ZLATM5
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
November 2006
Purpose
ZLATM5 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 ] )
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 ] )
Arguments
| PRTYPE |
(input) INTEGER
"Points" to a certian type of the matrices to generate
(see futher details). |
| M |
(input) INTEGER
Specifies the order of A and D and the number of rows in
C, F, R and L. |
| N |
(input) INTEGER
Specifies the order of B and E and the number of columns in
C, F, R and L. |
| A |
(output) COMPLEX*16 array, dimension (LDA, M).
On exit A M-by-M is initialized according to PRTYPE.
|
| LDA |
(input) INTEGER
The leading dimension of A.
|
| B |
(output) COMPLEX*16 array, dimension (LDB, N).
On exit B N-by-N is initialized according to PRTYPE.
|
| LDB |
(input) INTEGER
The leading dimension of B.
|
| C |
(output) COMPLEX*16 array, dimension (LDC, N).
On exit C M-by-N is initialized according to PRTYPE.
|
| LDC |
(input) INTEGER
The leading dimension of C.
|
| D |
(output) COMPLEX*16 array, dimension (LDD, M).
On exit D M-by-M is initialized according to PRTYPE.
|
| LDD |
(input) INTEGER
The leading dimension of D.
|
| E |
(output) COMPLEX*16 array, dimension (LDE, N).
On exit E N-by-N is initialized according to PRTYPE.
|
| LDE |
(input) INTEGER
The leading dimension of E.
|
| F |
(output) COMPLEX*16 array, dimension (LDF, N).
On exit F M-by-N is initialized according to PRTYPE.
|
| LDF |
(input) INTEGER
The leading dimension of F.
|
| R |
(output) COMPLEX*16 array, dimension (LDR, N).
On exit R M-by-N is initialized according to PRTYPE.
|
| LDR |
(input) INTEGER
The leading dimension of R.
|
| L |
(output) COMPLEX*16 array, dimension (LDL, N).
On exit L M-by-N is initialized according to PRTYPE.
|
| LDL |
(input) INTEGER
The leading dimension of L.
|
| ALPHA |
(input) DOUBLE PRECISION
Parameter used in generating PRTYPE = 1 and 5 matrices.
|
| QBLCKA |
(input) 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 |
(input) INTEGER
When PRTYPE = 3, specifies the distance between 2-by-2
blocks on the diagonal in B. Otherwise, QBLCKB is not referenced. QBLCKB > 1. |
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.
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.