tbcon(3)

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version 3.12.1 · 9 versions
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💖 NAME 💖 — tbcon(3) from the Library Functions Manual

Okay bestie, welcome to tbcon(3). This is the condition-number-estimate page, and it is lowkey a whole vibe. ✨

  • tbcon — tbcon: condition number estimate 🫶

🌈 SYNOPSIS 🌈

✨ Functions ✨

Here are the four subroutine besties, exactly as they show up:

subroutine ctbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work,
    rwork, info)
    CTBCON
subroutine dtbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work,
    iwork, info)
    DTBCON
subroutine stbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work,
    iwork, info)
    STBCON
subroutine ztbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work,
    rwork, info)
    ZTBCON

🦋 Detailed Description 🦋

✨ The original page literally just drops this heading here and then moves on — no extra prose under it. ✨

🔥 Function Documentation 🔥

Okay bestie, here come the four precision-flavored subroutines. Same math, different types. 💅

🌸 ctbcon — CTBCON 🌸

subroutine ctbcon (character norm, character uplo, character diag, integer
    n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real
    rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer
    info)

CTBCON

✨ Purpose ✨

Bestie, CTBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm. It computes the norm of A and gets an estimate for norm(inv(A)), then computes the reciprocal of the condition number as:

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

💅 Parameters 💅

  • NORM — this one is 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.
  • UPLO — this one is UPLO is CHARACTER*1:
    • = 'U': A is upper triangular;
    • = 'L': A is lower triangular.
  • DIAG — this one is DIAG is CHARACTER*1:
    • = 'N': A is non-unit triangular;
    • = 'U': A is unit triangular.
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • KD — KD is INTEGER. The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.
  • AB — AB is COMPLEX array, dimension (LDAB,N). It's the upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.

  • LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
  • RCOND — RCOND is REAL. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
  • WORK — WORK is COMPLEX array, dimension (2*N).
  • RWORK — RWORK is REAL 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.

Definition at line 141 of file ctbcon.f.

🌺 dtbcon — DTBCON 🌺

subroutine dtbcon (character norm, character uplo, character diag, integer
    n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab,
    double precision rcond, double precision, dimension( * ) work, integer,
    dimension( * ) iwork, integer info)

DTBCON

✨ Purpose ✨

Bestie, DTBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm. It computes the norm of A and gets an estimate for norm(inv(A)), then computes the reciprocal of the condition number as:

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

💅 Parameters 💅

  • NORM — this one is 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.
  • UPLO — this one is UPLO is CHARACTER*1:
    • = 'U': A is upper triangular;
    • = 'L': A is lower triangular.
  • DIAG — this one is DIAG is CHARACTER*1:
    • = 'N': A is non-unit triangular;
    • = 'U': A is unit triangular.
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • KD — KD is INTEGER. The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.
  • AB — AB is DOUBLE PRECISION array, dimension (LDAB,N). It's the upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.

  • LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
  • RCOND — RCOND is DOUBLE PRECISION. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
  • WORK — WORK is DOUBLE PRECISION array, dimension (3*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.

Definition at line 141 of file dtbcon.f.

🌼 stbcon — STBCON 🌼

subroutine stbcon (character norm, character uplo, character diag, integer
    n, integer kd, real, dimension( ldab, * ) ab, integer ldab, real rcond,
    real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

STBCON

✨ Purpose ✨

Bestie, STBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm. It computes the norm of A and gets an estimate for norm(inv(A)), then computes the reciprocal of the condition number as:

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

💅 Parameters 💅

  • NORM — this one is 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.
  • UPLO — this one is UPLO is CHARACTER*1:
    • = 'U': A is upper triangular;
    • = 'L': A is lower triangular.
  • DIAG — this one is DIAG is CHARACTER*1:
    • = 'N': A is non-unit triangular;
    • = 'U': A is unit triangular.
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • KD — KD is INTEGER. The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.
  • AB — AB is REAL array, dimension (LDAB,N). It's the upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.

  • LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
  • RCOND — RCOND is REAL. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
  • WORK — WORK is REAL array, dimension (3*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.

Definition at line 141 of file stbcon.f.

🌟 ztbcon — ZTBCON 🌟

subroutine ztbcon (character norm, character uplo, character diag, integer
    n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab, double
    precision rcond, complex*16, dimension( * ) work, double precision,
    dimension( * ) rwork, integer info)

ZTBCON

✨ Purpose ✨

Bestie, ZTBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm. It computes the norm of A and gets an estimate for norm(inv(A)), then computes the reciprocal of the condition number as:

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

💅 Parameters 💅

  • NORM — this one is 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.
  • UPLO — this one is UPLO is CHARACTER*1:
    • = 'U': A is upper triangular;
    • = 'L': A is lower triangular.
  • DIAG —
  • DIAG — it’s CHARACTER*1, and it’s giving triangular-type realness: = 'N' means A is non-unit triangular; = 'U' means A is unit triangular. That’s the whole vibe, bestie 💅
  • N — INTEGER. The order of the matrix A. Constraint: N >= 0. No cap.
  • KD — INTEGER. The number of superdiagonals or subdiagonals of the triangular band matrix A. Constraint: KD >= 0. Slay.
  • AB — COMPLEX*16 array, dimension (LDAB,N). The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:
if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1. This is the storage tea ☕ — memorize the indexing, iykyk.

  • LDAB — INTEGER. The leading dimension of the array AB. Constraint: LDAB >= KD+1. Respect the leading dimension, periodt.
  • RCOND — DOUBLE PRECISION. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))). Math but make it fashion 💜
  • WORK — COMPLEX*16 array, dimension (2*N). That’s the work array, bestie.
  • RWORK — DOUBLE PRECISION array, dimension (N). Real work, real values.
  • INFO — INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. Read that again if you need to — negative INFO is the callout.

👑 Author

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

Definition at line 141 of file ztbcon.f.

🪄 Author

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That’s the whole tbcon(3) situation, bestie 🫶 — source/version/date footer vibe: LAPACK Version 3.12.0, tbcon(3). That’s the footer line, and we’re not inventing extra lore. 💖

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