langt(3)

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version 3.12.1 · 9 versions
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💅 langt(3) — general matrix, tridiagonal 💅

okay bestie, this is langt(3) from the Library Functions Manual, and its whole name is literally langt - langt: general matrix, tridiagonal. It’s the tridiagonal norm squad: four functions that measure a general tridiagonal matrix. no cap. 🫶

✨ NAME ✨

  • langt — langt: general matrix, tridiagonal

🌸 SYNOPSIS 🌸

Functions

  • real function clangt (norm, n, dl, d, du) — CLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.
  • double precision function dlangt (norm, n, dl, d, du) — DLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.
  • real function slangt (norm, n, dl, d, du) — SLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.
  • double precision function zlangt (norm, n, dl, d, du) — ZLANGT returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of a general tridiagonal matrix.

🫶 Detailed Description 🫶

Bestie, this is the map. The full function-by-function lore lives right below in Function Documentation, and every signature, parameter, author block, and source line is down there. 🎀

💖 Function Documentation 💖

🌸 real function clangt (character norm, integer n, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du) 🌸

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

Purpose

!>
!> CLANGT  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 tridiagonal matrix A.
!>

Returns

CLANGT

!>
!>    CLANGT = ( 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 CLANGT as described above.
  • N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, CLANGT is set to zero.
  • DL — DL is COMPLEX array, dimension (N-1). The (n-1) sub-diagonal elements of A.
  • D — D is COMPLEX array, dimension (N). The diagonal elements of A.
  • DU — DU is COMPLEX array, dimension (N-1). The (n-1) super-diagonal elements of A.

Author

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

Definition

Definition at line 105 of file clangt.f.

🌈 double precision function dlangt (character norm, integer n, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du) 🌈

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

Purpose

!>
!> DLANGT  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 tridiagonal matrix A.
!>

Returns

DLANGT

!>
!>    DLANGT = ( 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 DLANGT as described above.
  • N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, DLANGT is set to zero.
  • DL — DL is DOUBLE PRECISION array, dimension (N-1). The (n-1) sub-diagonal elements of A.
  • D — D is DOUBLE PRECISION array, dimension (N). The diagonal elements of A.
  • DU — DU is DOUBLE PRECISION array, dimension (N-1). The (n-1) super-diagonal elements of A.

Author

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

Definition

Definition at line 105 of file dlangt.f.

🦋 real function slangt (character norm, integer n, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du) 🦋

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

Purpose

!>
!> SLANGT  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 tridiagonal matrix A.
!>

Returns

SLANGT

!>
!>    SLANGT = ( 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 SLANGT as described above.
  • N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, SLANGT is set to zero.
  • DL — DL is REAL array, dimension (N-1). The (n-1) sub-diagonal elements of A.
  • D — D is REAL array, dimension (N). The diagonal elements of A.
  • DU — DU is REAL array, dimension (N-1). The (n-1) super-diagonal elements of A.

Author

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

Definition

Definition at line 105 of file slangt.f.

💜 double precision function zlangt (character norm, integer n, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du) 💜

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

Purpose

!>
!> ZLANGT  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 tridiagonal matrix A.
!>

Returns

ZLANGT

!>
!>    ZLANGT = ( 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 ZLANGT as described above.
  • N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, ZLANGT is set to zero.
  • DL — DL is COMPLEX*16 array, dimension (N-1). The (n-1) sub-diagonal elements of A.
  • D — D is COMPLEX*16 array, dimension (N). The diagonal elements of A.
  • DU — DU is COMPLEX*16 array, dimension (N-1). The (n-1) super-diagonal elements of A.

Author

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

Definition

Definition at line 105 of file zlangt.f.

👑 Author 👑

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