SRC/clantp.f(3)

💖 NAME 💖

SRC/clantp.f is the file, and this is page SRC/clantp.f(3) from the Library Functions Manual ✨ no cap, bestie, this is the whole CLANTP moment.

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

Okay so this one function is literally the main character: CLANTP 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. 💅

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🦋 Function/Subroutine Documentation 🦋

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

And yes, same energy, full signature: CLANTP 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. 🫶

🌸 Purpose 🌸

CLANTP 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. 💖

⭐ Returns ⭐

CLANTP is giving piecewise function, and it's iconic:

CLANTP = ( 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. 💀 dramatic but true.

💅 Parameters 💅

• NORM — NORM is CHARACTER*1; it specifies the value to be returned in CLANTP as described above.
• UPLO — UPLO is CHARACTER*1; it specifies whether the matrix A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• DIAG — DIAG is CHARACTER*1; it 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, CLANTP is set to zero.
• AP — AP is COMPLEX 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. 🫶

• 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 124 of file clantp.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole glow-up, bestie 🫶 This page is signed off by LAPACK, Version 3.12.0, and the file/page is SRC/clantp.f(3). The footer doesn't hand us a date, so we're not inventing one — no cap, just facts 💅✨