lange(3)

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version 3.12.1 · 9 versions
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🎀 lange(3) 🎀

okay bestie, this is lange(3) from the Library Functions Manual — the general-matrix norm girlies are all here, and they are serving 💅

✨ NAME ✨

lange - lange: general matrix

🦋 SYNOPSIS 🦋

🌈 Functions 🌈

  • real function clange (norm, m, n, a, lda, work)
    • CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.
  • double precision function dlange (norm, m, n, a, lda, work)
    • DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.
  • real function slange (norm, m, n, a, lda, work)
    • SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.
  • double precision function zlange (norm, m, n, a, lda, work)
    • ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.

💅 DETAILED DESCRIPTION 💅

This page is lowkey just the lange family lore drop, and then we get straight into the function docs. No extra side quests. 🫶

🧚 FUNCTION DOCUMENTATION 🧚

🌸 real function clange (character norm, integer m, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) work) 🌸

CLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.

💖 Purpose 💖

!>
!> CLANGE  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 matrix A.
!>

⭐ Returns ⭐

CLANGE

!>
!>    CLANGE = ( 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.
!>

🎀 Parameters 🎀

  • NORM — NORM is CHARACTER*1; specifies the value to be returned in CLANGE as described above.
  • M — M is INTEGER; the number of rows of the matrix A. M >= 0. When M = 0, CLANGE is set to zero.
  • N — N is INTEGER; the number of columns of the matrix A. N >= 0. When N = 0, CLANGE is set to zero.
  • A — A is COMPLEX array, dimension (LDA,N); the m by n matrix A.
  • 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 114 of file clange.f.

🌸 double precision function dlange (character norm, integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work) 🌸

DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.

💖 Purpose 💖

!>
!> DLANGE  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> real matrix A.
!>

⭐ Returns ⭐

DLANGE

!>
!>    DLANGE = ( 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.
!>

🎀 Parameters 🎀

  • NORM — NORM is CHARACTER*1; specifies the value to be returned in DLANGE as described above.
  • M — M is INTEGER; the number of rows of the matrix A. M >= 0. When M = 0, DLANGE is set to zero.
  • N — N is INTEGER; the number of columns of the matrix A. N >= 0. When N = 0, DLANGE is set to zero.
  • A — A is DOUBLE PRECISION array, dimension (LDA,N); the m by n matrix A.
  • 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 113 of file dlange.f.

🌸 real function slange (character norm, integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) work) 🌸

SLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.

💖 Purpose 💖

!>
!> SLANGE  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> real matrix A.
!>

⭐ Returns ⭐

SLANGE

!>
!>    SLANGE = ( 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.
!>

🎀 Parameters 🎀

  • NORM — NORM is CHARACTER*1; specifies the value to be returned in SLANGE as described above.
  • M — M is INTEGER; the number of rows of the matrix A. M >= 0. When M = 0, SLANGE is set to zero.
  • N — N is INTEGER; the number of columns of the matrix A. N >= 0. When N = 0, SLANGE is set to zero.
  • A — A is REAL array, dimension (LDA,N); the m by n matrix A.
  • 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 113 of file slange.f.

🌸 double precision function zlange (character norm, integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work) 🌸

ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general rectangular matrix.

💖 Purpose 💖

!>
!> ZLANGE  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 matrix A.
!>

⭐ Returns ⭐

ZLANGE

!>
!>    ZLANGE = ( 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.
!>

🎀 Parameters 🎀

  • NORM — NORM is CHARACTER*1; specifies the value to be returned in ZLANGE as described above.
  • M — M is INTEGER; the number of rows of the matrix A. M >= 0. When M = 0, ZLANGE is set to zero.
  • N — N is INTEGER; the number of columns of the matrix A. N >= 0. When N = 0, ZLANGE is set to zero.
  • A — A is COMPLEX*16 array, dimension (LDA,N); the m by n matrix A.
  • 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 114 of file zlange.f.

👑 AUTHOR 👑

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