SRC/slansf.f(3)

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version 3.12.1 · 4 versions
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💖 SRC/slansf.f 💖

Straight out of the Library Functions Manual, bestie — this is the SLANSF page for SRC/slansf.f(3). It's giving norm-core, RFP format, and main character energy. No cap. 💅

✨ NAME ✨

SRC/slansf.f — that's the name, periodt. 🫶

🦋 SYNOPSIS 🦋

🧚 Functions/Subroutines 🧚

   Functions/Subroutines
       real function slansf (norm, transr, uplo, n, a, work)
           SLANSF

💖 Function/Subroutine Documentation 💖

Here's the full signature, literally:

   real function slansf (character norm, character transr, character uplo,
       integer n, real, dimension( 0: * ) a, real, dimension( 0: * ) work)
       SLANSF

🌸 Purpose 🌸

SLANSF 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 in RFP format. Obsessed with how specific that is. ✨

💫 Returns 💫

SLANSF is defined like this, exactly:

!>
!>    SLANSF = ( 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.
!>

🎀 Parameters 🎀

  • NORM — NORM is CHARACTER*1. It specifies the value to be returned in SLANSF as described above. 🫶
  • TRANSR — TRANSR is CHARACTER*1. It specifies whether the RFP format of A is normal or transposed format. = 'N': RFP format is Normal; = 'T': RFP format is Transpose. 👑
  • UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the RFP matrix A came from an upper or lower triangular matrix as follows: = 'U': RFP A came from an upper triangular matrix; = 'L': RFP A came from a lower triangular matrix. 🦋
  • N — N is INTEGER. The order of the matrix A. N >= 0. When N = 0, SLANSF is set to zero. Periodt. 💅
  • A — A is REAL array, dimension ( N*(N+1)/2 ); On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L') part of the symmetric matrix A stored in RFP format. See the below for more details. Unchanged on exit. 🌈
  • 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.

🌟 Further Details 🌟

Okay so here's the RFP format lore, bestie. We first consider Rectangular Full Packed (RFP) 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 the 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 the transpose of the last three columns of AP lower.

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 = 'T'. RFP A in both UPLO cases is just the 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 then consider Rectangular Full Packed (RFP) 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 the 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 the transpose of the last two columns of AP lower.

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 = 'T'. RFP A in both UPLO cases is just the 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 208 of file slansf.f. 📌

💀 Author 💀

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