SLAEXC(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/slaexc.f — okay so bestie, this is the Fortran source file for SLAEXC, and the title/manual-name situation up top is literally the Library Functions Manual with /home/abui...RC/slaexc.f(3) energy. Iconic, no cap. 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

Functions/Subroutines
    subroutine SLAEXC (wantq, n, t, ldt, q, ldq, j1, n1, n2, work, info)
        SLAEXC swaps adjacent diagonal blocks of a real upper quasi-
        triangular matrix in Schur canonical form, by an orthogonal
        similarity transformation.

🎀 Function/Subroutine Documentation 🎀

subroutine SLAEXC (logical wantq, integer n, real, dimension( ldt, * ) t,
    integer ldt, real, dimension( ldq, * ) q, integer ldq, integer j1,
    integer n1, integer n2, real, dimension( * ) work, integer info)

SLAEXC swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonical form, by an orthogonal similarity transformation. It’s giving linear algebra main character energy, fr fr. ✨

🦋 Purpose 🦋

So here’s the tea, bestie: SLAEXC swaps adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation.

T must be in Schur canonical form, that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign. Periodt. 💜

💅 Parameters

WANTQ

WANTQ is LOGICAL

  • = .TRUE. : accumulate the transformation in the matrix Q;
  • = .FALSE.: do not accumulate the transformation.

N

N is INTEGER

The order of the matrix T. N >= 0.

T

T is REAL array, dimension (LDT,N)

On entry, the upper quasi-triangular matrix T, in Schur canonical form.

On exit, the updated matrix T, again in Schur canonical form.

LDT

LDT is INTEGER

The leading dimension of the array T. LDT >= max(1,N).

Q

Q is REAL array, dimension (LDQ,N)

On entry, if WANTQ is .TRUE., the orthogonal matrix Q.

On exit, if WANTQ is .TRUE., the updated matrix Q.

If WANTQ is .FALSE., Q is not referenced. like, not even a little bit 🙈

LDQ

LDQ is INTEGER

The leading dimension of the array Q.

LDQ >= 1; and if WANTQ is .TRUE., LDQ >= N.

J1

J1 is INTEGER

The index of the first row of the first block T11.

N1

N1 is INTEGER

The order of the first block T11. N1 = 0, 1 or 2.

N2

N2 is INTEGER

The order of the second block T22. N2 = 0, 1 or 2.

WORK

WORK is REAL array, dimension (N)

INFO

INFO is INTEGER

  • = 0: successful exit
  • = 1: the transformed matrix T would be too far from Schur form; the blocks are not swapped and T and Q are unchanged.
lowkey important: that INFO = 1 case means no swap happened and both T and Q are unchanged. Read the room, bestie. 💀

👑 Author

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

Definition at line 136 of file slaexc.f.

⭐ Author ⭐

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