gtcon(3)

📦

version 3.12.1 · 9 versions

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3.12.1 · ubuntu stonking
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3.12.1 · debian trixie

okay bestie, welcome to gtcon(3) from the Library Functions Manual 💅 This page is all about condition number estimates, and it comes in four flavors — c, d, s, and z — because of course it does. Let’s get into it ✨

🌸 NAME 🌸

gtcon — gtcon: condition number estimate 🎀

✨ SYNOPSIS ✨

🦋 Functions 🦋

subroutine cgtcon (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work,
    info)
    CGTCON
subroutine dgtcon (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work,
    iwork, info)
    DGTCON
subroutine sgtcon (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work,
    iwork, info)
    SGTCON
subroutine zgtcon (norm, n, dl, d, du, du2, ipiv, anorm, rcond, work,
    info)
    ZGTCON

🌈 Detailed Description 🌈

This part is literally just the doorway into the function docs, bestie — no extra side quest here 💫

💖 Function Documentation 💖

🦋 cgtcon / CGTCON 🦋

subroutine cgtcon (character norm, integer n, complex, dimension( * ) dl,
    complex, dimension( * ) d, complex, dimension( * ) du, complex,
    dimension( * ) du2, integer, dimension( * ) ipiv, real anorm, real
    rcond, complex, dimension( * ) work, integer info)

🎯 Purpose

CGTCON estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF.

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

NORM — is CHARACTER*1. It specifies whether the 1-norm condition number or the infinity-norm condition number is required:
- = '1' or 'O': 1-norm;
- = 'I': Infinity-norm.
N — is INTEGER. The order of the matrix A. N >= 0.
DL — is COMPLEX array, dimension (N-1). The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by CGTTRF.
D — is COMPLEX array, dimension (N). The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
DU — is COMPLEX array, dimension (N-1). The (n-1) elements of the first superdiagonal of U.
DU2 — is COMPLEX array, dimension (N-2). The (n-2) elements of the second superdiagonal of U.
IPIV — is INTEGER array, dimension (N). The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required.
ANORM — is REAL. If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A.
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 — is COMPLEX array, dimension (2*N).
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.

Definition at line 139 of file cgtcon.f. 📌

💜 dgtcon / DGTCON 💜

subroutine dgtcon (character norm, integer n, double precision, dimension( *
    ) dl, double precision, dimension( * ) d, double precision, dimension( *
    ) du, double precision, dimension( * ) du2, integer, dimension( * )
    ipiv, double precision anorm, double precision rcond, double precision,
    dimension( * ) work, integer, dimension( * ) iwork, integer info)

🎯 Purpose

DGTCON estimates the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by DGTTRF.

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

NORM — is CHARACTER*1. It specifies whether the 1-norm condition number or the infinity-norm condition number is required:
- = '1' or 'O': 1-norm;
- = 'I': Infinity-norm.
N — is INTEGER. The order of the matrix A. N >= 0.
DL — is DOUBLE PRECISION array, dimension (N-1). The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by DGTTRF.
D — is DOUBLE PRECISION array, dimension (N). The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
DU — is DOUBLE PRECISION array, dimension (N-1). The (n-1) elements of the first superdiagonal of U.
DU2 — is DOUBLE PRECISION array, dimension (N-2). The (n-2) elements of the second superdiagonal of U.
IPIV — is INTEGER array, dimension (N). The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required.
ANORM — is DOUBLE PRECISION. If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A.
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 — is DOUBLE PRECISION array, dimension (2*N).
IWORK — is INTEGER array, dimension (N).
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.

Definition at line 144 of file dgtcon.f. 📌

🎀 sgtcon / SGTCON 🎀

subroutine sgtcon (character norm, integer n, real, dimension( * ) dl, real,
    dimension( * ) d, real, dimension( * ) du, real, dimension( * ) du2,
    integer, dimension( * ) ipiv, real anorm, real rcond, real, dimension( *
    ) work, integer, dimension( * ) iwork, integer info)

🎯 Purpose

SGTCON estimates the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by SGTTRF.

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

NORM — is CHARACTER*1. It specifies whether the 1-norm condition number or the infinity-norm condition number is required:
- = '1' or 'O': 1-norm;
- = 'I': Infinity-norm.
N — is INTEGER. The order of the matrix A. N >= 0.
DL — is REAL array, dimension (N-1). The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by SGTTRF.
D — is REAL array, dimension (N). The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
DU — is REAL array, dimension (N-1). The (n-1) elements of the first superdiagonal of U.
DU2 — is REAL array, dimension (N-2). The (n-2) elements of the second superdiagonal of U.
IPIV — is INTEGER array, dimension (N). The pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required.
ANORM — is REAL. If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A.
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 — is REAL array, dimension (2*N).
IWORK — is INTEGER array, dimension (N).
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.

Definition at line 144 of file sgtcon.f. 📌

🦋 zgtcon / ZGTCON 🦋

subroutine zgtcon (character norm, integer n, complex*16, dimension( * ) dl,
    complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16,
    dimension( * ) du2, integer, dimension( * ) ipiv, double precision
    anorm, double precision rcond, complex*16, dimension( * ) work, integer
    info)

🎯 Purpose

ZGTCON estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF.

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

NORM — part 2 picks up right here, bestie; this is where part 1 ends 🫶
NORM is CHARACTER*1 — tells us which condition-number flavor we're serving: the 1-norm condition number or the infinity-norm condition number. The recipe:
- '1' or 'O': 1-norm;
- 'I': infinity-norm.
N is INTEGER — the order of matrix A. N >= 0, bestie, no negative-order nonsense.
DL is COMPLEX*16 array, dimension (N-1) — the (n-1) multipliers that define the matrix L from the LU factorization of A as computed by ZGTTRF. Slay, that's the lower-triangular tea.
D is COMPLEX*16 array, dimension (N) — the n diagonal elements of the upper triangular matrix U from the LU factorization of A.
DU is COMPLEX*16 array, dimension (N-1) — the (n-1) elements of the first superdiagonal of U.
DU2 is COMPLEX*16 array, dimension (N-2) — the (n-2) elements of the second superdiagonal of U.
IPIV is INTEGER array, dimension (N) — the pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required. No cap, that's the whole pivot story.
ANORM is DOUBLE PRECISION — if NORM = '1' or 'O', this is the 1-norm of the original matrix A. If NORM = 'I', it's the infinity-norm of the original matrix A.
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.
WORK is COMPLEX*16 array, dimension (2*N) — workspace, doing its lil behind-the-scenes thing. ✨
INFO is INTEGER — the vibe check:
- = 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 139 of file zgtcon.f.

🎀 Author

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