ZLANHF(3)

📦 version 3.12.0, in opensuse-leap 16.0

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zlanhf.f

That's the file, bestie — and this is the Library Functions Manual page for zlanhf.f(3). The function in question is ZLANHF, and she is lowkey iconic. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

double precision function ZLANHF (norm, transr, uplo, n, a, work)
    ZLANHF returns the value of the 1-norm, or the Frobenius norm, or
    the infinity norm, or the element of largest absolute value of a
    Hermitian matrix in RFP format.

🧚 Function/Subroutine Documentation 🧚

double precision function ZLANHF (character norm, character transr,
    character uplo, integer n, complex*16, dimension( 0: * ) a, double
    precision, dimension( 0: * ) work)

ZLANHF returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian matrix in RFP format. No cap. 🌸

Purpose

Okay so here's the vibe: ZLANHF 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 in RFP format. Periodt. ✨

Returns

ZLANHF

!>    ZLANHF = ( 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 matrix norm. Bestie, do not come for her like that. 😭

Parameters

NORM

  • NORM is CHARACTER — Specifies the value to be returned in ZLANHF as described above.

TRANSR

  • TRANSR is CHARACTER — Specifies whether the RFP format of A is normal or conjugate-transposed format.
    • = 'N': RFP format is Normal
    • = 'C': RFP format is Conjugate-transposed

UPLO

  • UPLO is CHARACTER — On entry, UPLO specifies whether the RFP matrix A came from an upper or lower triangular matrix as follows:
    • UPLO = 'U' or 'u': RFP A came from an upper triangular matrix
    • UPLO = 'L' or 'l': RFP A came from a lower triangular matrix

N

  • N is INTEGER — The order of the matrix A. N >= 0. When N = 0, ZLANHF is set to zero.

A

  • A is COMPLEX*16 array, dimension ( N*(N+1)/2 ); — On entry, the matrix A in RFP Format. RFP Format is described by TRANSR, UPLO and N as follows:
    • If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even; K=N/2.
    • RFP A is (0:N-1,0:K) when N is odd; K=N/2.
    • If TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A as defined when TRANSR = 'N'.
    • The contents of RFP A are defined by UPLO as follows: If UPLO = 'U' the RFP A contains the ( N*(N+1)/2 ) elements of upper packed A either in normal or conjugate-transpose Format. If UPLO = 'L' the RFP A contains the ( N*(N+1) /2 ) elements of lower packed A either in normal or conjugate-transpose Format.
    • The LDA of RFP A is (N+1)/2 when TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is even and is N when is odd. See the Note below for more details.
    • Unchanged on exit.

WORK

  • WORK is DOUBLE PRECISION array, dimension (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.

Further Details:

Here's the whole RFP format tea, straight from the source — diagrams and all. 🫶

!>
!>  We first consider Standard Packed Format when N is even.
!>  We give an example where N = 6.
!>
!>      AP is Upper             AP is Lower
!>
!>   00 01 02 03 04 05       00
!>      11 12 13 14 15       10 11
!>         22 23 24 25       20 21 22
!>            33 34 35       30 31 32 33
!>               44 45       40 41 42 43 44
!>                  55       50 51 52 53 54 55
!>
!>
!>  Let TRANSR = 'N'. RFP holds AP as follows:
!>  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
!>  three columns of AP upper. The lower triangle A(4:6,0:2) consists of
!>  conjugate-transpose of the first three columns of AP upper.
!>  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
!>  three columns of AP lower. The upper triangle A(0:2,0:2) consists of
!>  conjugate-transpose of the last three columns of AP lower.
!>  To denote conjugate we place -- above the element. This covers the
!>  case N even and TRANSR = 'N'.
!>
!>         RFP A                   RFP A
!>
!>                                -- -- --
!>        03 04 05                33 43 53
!>                                   -- --
!>        13 14 15                00 44 54
!>                                      --
!>        23 24 25                10 11 55
!>
!>        33 34 35                20 21 22
!>        --
!>        00 44 45                30 31 32
!>        -- --
!>        01 11 55                40 41 42
!>        -- -- --
!>        02 12 22                50 51 52
!>
!>  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
!>  transpose of RFP A above. One therefore gets:
!>
!>
!>           RFP A                   RFP A
!>
!>     -- -- -- --                -- -- -- -- -- --
!>     03 13 23 33 00 01 02    33 00 10 20 30 40 50
!>     -- -- -- -- --                -- -- -- -- --
!>     04 14 24 34 44 11 12    43 44 11 21 31 41 51
!>     -- -- -- -- -- --                -- -- -- --
!>     05 15 25 35 45 55 22    53 54 55 22 32 42 52
!>
!>
!>  We next  consider Standard Packed Format when N is odd.
!>  We give an example where N = 5.
!>
!>     AP is Upper                 AP is Lower
!>
!>   00 01 02 03 04              00
!>      11 12 13 14              10 11
!>         22 23 24              20 21 22
!>            33 34              30 31 32 33
!>               44              40 41 42 43 44
!>
!>
!>  Let TRANSR = 'N'. RFP holds AP as follows:
!>  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
!>  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
!>  conjugate-transpose of the first two   columns of AP upper.
!>  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
!>  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
!>  conjugate-transpose of the last two   columns of AP lower.
!>  To denote conjugate we place -- above the element. This covers the
!>  case N odd  and TRANSR = 'N'.
!>
!>         RFP A                   RFP A
!>
!>                                   -- --
!>        02 03 04                00 33 43
!>                                      --
!>        12 13 14                10 11 44
!>
!>        22 23 24                20 21 22
!>        --
!>        00 33 34                30 31 32
!>        -- --
!>        01 11 44                40 41 42
!>
!>  Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate-
!>  transpose of RFP A above. One therefore gets:
!>
!>
!>           RFP A                   RFP A
!>
!>     -- -- --                   -- -- -- -- -- --
!>     02 12 22 00 01             00 10 20 30 40 50
!>     -- -- -- --                   -- -- -- -- --
!>     03 13 23 33 11             33 11 21 31 41 51
!>     -- -- -- -- --                   -- -- -- --
!>     04 14 24 34 44             43 44 22 32 42 52
!>

Definition at line 245 of file zlanhf.f.

Yup, line 245 of file zlanhf.f is where she's defined. 💅

🌈 Author 🌈

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