lantr(3)

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💅 lantr(3) — Library Functions Manual 💅

okay bestie, welcome to lantr(3) — the page where triangular and trapezoidal matrices get their norm moment. no cap, this is the group chat for matrix norms. 💖

💖 NAME 💖

lantr — triangular matrix

✨ SYNOPSIS ✨

🌈 Functions 🌈

  • real function clantr (norm, uplo, diag, m, n, a, lda, work) — CLANTR returns the value of the 1-norm, the Frobenius norm, the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.
  • double precision function dlantr (norm, uplo, diag, m, n, a, lda, work) — DLANTR returns the value of the 1-norm, the Frobenius norm, the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.
  • real function slantr (norm, uplo, diag, m, n, a, lda, work) — SLANTR returns the value of the 1-norm, the Frobenius norm, the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.
  • double precision function zlantr (norm, uplo, diag, m, n, a, lda, work) — ZLANTR returns the value of the 1-norm, the Frobenius norm, the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.

🧚 Detailed Description 🧚

scroll down, bestie — the function-by-function tea is right below. 🫶

💜 Function 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, the Frobenius norm, the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix. iconic behavior, honestly. ✨

🎀 Purpose 🎀

CLANTR returns the value of the one norm, the Frobenius norm, the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A. lowkey the whole point. 💅

🌟 Returns 🌟

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). note that max(abs(A(i,j))) is not a consistent matrix norm. periodt. 💀

🎁 Parameters 🎁

  • NORM — NORM is CHARACTER*1. Specifies the value to be returned in CLANTR as described above.
  • UPLO — UPLO is CHARACTER*1. Specifies whether 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 matrix A has unit diagonal. = 'N': Non-unit diagonal. = 'U': Unit diagonal.
  • M — M is INTEGER. The number of rows of matrix A. M >= 0, and if UPLO = 'U', M <= N. When M = 0, CLANTR is set to zero.
  • N — N is INTEGER. The number of columns of matrix A. N >= 0, and if UPLO = 'L', N <= M. When N = 0, CLANTR is set to zero.
  • A — 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 — LDA is INTEGER. The leading dimension of the array A. LDA >= max(M,1).
  • WORK — 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.

🦋 double precision function dlantr (character norm, character uplo, character diag, integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work) 🦋

DLANTR returns the value of the 1-norm, the Frobenius norm, the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix. double precision edition, obviously. 💖

🎀 Purpose 🎀

DLANTR returns the value of the one norm, the Frobenius norm, the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A. yes bestie, same energy, different precision. ✨

🌟 Returns 🌟

DLANTR = ( 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). and again: max(abs(A(i,j))) is not a consistent matrix norm. don't forget it. 💅

🎁 Parameters 🎁

  • NORM — NORM is CHARACTER*1. Specifies the value to be returned in DLANTR as described above.
  • UPLO — UPLO is CHARACTER*1. Specifies whether 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 matrix A has unit diagonal. = 'N': Non-unit diagonal. = 'U': Unit diagonal.
  • M — M is INTEGER. The number of rows of matrix A. M >= 0, and if UPLO = 'U', M <= N. When M = 0, DLANTR is set to zero.
  • N — N is INTEGER. The number of columns of matrix A. N >= 0, and if UPLO = 'L', N <= M. When N = 0, DLANTR is set to zero.
  • A — A is DOUBLE PRECISION 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.

🌸 Author 🌸

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

Definition at line 139 of file dlantr.f.

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

SLANTR returns the value of the 1-norm, the Frobenius norm, the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix. the real-real one, slay. 🌸

🎀 Purpose 🎀

SLANTR returns the value of the one norm, the Frobenius norm, the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A. no cap. ✨

🌟 Returns 🌟

SLANTR = ( 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). and yes, max(abs(A(i,j))) is not a consistent matrix norm. iykyk. 💅

🎁 Parameters 🎁

  • NORM — NORM is CHARACTER*1. Specifies the value to be returned in SLANTR as described above.
  • UPLO — UPLO is CHARACTER*1. Specifies whether 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 matrix A has unit diagonal. = 'N': Non-unit diagonal. = 'U': Unit diagonal.
  • M — M is INTEGER. The number of rows of matrix A. M >= 0, and if UPLO = 'U', M <= N. When M = 0, SLANTR is set to zero.
  • N — N is INTEGER. The number of columns of matrix A. N >= 0, and if UPLO = 'L', N <= M. When N = 0, SLANTR is set to zero.
  • A
  • A — REAL array, dimension (LDA,N). This is your trapezoidal matrix, bestie (and like, she's triangular if M = N — glow-up, honestly 🔺). If UPLO = 'U', the leading m by n upper trapezoidal part of the array A holds the upper trapezoidal matrix, and the strictly lower triangular part of A is not referenced — nobody's looking at her, she's off duty 💅. If UPLO = 'L', then the leading m by n lower trapezoidal part of A holds the lower trapezoidal matrix, and the strictly upper triangular part is not referenced. Also lowkey important: when DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be one — the vibes are implied, no cap 🫶.
  • LDA — INTEGER, the leading dimension of the array A. Rule of the day: LDA >= max(M,1). That's the whole assignment, periodt ✨.
  • WORK — REAL array, dimension (MAX(1,LWORK)), where LWORK >= M when NORM = 'I'. Otherwise, WORK is not referenced — she's not even invited to the function, honestly 😭.

👑 Author

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

📍 Definition

At line 139 of file slantr.f. Like, that's literally where she lives 🏠.

💜 zlantr — the double precision one, and yes she's complex

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. Four moods, one function. Versatile queen 👑.

🎯 Purpose

!>
!> 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.
!>

🌈 Returns

ZLANTR — and it comes in four flavours, pick your fighter:

!>
!>    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).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.
!>
⚠️ Heads up girlies: max(abs(A(i,j))) is not a consistent matrix norm. She's built different and she knows it 💀 — don't treat her like the other three.

🎀 Parameters

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

And note that A is triangular instead of trapezoidal if M = N — she switches labels depending on the crowd, iykyk 💅.

  • DIAG — CHARACTER*1. Specifies whether or not the matrix A has unit diagonal.
    • = 'N': Non-unit diagonal
    • = 'U': Unit diagonal
  • M — INTEGER, the number of rows of the matrix A. M >= 0, and if UPLO = 'U', then M <= N. When M = 0, ZLANTR is set to zero. Empty girlies get a zero, that's the rule 🌸.
  • N — INTEGER, the number of columns of the matrix A. N >= 0, and if UPLO = 'L', then N <= M. When N = 0, ZLANTR is set to zero. Same energy, different axis ✨.
  • A — COMPLEX*16 array, dimension (LDA,N). The trapezoidal matrix A (and again — 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 — she's not reading that part, it's giving "left on read" 🙈. If UPLO = 'L', the leading m by n lower trapezoidal part of A contains the lower trapezoidal matrix, and the strictly upper triangular part of A is not referenced. And note that when DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be one — assumed, not checked. Trust fall 🫶.
  • LDA — INTEGER, the leading dimension of the array A. LDA >= max(M,1). Non-negotiable ✋.
  • WORK — DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= M when NORM = 'I'. Otherwise, WORK is not referenced. She only shows up for the infinity norm gig, iconic behaviour honestly 😭🔥.

👑 Author

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

📍 Definition

At line 140 of file zlantr.f. Right next door to her single-precision sister, cute 🎀.

🌸 Author

Generated automatically by Doxygen for LAPACK from the source code. Not a human, just a very efficient little bot doing its thing 🤖💖.

And that's the whole page, bestie! This lil masterpiece comes to you courtesy of LAPACK, version 3.12.0, and it goes by lantr(3) down in the man page section — go forth and norm responsibly, ily, mwah 💋🌈⭐

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