SLANSF(3)

✨ SLANSF(3) — Library Functions Manual ✨

Bestie, welcome to the page for slansf.f(3), the Library Functions Manual entry that’s lowkey iconic. The file lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slansf.f, and today we’re checking norms of a real symmetric matrix in RFP format. No cap, this one is giving serious LAPACK energy. 💅

💖 NAME 💖

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

🦋 SYNOPSIS 🦋

🌈 Functions/Subroutines 🌈

real function SLANSF (norm, transr, uplo, n, a, work)
    SLANSF

💅 Function/Subroutine Documentation 💅

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

SLANSF

🎀 Purpose 🎀

Okay so 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. That’s the whole assignment, bestie. ✨

🌸 Returns 🌸

SLANSF gives you this:

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. Important little disclaimer, okay? 😭

👑 Parameters 👑

• NORM — NORM is CHARACTER*1 and specifies the value to be returned in SLANSF as described above. ✨
• TRANSR — TRANSR is CHARACTER*1 and 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. Zero era, honestly. 💀
• 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 bestie, RFP format time. 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 🌟

Generated automatically by Doxygen for LAPACK from the source code.

---

That’s the whole page, bestie — brought to you by LAPACK Version 3.12.0 and the path /home/abui...RC/slansf.f(3). Byeee 💖✨🎀