/home/abui...N/slatm5.f(3)

🌸 NAME 🌸

Hey bestie 💖 the manual name is /home/abui...N/slatm5.f(3) — folded in right here so we're not doing the double-header thing. This is a Library Functions Manual page, and the actual NAME-section path is:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/MATGEN/slatm5.f

That's it, that's the name, periodt ✨.

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine SLATM5 (prtype, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde,
    f, ldf, r, ldr, l, ldl, alpha, qblcka, qblckb)
   SLATM5

💖 Function/Subroutine Documentation 💖

subroutine SLATM5 (integer prtype, integer m, integer n, real, dimension(
    lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real,
    dimension( ldc, * ) c, integer ldc, real, dimension( ldd, * ) d, integer
    ldd, real, dimension( lde, * ) e, integer lde, real, dimension( ldf, * )
    f, integer ldf, real, dimension( ldr, * ) r, integer ldr, real,
    dimension( ldl, * ) l, integer ldl, real alpha, integer qblcka, integer
    qblckb)
   SLATM5

Purpose

Okay so SLATM5 generates matrices involved in the Generalized Sylvester equation:

A * R - L * B = C
D * R - L * E = F

They also satisfy (the diagonalization condition):

 [ I -L ] ( [ A  -C ], [ D -F ] ) [ I  R ] = ( [ A    ], [ D    ] )
 [    I ] ( [     B ]  [    E ] ) [    I ]   ( [    B ]  [    E ] )

Parameters

PRTYPE

PRTYPE is INTEGER — it selects a certain type of the matrices to generate (see Further Details, bestie).

M

M is INTEGER — Specifies the order of A and D and the number of rows in C, F, R and L.

N

N is INTEGER — Specifies the order of B and E and the number of columns in C, F, R and L.

A

A is REAL array, dimension (LDA, M). On exit A M-by-M is initialized according to PRTYPE.

LDA

LDA is INTEGER — The leading dimension of A.

B

B is REAL array, dimension (LDB, N). On exit B N-by-N is initialized according to PRTYPE.

LDB

LDB is INTEGER — The leading dimension of B.

C

C is REAL array, dimension (LDC, N). On exit C M-by-N is initialized according to PRTYPE.

LDC

LDC is INTEGER — The leading dimension of C.

D

D is REAL array, dimension (LDD, M). On exit D M-by-M is initialized according to PRTYPE.

LDD

LDD is INTEGER — The leading dimension of D.

E

E is REAL array, dimension (LDE, N). On exit E N-by-N is initialized according to PRTYPE.

LDE

LDE is INTEGER — The leading dimension of E.

F

F is REAL array, dimension (LDF, N). On exit F M-by-N is initialized according to PRTYPE.

LDF

LDF is INTEGER — The leading dimension of F.

R

R is REAL array, dimension (LDR, N). On exit R M-by-N is initialized according to PRTYPE.

LDR

LDR is INTEGER — The leading dimension of R.

L

L is REAL array, dimension (LDL, N). On exit L M-by-N is initialized according to PRTYPE.

LDL

LDL is INTEGER — The leading dimension of L.

ALPHA

ALPHA is REAL — Parameter used in generating PRTYPE = 1 and 5 matrices.

QBLCKA

QBLCKA is INTEGER — When PRTYPE = 3, specifies the distance between 2-by-2 blocks on the diagonal in A. Otherwise, QBLCKA is not referenced. QBLCKA > 1.

QBLCKB

QBLCKB is INTEGER — When PRTYPE = 3, specifies the distance between 2-by-2 blocks on the diagonal in B. Otherwise, QBLCKB is not referenced. QBLCKB > 1.

Author

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

Further Details

PRTYPE = 1: A and B are Jordan blocks, D and E are identity matrices.

             A : if (i == j) then A(i, j) = 1.0
                 if (j == i + 1) then A(i, j) = -1.0
                 else A(i, j) = 0.0,            i, j = 1...M

             B : if (i == j) then B(i, j) = 1.0 - ALPHA
                 if (j == i + 1) then B(i, j) = 1.0
                 else B(i, j) = 0.0,            i, j = 1...N

             D : if (i == j) then D(i, j) = 1.0
                 else D(i, j) = 0.0,            i, j = 1...M

             E : if (i == j) then E(i, j) = 1.0
                 else E(i, j) = 0.0,            i, j = 1...N

             L =  R are chosen from [-10...10],
                  which specifies the right hand sides (C, F).

PRTYPE = 2 or 3: Triangular and/or quasi- triangular.

          A : if (i <= j) then A(i, j) = [-1...1]
              else A(i, j) = 0.0,             i, j = 1...M

              if (PRTYPE = 3) then
                 A(k + 1, k + 1) = A(k, k)
                 A(k + 1, k) = [-1...1]
                 sign(A(k, k + 1) = -(sin(A(k + 1, k))
                     k = 1, M - 1, QBLCKA

          B : if (i <= j) then B(i, j) = [-1...1]
              else B(i, j) = 0.0,            i, j = 1...N

              if (PRTYPE = 3) then
                 B(k + 1, k + 1) = B(k, k)
                 B(k + 1, k) = [-1...1]
                 sign(B(k, k + 1) = -(sign(B(k + 1, k))
                     k = 1, N - 1, QBLCKB

          D : if (i <= j) then D(i, j) = [-1...1].
              else D(i, j) = 0.0,            i, j = 1...M


          E : if (i <= j) then D(i, j) = [-1...1]
              else E(i, j) = 0.0,            i, j = 1...N

              L, R are chosen from [-10...10],
              which specifies the right hand sides (C, F).

PRTYPE = 4 Full

            A(i, j) = [-10...10]
            D(i, j) = [-1...1]    i,j = 1...M
            B(i, j) = [-10...10]
            E(i, j) = [-1...1]    i,j = 1...N
            R(i, j) = [-10...10]
            L(i, j) = [-1...1]    i = 1..M ,j = 1...N

            L, R specifies the right hand sides (C, F).

PRTYPE = 5 special case common and/or close eigs.

Bestie, I did not “fix” the sin or the E line that says D — that's literally what the source says, and I am not out here rewriting LAPACK lore 💅.

Definition at line

Definition at line 265 of file slatm5.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

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Okay bestie, that's the whole page 💖 Final footer vibe: LAPACK Version 3.12.0 and /home/abui...N/slatm5.f(3). Go generate those matrices and slay ✨👑.