lanhp(3)

📦

version 3.12.1 · 9 versions

3.12.1 · arch rolling (latest)
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3.12.1 · ubuntu stonking
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3.12.1 · ubuntu resolute
3.12.1 · debian trixie

💅 lanhp(3) — lan{hp,sp}: Hermitian/symmetric matrix, packed

okay bestie, welcome to the Library Functions Manual corner of the universe 🎀. this is the lore on lanhp — and honestly the whole lan{hp,sp} fam — aka the routines that hand you the norm of a Hermitian or symmetric matrix when you've got it packed like a little sardine can 🐟. stay with me, it slaps.

✨ NAME ✨

lanhp — lan{hp,sp}: Hermitian/symmetric matrix, packed. periodt.

🌸 SYNOPSIS 🌸

🫶 Functions

real function clanhp (norm, uplo, n, ap, work) — CLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix supplied in packed form.
real function clansp (norm, uplo, n, ap, work) — CLANSP 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.
double precision function dlansp (norm, uplo, n, ap, work) — DLANSP 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.
real function slansp (norm, uplo, n, ap, work) — SLANSP 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.
double precision function zlanhp (norm, uplo, n, ap, work) — ZLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix supplied in packed form.
double precision function zlansp (norm, uplo, n, ap, 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.

🌈 Detailed Description 🌈

it's giving "the whole squad shows up to take your matrix's norm" 💅. six icons, one mission. keep scrolling for the individual character studies 🎀.

💖 Function Documentation 💖

🦋 `real function clanhp`

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

CLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix supplied in packed form. no cap, that's the whole vibe ✨.

💜 Purpose

lowkey the receipts, verbatim:

!>
!> CLANHP  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 hermitian matrix A,  supplied in packed form.
!>

⭐ Returns

!>
!>    CLANHP = ( 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.
!>

⚠️ heads up bestie: max(abs(A(i,j))) is not a consistent matrix norm. it's built different. respect it. 💀

🌸 Parameters

NORM

!>          NORM is CHARACTER*1
!>          Specifies the value to be returned in CLANHP as described
!>          above.

UPLO

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

N

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

AP

!>          AP is COMPLEX array, dimension (N*(N+1)/2)
!>          The upper or lower triangle of the hermitian 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 the  imaginary parts of the diagonal elements need
!>          not be set and are assumed to be zero.

WORK

!>          WORK is REAL array, dimension (MAX(1,LWORK)),
!>          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
!>          WORK is not referenced.

🎀 Author

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

Definition at line 116 of file clanhp.f. 📌

🧚 `real function clansp`

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

CLANSP 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. icon behavior 💅.

💜 Purpose

!>
!> CLANSP  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

!>
!>    CLANSP = ( 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 caveat as above bestie: max(abs(A(i,j))) is not a consistent matrix norm. don't @ me. 😭

🌸 Parameters

NORM

!>          NORM is CHARACTER*1
!>          Specifies the value to be returned in CLANSP as described
!>          above.

UPLO

!>          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

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

AP

!>          AP is COMPLEX 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

!>          WORK is REAL array, dimension (MAX(1,LWORK)),
!>          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
!>          WORK is not referenced.

🎀 Author

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

Definition at line 114 of file clansp.f. 📌

🦋 `double precision function dlansp`

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

DLANSP 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. double precision, double slay 🔥.

💜 Purpose

!>
!> DLANSP  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> real symmetric matrix A,  supplied in packed form.
!>

⭐ Returns

!>
!>    DLANSP = ( 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 it's the same warning, it's a whole running theme: max(abs(A(i,j))) is not a consistent matrix norm 🫶.

🌸 Parameters

NORM

!>          NORM is CHARACTER*1
!>          Specifies the value to be returned in DLANSP as described
!>          above.

UPLO

!>          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

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

AP

!>          AP is DOUBLE PRECISION 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

!>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
!>          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
!>          WORK is not referenced.

🎀 Author

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

Definition at line 113 of file dlansp.f. 📌

🧚 `real function slansp`

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

SLANSP 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. single precision, still iconic ✨.

💜 Purpose

!>
!> SLANSP  returns the value of the one norm,  or the Frobenius norm, or
!> the  infinity norm,  or the  element of  largest absolute value  of a
!> real symmetric matrix A,  supplied in packed form.
!>

⭐ Returns

SLANSP — (okay bestie, this is exactly where part 1 of the page cuts off, so the Returns breakdown for SLANSP and everything after it lives over in part 2 💖). the formula, the parameters, the author block, the iykyk details — all of it's waiting for you there 🫶

okay so when you call SLANSP, the return value is literally this whole mood:

!>
!>    SLANSP = ( 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.
!>

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 — that's a real caveat, bestie, don't forget it 💅

💅 Parameters (SLANSP)

NORM — NORM is CHARACTER*1. Specifies the value to be returned in SLANSP as described above.
UPLO — 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 — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, SLANSP is set to zero.
AP — AP is REAL 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 — WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced.

🌸 Author (SLANSP)

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

Definition at line 113 of file slansp.f.

🦋 `zlanhp` — double precision function

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

ZLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix supplied in packed form.

✨ Purpose

ZLANHP 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 hermitian matrix A, supplied in packed form. iconic behavior, honestly 💖

🎀 Returns (ZLANHP)

!>
!>    ZLANHP = ( 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 warning as before: max(abs(A(i,j))) is not a consistent matrix norm, so don't let anyone tell you otherwise 😭

💖 Parameters (ZLANHP)

NORM — NORM is CHARACTER*1. Specifies the value to be returned in ZLANHP as described above.
UPLO — UPLO is CHARACTER*1. Specifies whether the upper or lower triangular part of the hermitian matrix A is supplied.
- = 'U': Upper triangular part of A is supplied
- = 'L': Lower triangular part of A is supplied
N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, ZLANHP is set to zero.
AP — AP is COMPLEX*16 array, dimension (N*(N+1)/2). The upper or lower triangle of the hermitian 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 the imaginary parts of the diagonal elements need not be set and are assumed to be zero.
WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced.

👑 Author (ZLANHP)

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

Definition at line 116 of file zlanhp.f.

🌈 `zlansp` — double precision function

   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.

⭐ 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. main character energy fr fr ✨

🦋 Returns (ZLANSP)

!>
!>    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.
!>

yes bestie, same note again: max(abs(A(i,j))) is not a consistent matrix norm 🫶

🍓 Parameters (ZLANSP)

NORM — NORM is CHARACTER*1. Specifies the value to be returned in ZLANSP as described above.
UPLO — 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 — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, ZLANSP is set to zero.
AP — 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 — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced.

💜 Author (ZLANSP)

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

Definition at line 114 of file zlansp.f.

🧚 Author

Generated automatically by Doxygen for LAPACK from the source code.

okay that's the whole math-y group chat 💖 source/version is LAPACK, Version 3.12.0, the page is lanhp(3), and the footer doesn't give a date here — but the vibes are immaculate anyway 💅✨🎀

📦 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

lanhp(3)

💅 lanhp(3) — lan{hp,sp}: Hermitian/symmetric matrix, packed

✨ NAME ✨

🌸 SYNOPSIS 🌸

🫶 Functions

🌈 Detailed Description 🌈

💖 Function Documentation 💖

🦋 real function clanhp

💜 Purpose

⭐ Returns

🌸 Parameters

🎀 Author

🧚 real function clansp

💜 Purpose

⭐ Returns

🌸 Parameters

🎀 Author

🦋 double precision function dlansp

💜 Purpose

⭐ Returns

🌸 Parameters

🎀 Author

🧚 real function slansp

💜 Purpose

⭐ Returns

💅 Parameters (SLANSP)

🌸 Author (SLANSP)

🦋 zlanhp — double precision function

✨ Purpose

🎀 Returns (ZLANHP)

💖 Parameters (ZLANHP)

👑 Author (ZLANHP)

🌈 zlansp — double precision function

⭐ Purpose

🦋 Returns (ZLANSP)

🍓 Parameters (ZLANSP)

💜 Author (ZLANSP)

🧚 Author

🦋 `real function clanhp`

🧚 `real function clansp`

🦋 `double precision function dlansp`

🧚 `real function slansp`

🦋 `zlanhp` — double precision function

🌈 `zlansp` — double precision function