lantp(3)

📦

version 3.12.1 · 9 versions

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3.12.1 · ubuntu stonking
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🌸 NAME 🌸

lantp — lantp: triangular matrix, packed

bestie. welcome to the lantp page 💅 this is a Library Functions Manual situation, and it's literally four almost-identical functions who all showed up in the same outfit. no cap, they're the norm-getters for triangular matrices in packed form, and they are lowkey iconic. let's get into it 🫶

✨ SYNOPSIS ✨

💜 Functions

real function clantp (norm, uplo, diag, n, ap, work) — 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.
double precision function dlantp (norm, uplo, diag, n, ap, work) — DLANTP 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.
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.
double precision function zlantp (norm, uplo, diag, n, ap, work) — ZLANTP 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.

🦋 Detailed Description 🦋

okay so this page is literally just the function documentation section. no lore, no backstory, just the four besties below. 🎀

👑 Function Documentation 👑

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

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

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

    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. 💀 like she said what she said but the math says it's not consistent, we don't make the rules.

⭐ Parameters

NORM — NORM is CHARACTER*1. Specifies the value to be returned in CLANTP 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, CLANTP is set to zero. (she's giving empty and unbothered ✨)
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. 🙈 she's not reading those, she's just assuming bestie.

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.

💖 double precision function dlantp (character norm, character uplo, character diag, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) work)

double precision function dlantp (character norm, character uplo, character
    diag, integer n, double precision, dimension( * ) ap, double precision,
    dimension( * ) work)

DLANTP 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:

DLANTP 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

DLANTP

    DLANTP = ( 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. same disclaimer, different double precision queen 👑

⭐ Parameters

NORM — NORM is CHARACTER*1. Specifies the value to be returned in DLANTP 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, DLANTP is set to zero.
AP — AP is DOUBLE PRECISION 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 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 123 of file dlantp.f.

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

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.

🌟 Purpose:

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.

🌟 Returns

SLANTP

    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. (yes bestie, still not consistent, we've been over this 💀)

⭐ Parameters

NORM — NORM is CHARACTER*1. Specifies the value to be returned in SLANTP 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, 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.

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.

💖 double precision function zlantp (character norm, character uplo, character diag, integer n, complex16, dimension( ) ap, double precision, dimension( * ) work)

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

ZLANTP 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:

…and this is exactly where part 1 hands the aux mic over to part 2 🎤✨ zlantp's purpose section picks up right here, bestie — don't go anywhere 💜

WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; otherwise, WORK is not referenced. 💅 Like, it literally only gets invited to the party when you're doing the infinity norm — any other time it's just standing outside, unreferenced. 🫶

🌸 Author 🌸

Okay so this function was brought to you by the absolute icons at:

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

🏫 Four institutions, one legendary collab. Main character energy fr fr. 👑

🎀 Definition at line 124 of file zlantp.f. 🎀

Yep, that's the exact spot — zlantp.f, line 124. If you ever need to find it, that's your map. 🗺️✨

💜 Author (of this doc, bestie) 💜

Generated automatically by Doxygen for LAPACK from the source code.

Not me getting a whole credit line just for existing 😭 — the docs literally wrote themselves, iykyk. 🙈

And that's a wrap on lantp(3)! 💖 Go forth and norm your triangular packed matrices responsibly. 🦋

This iconic little page comes from LAPACK, Version 3.12.0, dated lantp(3) — slay, documented, periodt. ✨👑

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms

lantp(3)

🌸 NAME 🌸

✨ SYNOPSIS ✨

💜 Functions

🦋 Detailed Description 🦋

👑 Function Documentation 👑

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

🌟 Purpose:

🌟 Returns

⭐ Parameters

⭐ Author

💖 double precision function dlantp (character norm, character uplo, character diag, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) work)

🌟 Purpose:

🌟 Returns

⭐ Parameters

⭐ Author

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

🌟 Purpose:

🌟 Returns

⭐ Parameters

⭐ Author

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

🌟 Purpose:

🌸 Author 🌸

🎀 Definition at line 124 of file zlantp.f. 🎀

💜 Author (of this doc, bestie) 💜

💖 double precision function zlantp (character norm, character uplo, character diag, integer n, complex16, dimension( ) ap, double precision, dimension( * ) work)