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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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| subroutine clatm5 | ( | integer | PRTYPE, |
| integer | M, | ||
| integer | N, | ||
| complex, dimension( lda, * ) | A, | ||
| integer | LDA, | ||
| complex, dimension( ldb, * ) | B, | ||
| integer | LDB, | ||
| complex, dimension( ldc, * ) | C, | ||
| integer | LDC, | ||
| complex, dimension( ldd, * ) | D, | ||
| integer | LDD, | ||
| complex, dimension( lde, * ) | E, | ||
| integer | LDE, | ||
| complex, dimension( ldf, * ) | F, | ||
| integer | LDF, | ||
| complex, dimension( ldr, * ) | R, | ||
| integer | LDR, | ||
| complex, dimension( ldl, * ) | L, | ||
| integer | LDL, | ||
| real | ALPHA, | ||
| integer | QBLCKA, | ||
| integer | QBLCKB | ||
| ) |
CLATM5
CLATM5 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 ] ) | [in] | PRTYPE | PRTYPE is INTEGER
"Points" to a certain type of the matrices to generate
(see further details). |
| [in] | M | M is INTEGER
Specifies the order of A and D and the number of rows in
C, F, R and L. |
| [in] | N | N is INTEGER
Specifies the order of B and E and the number of columns in
C, F, R and L. |
| [out] | A | A is COMPLEX array, dimension (LDA, M).
On exit A M-by-M is initialized according to PRTYPE. |
| [in] | LDA | LDA is INTEGER
The leading dimension of A. |
| [out] | B | B is COMPLEX array, dimension (LDB, N).
On exit B N-by-N is initialized according to PRTYPE. |
| [in] | LDB | LDB is INTEGER
The leading dimension of B. |
| [out] | C | C is COMPLEX array, dimension (LDC, N).
On exit C M-by-N is initialized according to PRTYPE. |
| [in] | LDC | LDC is INTEGER
The leading dimension of C. |
| [out] | D | D is COMPLEX array, dimension (LDD, M).
On exit D M-by-M is initialized according to PRTYPE. |
| [in] | LDD | LDD is INTEGER
The leading dimension of D. |
| [out] | E | E is COMPLEX array, dimension (LDE, N).
On exit E N-by-N is initialized according to PRTYPE. |
| [in] | LDE | LDE is INTEGER
The leading dimension of E. |
| [out] | F | F is COMPLEX array, dimension (LDF, N).
On exit F M-by-N is initialized according to PRTYPE. |
| [in] | LDF | LDF is INTEGER
The leading dimension of F. |
| [out] | R | R is COMPLEX array, dimension (LDR, N).
On exit R M-by-N is initialized according to PRTYPE. |
| [in] | LDR | LDR is INTEGER
The leading dimension of R. |
| [out] | L | L is COMPLEX array, dimension (LDL, N).
On exit L M-by-N is initialized according to PRTYPE. |
| [in] | LDL | LDL is INTEGER
The leading dimension of L. |
| [in] | ALPHA | ALPHA is REAL
Parameter used in generating PRTYPE = 1 and 5 matrices. |
| [in] | 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. |
| [in] | 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. |
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. 
1.9.4