lantb(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

✨ NAME ✨

okay so bestie, this is the lantb(3) manual page — and lantb is literally “triangular matrix, banded.” that’s the whole name, no cap. this page is the group chat for the clantb, dlantb, slantb, and zlantb girlies, and they all return a norm or the largest absolute value of a triangular band matrix. iconic behavior. 💅

🌸 SYNOPSIS 🌸

🫶 Functions

  • real function clantb (norm, uplo, diag, n, k, ab, ldab, work) — CLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.
  • double precision function dlantb (norm, uplo, diag, n, k, ab, ldab, work) — DLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.
  • real function slantb (norm, uplo, diag, n, k, ab, ldab, work) — SLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.
  • double precision function zlantb (norm, uplo, diag, n, k, ab, ldab, work) — ZLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.

🌈 Detailed Description 🌈

bestie, the source page just puts up the Detailed Description heading and then immediately slides into Function Documentation. no extra lore, no side quests. minimal queen behavior. 🎀

🎀 Function Documentation 🎀

💖 real function clantb (character norm, character uplo, character diag, integer n, integer k, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work)

CLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.

Purpose:

!>
!> CLANTB  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the element of  largest absolute value  of an
!> n by n triangular band matrix A,  with ( k + 1 ) diagonals.
!>

💖 Returns

CLANTB

!>
!>    CLANTB = ( 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 CLANTB as described
!>          above.
!>

UPLO

!>          UPLO is CHARACTER*1
!>          Specifies whether the matrix A is upper or lower triangular.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>

DIAG

!>          DIAG is CHARACTER*1
!>          Specifies whether or not the matrix A is unit triangular.
!>          = 'N':  Non-unit triangular
!>          = 'U':  Unit triangular
!>

N

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.  When N = 0, CLANTB is
!>          set to zero.
!>

K

!>          K is INTEGER
!>          The number of super-diagonals of the matrix A if UPLO = 'U',
!>          or the number of sub-diagonals of the matrix A if UPLO = 'L'.
!>          K >= 0.
!>

AB

!>          AB is COMPLEX array, dimension (LDAB,N)
!>          The upper or lower triangular band matrix A, stored in the
!>          first k+1 rows of AB.  The j-th column of A is stored
!>          in the j-th column of the array AB as follows:
!>          if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).
!>          Note that when DIAG = 'U', the elements of the array AB
!>          corresponding to the diagonal elements of the matrix A are
!>          not referenced, but are assumed to be one.
!>

LDAB

!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= K+1.
!>

WORK

!>          WORK is REAL array, dimension (MAX(1,LWORK)),
!>          where LWORK >= N 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 clantb.f.

💜 double precision function dlantb (character norm, character uplo, character diag, integer n, integer k, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) work)

DLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.

Purpose:

!>
!> DLANTB  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the element of  largest absolute value  of an
!> n by n triangular band matrix A,  with ( k + 1 ) diagonals.
!>

💖 Returns

DLANTB

!>
!>    DLANTB = ( 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 DLANTB as described
!>          above.
!>

UPLO

!>          UPLO is CHARACTER*1
!>          Specifies whether the matrix A is upper or lower triangular.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>

DIAG

!>          DIAG is CHARACTER*1
!>          Specifies whether or not the matrix A is unit triangular.
!>          = 'N':  Non-unit triangular
!>          = 'U':  Unit triangular
!>

N

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.  When N = 0, DLANTB is
!>          set to zero.
!>

K

!>          K is INTEGER
!>          The number of super-diagonals of the matrix A if UPLO = 'U',
!>          or the number of sub-diagonals of the matrix A if UPLO = 'L'.
!>          K >= 0.
!>

AB

!>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
!>          The upper or lower triangular band matrix A, stored in the
!>          first k+1 rows of AB.  The j-th column of A is stored
!>          in the j-th column of the array AB as follows:
!>          if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).
!>          Note that when DIAG = 'U', the elements of the array AB
!>          corresponding to the diagonal elements of the matrix A are
!>          not referenced, but are assumed to be one.
!>

LDAB

!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= K+1.
!>

WORK

!>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
!>          where LWORK >= N 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 138 of file dlantb.f.

🦋 real function slantb (character norm, character uplo, character diag, integer n, integer k, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work)

SLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.

Purpose:

!>
!> SLANTB  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the element of  largest absolute value  of an
!> n by n triangular band matrix A,  with ( k + 1 ) diagonals.
!>

💖 Returns

SLANTB

!>
!>    SLANTB = ( 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 SLANTB as described
!>          above.
!>

UPLO

!>          UPLO is CHARACTER*1
!>          Specifies whether the matrix A is upper or lower triangular.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>

DIAG

!>          DIAG is CHARACTER*1
!>          Specifies whether or not the matrix A is unit triangular.
!>          = 'N':  Non-unit triangular
!>          = 'U':  Unit triangular
!>

N

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.  When N = 0, SLANTB is
!>          set to zero.
!>

K

!>          K is INTEGER
!>          The number of super-diagonals of the matrix A if UPLO = 'U',
!>          or the number of sub-diagonals of the matrix A if UPLO = 'L'.
!>          K >= 0.
!>

AB

Okay bestie, AB is a REAL array, dimension (LDAB,N) — and it's literally holding your upper or lower triangular band matrix A in the first k+1 rows. The j-th column of A is stored in the j-th column of the array AB as follows:

if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).

Heads up, queen: when DIAG = 'U', the elements of the array AB corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one. So those slots are lowkey imaginary — but make them one in your heart 💖.

LDAB

LDAB is INTEGER — it's the leading dimension of the array AB, and the vibe check is LDAB >= K+1. No cap.

WORK

WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. So if you're not doing the infinity norm, this array is just chilling, unbothered 🫶.

Author

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

Definition at line 138 of file slantb.f. Slay.

zlantb

Here's the signature, bestie — copy it exactly or the compiler will absolutely clock you:

double precision function zlantb (character norm, character uplo, character
    diag, integer n, integer k, complex*16, dimension( ldab, * ) ab, integer
    ldab, double precision, dimension( * ) work)

ZLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix. Main character energy fr fr 👑.

Purpose

ZLANTB returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals. Iconic.

Returns

ZLANTB is giving:

   ZLANTB = ( 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: max(abs(A(i,j))) is not a consistent matrix norm. Don't let anyone tell you otherwise 💀.

Parameters

NORM — NORM is CHARACTER*1. Specifies the value to be returned in ZLANTB as described above. It's the vibe selector, basically ✨.

UPLO — UPLO is CHARACTER*1. Specifies whether the matrix A is upper or lower triangular.

  • = 'U': Upper triangular
  • = 'L': Lower triangular

DIAG — DIAG is CHARACTER*1. Specifies whether or not the matrix A is unit triangular.

  • = 'N': Non-unit triangular
  • = 'U': Unit triangular

N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, ZLANTB is set to zero. Tiny matrix? Zero. We love a clean edge case 🎀.

K — K is INTEGER. The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals of the matrix A if UPLO = 'L'. K >= 0.

AB — AB is COMPLEX*16 array, dimension (LDAB,N). The upper or lower triangular band matrix A, stored in the first k+1 rows of AB. The j-th column of A is stored in the j-th column of the array AB as follows:

if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).

Note, bestie: when DIAG = 'U', the elements of the array AB corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one. So those slots are lowkey imaginary — but make them one in your heart 💖.

LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= K+1. Periodt.

WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. Again: infinity norm only, otherwise she's not invited to the function 🦋.

Author

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

Definition at line 139 of file zlantb.f. No cap.

And that's the whole vibe check, bestie 🌈. Doxygen auto-generated this for LAPACK from the source code — it's serving LAPACK Version 3.12.0, dated lantb(3), and it ate, left no crumbs 💅✨.

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