zlatm5.f - Man Page
TESTING/MATGEN/zlatm5.f
Synopsis
Functions/Subroutines
subroutine zlatm5 (prtype, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, lde, f, ldf, r, ldr, l, ldl, alpha, qblcka, qblckb)
ZLATM5
Function/Subroutine Documentation
subroutine zlatm5 (integer prtype, integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( ldd, * ) d, integer ldd, complex*16, dimension( lde, * ) e, integer lde, complex*16, dimension( ldf, * ) f, integer ldf, complex*16, dimension( ldr, * ) r, integer ldr, complex*16, dimension( ldl, * ) l, integer ldl, double precision alpha, integer qblcka, integer qblckb)
ZLATM5
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 ] )
- Parameters
PRTYPE
PRTYPE is INTEGER 'Points' to a certain type of the matrices to generate (see further details).
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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 DOUBLE PRECISION 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.
Definition at line 265 of file zlatm5.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Referenced By
The man page zlatm5(3) is an alias of zlatm5.f(3).
Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK