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LAPACK
3.6.1
LAPACK: Linear Algebra PACKage
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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
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 ] )
[in] | PRTYPE | PRTYPE is INTEGER "Points" to a certain type of the matrices to generate (see futher 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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.
Definition at line 270 of file slatm5.f.