SRC/zlangt.f(3)

💅 NAME

okay so welcome to SRC/zlangt.f(3), bestie — this page lives in the Library Functions Manual, and the main character is zlangt. 💖

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🦋 SYNOPSIS

• double precision function zlangt (norm, n, dl, d, du) — ZLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.

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✨ Function/Subroutine Documentation

double precision function zlangt (character norm, integer n, complex*16,
       dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension(
       * ) du)

The official one-liner is literally: ZLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix. periodt ✨

🎀 Purpose

ZLANGT returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex tridiagonal matrix A. iykyk 💅

🌸 Returns

The function gives you back ZLANGT, and here's the exact mapping, no cap:

ZLANGT = ( max(abs(A(i,j))), NORM = 'M' or 'm'
          (
          ( norm1(A),         NORM = '1', 'O' or 'o'
          (
          ( normI(A),         NORM = 'I' or 'i'
          (
          ( normF(A),         NORM = 'F', 'f', 'E' or 'e'

where  norm1  denotes the  one norm of a matrix (maximum column sum),
normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
normF  denotes the  Frobenius norm of a matrix (square root of sum of
squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.

not me pointing out that max(abs(A(i,j))) is not a consistent matrix norm — that's straight from the source, bestie 💀

🧚 Parameters

💖 NORM

NORM is CHARACTER*1 and specifies the value to be returned in ZLANGT as described above. vibe check passed 🫶

💖 N

N is INTEGER: the order of the matrix A. N >= 0. When N = 0, ZLANGT is set to zero. zero case handled, slay ✨

💖 DL

DL is COMPLEX*16 array, dimension (N-1) — the (n-1) sub-diagonal elements of A. 🦋

💖 D

D is COMPLEX*16 array, dimension (N) — the diagonal elements of A. 🌸

💖 DU

DU is COMPLEX*16 array, dimension (N-1) — the (n-1) super-diagonal elements of A. 🎀

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👑 Author

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

Definition at line 105 of file zlangt.f. 👑

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🌈 Author

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