SRC/zlansp.f(3)

okay so bestie, welcome to the SRC/zlansp.f(3) page from the Library Functions Manual 💖 this is the whole lore, and we're keeping every array bound, every norm letter, and every tiny detail, periodt ✨

✨ NAME ✨

SRC/zlansp.f — yes, that's the name, no cap 💅

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

• double precision function zlansp (norm, uplo, n, ap, work) — okay so ZLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form. slay 💖

🦋 Function/Subroutine Documentation 🦋

here's the full signature, bestie — same facts, all dolled up:

double precision function zlansp (character norm, character uplo, integer n,
     complex*16, dimension( * ) ap, double precision, dimension( * ) work)

ZLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form. iconic 🎀

✨ Purpose ✨

ZLANSP 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 symmetric matrix A, supplied in packed form. 🦋

🎀 Returns 🎀

ZLANSP

the return value is literally:

!>    ZLANSP = ( 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 — say it with me, bestie, not consistent 😭

💅 Parameters 💅

• NORM is CHARACTER*1 — specifies the value to be returned in ZLANSP as described above. 👑
• UPLO is CHARACTER*1 — specifies whether the upper or lower triangular part of the symmetric matrix A is supplied.
  • = 'U': upper triangular part of A is supplied 💖
  • = 'L': lower triangular part of A is supplied 💖
• N is INTEGER — the order of the matrix A. N >= 0. when N = 0, ZLANSP is set to zero. no cap 🫶
• AP is COMPLEX*16 array, dimension (N*(N+1)/2) — the upper or lower triangle of the symmetric 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.
• WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced. literally 😌

🌈 Author 🌈

the author squad is:

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

⭐ Definition at line ⭐

Definition at line 114 of file zlansp.f. periodt 💅

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code. 💖

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and that's the whole page, bestie 🎀 signed off with LAPACK Version 3.12.0, page SRC/zlansp.f(3), and all the packed-symmetric-norm energy you could ever need. mwah 💋✨