Visible to Intel only — GUID: GUID-1967BFC8-D7D4-4B40-9CFE-D533B663AEDC
Visible to Intel only — GUID: GUID-1967BFC8-D7D4-4B40-9CFE-D533B663AEDC
?latm5
Generates matrices involved in the Generalized Sylvester equation.
Syntax
call slatm5( prtype, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde, f, ldf, r, ldr, l, ldl, alpha, qblcka, qblckb )
call dlatm5( prtype, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde, f, ldf, r, ldr, l, ldl, alpha, qblcka, qblckb )
call clatm5( prtype, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde, f, ldf, r, ldr, l, ldl, alpha, qblcka, qblckb )
call zlatm5( prtype, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde, f, ldf, r, ldr, l, ldl, alpha, qblcka, qblckb )
Include Files
- mkl.fi
Description
The ?latm5 routine generates matrices involved in the Generalized Sylvester equation:
A * R - L * B = C
D * R - L * E = F
They also satisfy the diagonalization condition:
Input Parameters
- prtype
-
INTEGER. Specifies the type of matrices to generate.
If prtype = 1, A and B are Jordan blocks, D and E are identity matrices.
A:
If (i == j) then Ai, j = 1.0.
If (j == i + 1) then Ai, j = -1.0.
Otherwise Ai, j = 0.0, i, j = 1...m
B:
If (i == j) then Bi, j = 1.0 - alpha.
If (j == i + 1) then Bi, j = 1.0 .
Otherwise Bi, j = 0.0, i, j = 1...n.
D:
If (i == j) then Di, j = 1.0.
Otherwise Di, j = 0.0, i, j = 1...m.
E:
If (i == j) then Ei, j = 1.0
Otherwise Ei, j = 0.0, i, j = 1...n.
L = R are chosen from [-10...10], which specifies the right hand sides (C, F).
If prtype = 2 or 3: Triangular and/or quasi- triangular.
A:
If (i ≤ j) then Ai, j = [-1...1].
Otherwise Ai, j = 0.0, i, j = 1...M.
If (prtype = 3) then Ak + 1, k + 1 = Ak, k;
Ak + 1, k = [-1...1];
sign(Ak, k + 1) = -(sign(Ak + 1, k).
k = 1, m- 1, qblcka
B :
If (i ≤ j) then Bi, j = [-1...1].
Otherwise Bi, j = 0.0, i, j = 1...n.
If (prtype = 3) thenBk + 1, k + 1 = Bk, k
Bk + 1, k = [-1...1]
sign(Bk, k + 1)= -(sign(Bk + 1, k)
k = 1, n - 1, qblckb.
D:
If (i ≤ j) then Di, j = [-1...1].
Otherwise Di, j = 0.0, i, j = 1...m.
E:
If (i <= j) then Ei, j = [-1...1].
Otherwise Ei, j = 0.0, i, j = 1...N.
L, R are chosen from [-10...10], which specifies the right hand sides (C, F).
If prtype = 4 Full
Ai, j = [-10...10]
Di, j = [-1...1] i,j = 1...m
Bi, j = [-10...10]
Ei, j = [-1...1] i,j = 1...n
Ri, j = [-10...10]
Li, j = [-1...1] i = 1..m ,j = 1...n
L and R specifies the right hand sides (C, F).
If prtype = 5 special case common and/or close eigs.
- m
-
INTEGER. Specifies the order of A and D and the number of rows in C, F, R and L.
- n
-
INTEGER. Specifies the order of B and E and the number of columns in C, F, R and L.
- lda
-
INTEGER. The leading dimension of a.
- ldb
-
INTEGER. The leading dimension of b.
- ldc
-
INTEGER. The leading dimension of c.
- ldd
-
INTEGER. The leading dimension of d.
- lde
-
INTEGER. The leading dimension of e.
- ldf
-
INTEGER. The leading dimension of f.
- ldr
-
INTEGER. The leading dimension of r.
- ldl
-
INTEGER. The leading dimension of l.
- alpha
-
REAL for slatm5,
DOUBLE PRECISION for dlatm5,
REAL for clatm5,
DOUBLE PRECISION for zlatm5,
Parameter used in generating prtype = 1 and 5 matrices.
- qblcka
-
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
-
INTEGER. When prtype = 3, specifies the distance between 2-by-2 blocks on the diagonal in B. Otherwise, qblckb is not referenced. qblckb > 1.
Output Parameters
- a
-
REAL for slatm5,
DOUBLE PRECISION for dlatm5,
COMPLEX for clatm5,
DOUBLE COMPLEX for zlatm5,
Array, size (lda, m). On exit a contains them-by-m array A initialized according to prtype.
- b
-
REAL for slatm5,
DOUBLE PRECISION for dlatm5,
COMPLEX for clatm5,
DOUBLE COMPLEX for zlatm5,
Array, size (ldb, n). On exit b contains the n-by-n array B initialized according to prtype.
- c
-
REAL for slatm5,
DOUBLE PRECISION for dlatm5,
COMPLEX for clatm5,
DOUBLE COMPLEX for zlatm5,
Array, size (ldc, n). On exit c contains the m-by-n array C initialized according to prtype.
- d
-
REAL for slatm5,
DOUBLE PRECISION for dlatm5,
COMPLEX for clatm5,
DOUBLE COMPLEX for zlatm5,
Array, size (ldd, m). On exit d contains the m-by-m array D initialized according to prtype.
- e
-
REAL for slatm5,
DOUBLE PRECISION for dlatm5,
COMPLEX for clatm5,
DOUBLE COMPLEX for zlatm5,
Array, size (lde, n). On exit e contains the n-by-n array E initialized according to prtype.
- f
-
REAL for slatm5,
DOUBLE PRECISION for dlatm5,
COMPLEX for clatm5,
DOUBLE COMPLEX for zlatm5,
Array, size (ldf, n). On exit f contains the m-by-n array F initialized according to prtype.
- r
-
REAL for slatm5,
DOUBLE PRECISION for dlatm5,
COMPLEX for clatm5,
DOUBLE COMPLEX for zlatm5,
Array, size (ldr, n). On exit R contains the m-by-n array R initialized according to prtype.
- l
-
REAL for slatm5,
DOUBLE PRECISION for dlatm5,
COMPLEX for clatm5,
DOUBLE COMPLEX for zlatm5,
Array, size (ldl, n). On exit l contains the m-by-narray L initialized according to prtype.