SRC/slantp.f(3)

🌸 NAME 🌸

okay so bestie, welcome to SRC/slantp.f(3) from the Library Functions Manual 💖. The name on this page is literally SRC/slantp.f, and it's giving very specific triangular-matrix-norm main character energy. No cap.

✨ SYNOPSIS ✨

Functions/Subroutines

• real function slantp (norm, uplo, diag, n, ap, work) — SLANTP 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 matrix supplied in packed form. iconic behavior honestly 🫶

real function slantp (norm, uplo, diag, n, ap, work)

💅 Function/Subroutine Documentation 💅

The full signature is right here, bestie:

real function slantp (character norm, character uplo, character diag,
       integer n, real, dimension( * ) ap, real, dimension( * ) work)

SLANTP 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 matrix supplied in packed form. That's the whole assignment, and it ate. 💅

🎀 Purpose 🎀

okay so SLANTP returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form. periodt. ✨

⭐ Returns ⭐

SLANTP is the return value, and the norm-mapping is literally this:

!>
!>    SLANTP = ( 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.
!>

so yeah: norm1 is the maximum column sum, normI is the maximum row sum, normF is the square root of the sum of squares, and max(abs(A(i,j))) is not a consistent matrix norm — important, bestie, don't call it one 💀

🦋 Parameters 🦋

🌟 NORM 🌟

NORM is CHARACTER*1 — Specifies the value to be returned in SLANTP as described above. iykyk.

🎀 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, SLANTP is set to zero.

🌸 AP 🌸

AP is REAL array, dimension (N*(N+1)/2) — The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:

• if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
• if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

Note that when DIAG = 'U', the elements of the array AP corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one. bestie, they're assumed to be one, so don't come for them 😌

🧚 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 123 of file slantp.f.

💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole page. The footer sign-off is LAPACK Version 3.12.0 and SRC/slantp.f(3) — that's the source/version line, and there's no separate date shown in the footer, so I'm not inventing one. mwah 💋✨