SRC/clantr.f(3)

💖 NAME 💖

SRC/clantr.f — okay bestie, this is the SRC/clantr.f(3) page from the Library Functions Manual, and it's all about the CLANTR function. 🎀

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

real function clantr (norm, uplo, diag, m, n, a, lda, work)

CLANTR 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. slay. 💅

🌸 Function/Subroutine Documentation 🌸

real function clantr (character norm, character uplo, character diag,
    integer m, integer n, complex, dimension( lda, * ) a, integer lda, real,
    dimension( * ) work)

CLANTR 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. no cap, that's the whole vibe. ✨

🎯 Purpose 🎯

okay so the purpose is: CLANTR 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 mission. 🫶

🌀 Returns 🌀

CLANTR comes back with one of these, depending on NORM:

CLANTR = ( 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). 💖

heads up, bestie: max(abs(A(i,j))) is not a consistent matrix norm. important.

🧸 Parameters 🧸

• NORM — is CHARACTER*1. Specifies the value to be returned in CLANTR as described above. 👑
• 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 — is CHARACTER*1. Specifies whether or not the matrix A has unit diagonal.
  • = 'N': Non-unit diagonal
  • = 'U': Unit diagonal
• M — is INTEGER. The number of rows of the matrix A. M >= 0, and if UPLO = 'U', M <= N. When M = 0, CLANTR is set to zero.
• N — is INTEGER. The number of columns of the matrix A. N >= 0, and if UPLO = 'L', N <= M. When N = 0, CLANTR is set to zero.
• A — is COMPLEX 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 — is INTEGER. The leading dimension of the array A. LDA >= max(M,1).
• WORK — is REAL array, dimension (MAX(1,LWORK)), where LWORK >= M when NORM = 'I'; otherwise, WORK is not referenced.

👑 Author 👑

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

Definition at line 140 of file clantr.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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xoxo, LAPACK Version 3.12.0 — page SRC/clantr.f(3) 💅✨ (no date in the footer, so I’m not inventing one).