of the matrix A. N >= 0.
  • AP — 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 — INTEGER array, dimension (N). details of the interchanges and the block structure of D as determined by CSPTRF.
  • ANORM — REAL. the 1-norm of the original matrix A.
  • RCOND — 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 — COMPLEX array, dimension (2*N).
  • INFO — 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.

Definition at line 117 of file cspcon.f.

🔥 dspcon 🔥

subroutine dspcon (character uplo, integer n, double precision, dimension( *
    ) ap, integer, dimension( * ) ipiv, double precision anorm, double
    precision rcond, double precision, dimension( * ) work, integer,
    dimension( * ) iwork, integer info)

DSPCON

Purpose

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))). double the precision, double the icon behaviour 💅

Parameters

  • UPLO — 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 — INTEGER. the order of the matrix A. N >= 0.
  • AP — 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 — INTEGER array, dimension (N). details of the interchanges and the block structure of D as determined by DSPTRF.
  • ANORM — DOUBLE PRECISION. the 1-norm of the original matrix A.
  • RCOND — 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 — DOUBLE PRECISION array, dimension (2*N).
  • IWORK — INTEGER array, dimension (N).
  • INFO — 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.

Definition at line 123 of file dspcon.f.

🌸 sspcon 🌸

subroutine sspcon (character uplo, integer n, real, dimension( * ) ap,
    integer, dimension( * ) ipiv, real anorm, real rcond, real, dimension( *
    ) work, integer, dimension( * ) iwork, integer info)

SSPCON

Purpose

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))). the single-precision sibling, she ate 💅

Parameters

  • UPLO — 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 — INTEGER. the order of the matrix A. N >= 0.
  • AP — 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 — INTEGER array, dimension (N). details of the interchanges and the block structure of D as determined by SSPTRF.
  • ANORM — REAL. the 1-norm of the original matrix A.
  • RCOND — 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 — REAL array, dimension (2*N).
  • IWORK — INTEGER array, dimension (N).
  • INFO — 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.

Definition at line 123 of file sspcon.f.

🧚 zhpcon 🧚

subroutine zhpcon (character uplo, integer n, complex*16, dimension( * ) ap,
    integer, dimension( * ) ipiv, double precision anorm, double precision
    rcond, complex*16, dimension( * ) work, integer info)

ZHPCON

Purpose

🫶 and this is exactly where part one runs out, bestie — ZHPCON's purpose text starts right here and carries on into part two. no spoilers, no summing up, just vibes and a cliffhanger 🎀

so bestie, ZHPCON is literally the vibe-check for how close your complex Hermitian packed matrix A is to being singular 😭 it estimates the reciprocal of the condition number using the factorization A = U*D*U**H or A = L*D*L**H — and that factorization is the one computed by ZHPTRF, okay?? ✨ An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). no cap, that's the whole formula 💅

Parameters

  • UPLO — UPLO is CHARACTER*1 and it tells you whether the factorization details are stored as an upper or lower triangular matrix. The values are: = 'U': Upper triangular, form is A = U*D*U**H; and = 'L': Lower triangular, form is A = L*D*L**H. 🫶
  • N — N is INTEGER, the order of matrix A. Constraint: N >= 0. periodt.
  • AP — AP is COMPLEX*16 array, dimension (N*(N+1)/2). It's the block diagonal matrix D plus the multipliers used to obtain the factor U or L as computed by ZHPTRF, stored as a packed triangular matrix. iconic storage fr.
  • IPIV — IPIV is INTEGER array, dimension (N). It holds the details of the interchanges and the block structure of D as determined by ZHPTRF. 🔥
  • ANORM — ANORM is DOUBLE PRECISION, specifically the 1-norm of the original matrix A. 💅
  • RCOND — RCOND is DOUBLE PRECISION, the reciprocal of the condition number of matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine. math bestie.
  • WORK — WORK is COMPLEX*16 array, dimension (2*N). 🎀
  • INFO — INFO is INTEGER. = 0: successful exit and < 0: if INFO = -i, the i-th argument had an illegal value. slay, no surprises.

Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

📍 Definition at line 117 of file zhpcon.f.

subroutine zspcon

   subroutine zspcon (character uplo, integer n, complex*16, dimension( * ) ap,
       integer, dimension( * ) ipiv, double precision anorm, double precision
       rcond, complex*16, dimension( * ) work, integer info)

ZSPCON

Purpose

okay so 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))). literally the same energy but symmetric, not Hermitian 💜

Parameters

  • UPLO — UPLO is CHARACTER*1, specifying whether the factorization details are stored as an upper or lower triangular matrix. Values: = 'U': Upper triangular, form is A = U*D*U**T; and = 'L': Lower triangular, form is A = L*D*L**T. 🦋
  • N — N is INTEGER, the order of matrix A. Constraint: N >= 0. yes bestie, nonnegative only.
  • AP — AP is COMPLEX*16 array, dimension (N*(N+1)/2). It's 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. 💀 packed and powerful.
  • 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 matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine. same formula, same drama.
  • WORK — WORK is COMPLEX*16 array, dimension (2*N). ⭐
  • INFO — INFO is INTEGER. = 0: successful exit and < 0: if INFO = -i, the i-th argument had an illegal value. iykyk.

Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

📍 Definition at line 117 of file zspcon.f.

Author

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mwah 💖 and the footer vibe is source/version/date realness: LAPACK, Version 3.12.0, hpcon(3). bye bestie, go estimate those condition numbers responsibly 🫶✨

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