ZLANTB(3)

💅 ZLANTB(3)

okay bestie, welcome to the ZLANTB(3) glow-up 💖 this page is from the Library Functions Manual, and it's all about a double precision function named ZLANTB that does norm stuff on a triangular band matrix. no cap, it's giving “linear algebra but make it cute.” ✨

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🌸 NAME

the file this page is named for is:

/home/abuild/rpmbuild/BUILD/lapack-
static-3.12.0-build/lapack-3.12.0/SRC/zlantb.f

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✨ SYNOPSIS

Functions/Subroutines

here's the function vibe:

double precision function ZLANTB (norm, uplo, diag, n, k, ab, ldab,
    work)

and what it does, fr:

ZLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.

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🫶 Function/Subroutine Documentation

full signature, exactly:

double precision function ZLANTB (character norm, character uplo, character
    diag, integer n, integer k, complex*16, dimension( ldab, * ) ab, integer
    ldab, double precision, dimension( * ) work)

same energy as above: ZLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix. iconic. 💅

🎀 Purpose

ZLANTB returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals. yes bestie, that's the whole assignment. ✨

⭐ Returns

ZLANTB returns this whole norm menu:

!>
!>    ZLANTB = ( 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.
!>

so: norm1 is the one norm of a matrix (maximum column sum), normI is the infinity norm of a matrix (maximum row sum), and normF is 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. periodt. 💀

🦋 Parameters

NORM

• NORM is CHARACTER*1. it specifies the value to be returned in ZLANTB as described above. ✨

UPLO

• UPLO is CHARACTER*1. it says whether the matrix A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular

DIAG

• DIAG is CHARACTER*1. it says whether or not the matrix A is unit triangular.
  • = 'N': Non-unit triangular
  • = 'U': Unit triangular

N

• N is INTEGER. it's the order of the matrix A. N >= 0. when N = 0, ZLANTB is set to zero. okay math bestie, we see you. 🎀

K

• K is INTEGER. it's the number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals of the matrix A if UPLO = 'L'. K >= 0. slay that band structure. 💅

AB

• AB is COMPLEX*16 array, dimension (LDAB,N). it's the upper or lower triangular band matrix A, stored in the first k+1 rows of AB. the j-th column of A is stored in the j-th column of the array AB as follows:

if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).

• note that when DIAG = 'U', the elements of the array AB corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one. lowkey important. 🫶

LDAB

• LDAB is INTEGER. it's the leading dimension of the array AB. LDAB >= K+1. yes, respect the leading dimension. 👑

WORK

• WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. that's the tea. 🍓

👑 Author

credit where credit is due, bestie:

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

Definition at line 139 of file zlantb.f.

🧚 Author

this page was generated automatically by Doxygen for LAPACK from the source code. yes, Doxygen did that. 💅

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and that's the tea 🫶 the footer wraps it with LAPACK, Version 3.12.0, and /home/abui...RC/zlantb.f(3). no separate date is shown in the footer, just the version and source path, bestie. 💖