ZLANTR(3)

✨ NAME ✨

okay so this is ZLANTR(3), straight out of the LAPACK Library Functions Manual — yes, manual name folded in right here, cute little name tag and all. The page header path is /home/abui...RC/zlantr.f(3), and the official NAME line points at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zlantr.f. And what does it do? ZLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix. periodt. 💅

🦋 SYNOPSIS 🦋

🎀 Functions/Subroutines 🎀

double precision function ZLANTR (norm, uplo, diag, m, n, a, lda, work)

ZLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix. that's the whole assignment, bestie. ✨

🎀 Function/Subroutine Documentation 🎀

💖 double precision function ZLANTR 💖

double precision function ZLANTR (character norm, character uplo, character
    diag, integer m, integer n, complex*16, dimension( lda, * ) a, integer
    lda, double precision, dimension( * ) work)

ZLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix. iconic behavior, honestly. 💜

🌸 Purpose 🌸

okay so ZLANTR returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A. That's it, that's the purpose, no cap. 💖

🌈 Returns 🌈

The thing being returned is ZLANTR, and here's the exact mapping — do not come for me, I copied it character for character:

!>    ZLANTR = ( 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).

⚠️ important caveat: max(abs(A(i,j))) is not a consistent matrix norm. That's literally in the manual, bestie. 🫶

💜 Parameters 💜

• NORM — NORM is CHARACTER*1. Specifies the value to be returned in ZLANTR as described above. vibe selector, basically.
• UPLO — UPLO is CHARACTER*1. Specifies whether the matrix A is upper or lower trapezoidal.
  • = 'U': Upper trapezoidal
  • = 'L': Lower trapezoidal

Note that A is triangular instead of trapezoidal if M = N. 💅

• DIAG — DIAG is CHARACTER*1. Specifies whether or not the matrix A has unit diagonal.
  • = 'N': Non-unit diagonal
  • = 'U': Unit diagonal
• M — M is INTEGER. The number of rows of the matrix A. M >= 0, and if UPLO = 'U', M <= N. When M = 0, ZLANTR is set to zero.
• N — N is INTEGER. The number of columns of the matrix A. N >= 0, and if UPLO = 'L', N <= M. When N = 0, ZLANTR is set to zero.
• A — A is COMPLEX*16 array, dimension (LDA,N). The trapezoidal matrix A (A is triangular if M = N).
  • If UPLO = 'U', the leading m by n upper trapezoidal part of the array A contains the upper trapezoidal matrix, and the strictly lower triangular part of A is not referenced.
  • If UPLO = 'L', the leading m by n lower trapezoidal part of the array A contains the lower trapezoidal matrix, and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be one. 👀
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(M,1).
• WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= M when NORM = 'I'; otherwise, WORK is not referenced. that's the exact condition, bestie.

👑 Author 👑

The author squad for this one is:

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

📌 Definition at line 140 of file zlantr.f 📌

Definition at line 140 of file zlantr.f. yes, that's the exact line, bestie.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. So this second Author note is the auto-generated one, not a duplicate glitch. 💅

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cute sign-off time: source/version is LAPACK, Version 3.12.0, and the footer path is /home/abui...RC/zlantr.f(3). mwah, go slay your linear algebra homework. 💖✨