ptcon(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

💖 NAME 💖

ptcon — okay so this is the whole "condition number estimate" situation, bestie. That's the vibe. That's the whole thing.

✨ SYNOPSIS ✨

🎀 Functions

  • subroutine cptcon (n, d, e, anorm, rcond, rwork, info) — CPTCON
  • subroutine dptcon (n, d, e, anorm, rcond, work, info) — DPTCON
  • subroutine sptcon (n, d, e, anorm, rcond, work, info) — SPTCON
  • subroutine zptcon (n, d, e, anorm, rcond, rwork, info) — ZPTCON

🌸 Detailed Description 🌸

Like, the actual details are down in the function documentation below. That's where the main character energy lives. 🫶

🦋 Function Documentation 🦋

💅 subroutine cptcon (integer n, real, dimension( * ) d, complex, dimension( * ) e, real anorm, real rcond, real, dimension( * ) rwork, integer info)

subroutine cptcon (integer n, real, dimension( * ) d, complex, dimension( * ) e, real anorm, real rcond, real, dimension( * ) rwork, integer info)

CPTCON

🔥 Purpose:

Ok so CPTCON computes the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by CPTTRF. Iconic behavior, honestly.

Norm(inv(A)) is computed by a direct method, and the reciprocal of the condition number is computed as

RCOND = 1 / (ANORM * norm(inv(A))).

🍓 Parameters

  • N — N is INTEGER. It's the order of the matrix A. N >= 0. No negatives allowed, periodt.
  • D — D is REAL array, dimension (N). These are the n diagonal elements of the diagonal matrix D from the factorization of A, as computed by CPTTRF.
  • E — E is COMPLEX array, dimension (N-1). The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization of A, as computed by CPTTRF.
  • ANORM — ANORM is REAL. It's 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 the 1-norm of inv(A) computed in this routine.
  • RWORK — RWORK is REAL array, dimension (N). Just doing its little job. 🧚
  • 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.

⭐ Further Details:

The method used is described in Nicholas J. Higham, , SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.

Definition at line 118 of file cptcon.f.

💜 subroutine dptcon (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer info)

subroutine dptcon (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer info)

DPTCON

🔥 Purpose:

DPTCON computes the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by DPTTRF.

Norm(inv(A)) is computed by a direct method, and the reciprocal of the condition number is computed as

RCOND = 1 / (ANORM * norm(inv(A))).

🍓 Parameters

  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • D — D is DOUBLE PRECISION array, dimension (N). The n diagonal elements of the diagonal matrix D from the factorization of A, as computed by DPTTRF.
  • E — E is DOUBLE PRECISION array, dimension (N-1). The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization of A, as computed by DPTTRF. (Yes there are two spaces there, we don't gatekeep.)
  • 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 the 1-norm of inv(A) computed in this routine.
  • WORK — WORK is DOUBLE PRECISION array, dimension (N). Living its truth. ✨
  • 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.

⭐ Further Details:

The method used is described in Nicholas J. Higham, , SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.

Definition at line 117 of file dptcon.f.

💙 subroutine sptcon (integer n, real, dimension( * ) d, real, dimension( * ) e, real anorm, real rcond, real, dimension( * ) work, integer info)

subroutine sptcon (integer n, real, dimension( * ) d, real, dimension( * ) e, real anorm, real rcond, real, dimension( * ) work, integer info)

SPTCON

🔥 Purpose:

SPTCON computes the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite tridiagonal matrix using the factorization A = L*D*L**T or A = U**T*D*U computed by SPTTRF.

Norm(inv(A)) is computed by a direct method, and the reciprocal of the condition number is computed as

RCOND = 1 / (ANORM * norm(inv(A))).

🍓 Parameters

  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • D — D is REAL array, dimension (N). The n diagonal elements of the diagonal matrix D from the factorization of A, as computed by SPTTRF.
  • E — E is REAL array, dimension (N-1). The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization of A, as computed by SPTTRF.
  • 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 the 1-norm of inv(A) computed in this routine.
  • WORK — WORK is REAL array, dimension (N). Tiny little workspace bestie. 🌈
  • 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.

⭐ Further Details:

The method used is described in Nicholas J. Higham, , SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.

Definition at line 117 of file sptcon.f.

💚 subroutine zptcon (integer n, double precision, dimension( * ) d, complex*16, dimension( * ) e, double precision anorm, double precision rcond, double precision, dimension( * ) rwork, integer info)

subroutine zptcon (integer n, double precision, dimension( * ) d, complex*16, dimension( * ) e, double precision anorm, double precision rcond, double precision, dimension( * ) rwork, integer info)

ZPTCON

🔥 Purpose:

ZPTCON computes the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite tridiagonal matrix using the factorization A = L*D*L**H or A = U**H*D*U computed by ZPTTRF. Complex bestie hours fr fr. 💅

Norm(inv(A)) is computed by a direct method, and the reciprocal of the condition number is computed as

RCOND = 1 / (ANORM * norm(inv(A))).

🍓 Parameters

  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • D — D is DOUBLE PRECISION array, dimension (N). The n diagonal elements of the diagonal matrix D from the factorization of A, as computed by ZPTTRF.
  • E — E is COMPLEX*16 array, dimension (N-1). The (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization of A, as computed by ZPTTRF.
  • 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 the 1-norm of inv(A) computed in this routine.
  • RWORK — RWORK is DOUBLE PRECISION array, dimension (N). Carrying the real-valued workload so the complex girls can shine. 🦋
  • 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.

⭐ Further Details:

The method used is described in Nicholas J. Higham, , SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.

Definition at line 118 of file zptcon.f.

🧚 Author 🧚

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Ok that's the whole page bestie, no cap, every flag accounted for. 💖

LAPACK — Version 3.12.0 — ptcon(3) 🎀 That's the source, the version, and the date-ish, all wrapped up in a cute little sign-off. Mwah. 💋

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