?latm5
?latm5
Generates matrices involved in the Generalized Sylvester equation.
Syntax
void slatm5
(
*prtype
,
lapack_int
*m
,
lapack_int
*n
,
float
*a
,
lapack_int
*lda
,
float
*b
,
lapack_int
*ldb
,
float
*c
,
lapack_int
*ldc
,
float
*d
,
lapack_int
*ldd
,
float
*e
,
lapack_int
*lde
,
float
*f
,
lapack_int
*ldf
,
float
*r
,
lapack_int
*ldr
,
float
*l
,
lapack_int
*ldl
,
float
*alpha
,
lapack_int
*qblcka
,
lapack_int
*qblckb
);
void dlatm5
(
*prtype
,
lapack_int
*m
,
lapack_int
*n
,
double
*a
,
lapack_int
*lda
,
double
*b
,
lapack_int
*ldb
,
double
*c
,
lapack_int
*ldc
,
double
*d
,
lapack_int
*ldd
,
double
*e
,
lapack_int
*lde
,
double
*f
,
lapack_int
*ldf
,
double
*r
,
lapack_int
*ldr
,
double
*l
,
lapack_int
*ldl
,
double
*alpha
,
lapack_int
*qblcka
,
lapack_int
*qblckb
);
void clatm5
(
*prtype
,
lapack_int
*m
,
lapack_int
*n
,
lapack_complex_float
*a
,
lapack_int
*lda
,
lapack_complex_float
*b
,
lapack_int
*ldb
,
lapack_complex_float
*c
,
lapack_int
*ldc
,
lapack_complex_float
*d
,
lapack_int
*ldd
,
lapack_complex_float
*e
,
lapack_int
*lde
,
lapack_complex_float
*f
,
lapack_int
*ldf
,
lapack_complex_float
*r
,
lapack_int
*ldr
,
lapack_complex_float
*l
,
lapack_int
*ldl
,
float
*alpha
,
lapack_int
*qblcka
,
lapack_int
*qblckb
);
void zlatm5
(
*prtype
,
lapack_int
*m
,
lapack_int
*n
,
lapack_complex_double
*a
,
lapack_int
*lda
,
lapack_complex_double
*b
,
lapack_int
*ldb
,
lapack_complex_double
*c
,
lapack_int
*ldc
,
lapack_complex_double
*d
,
lapack_int
*ldd
,
lapack_complex_double
*e
,
lapack_int
*lde
,
lapack_complex_double
*f
,
lapack_int
*ldf
,
lapack_complex_double
*r
,
lapack_int
*ldr
,
lapack_complex_double
*l
,
lapack_int
*ldl
,
float
*alpha
,
lapack_int
*qblcka
,
lapack_int
*qblckb
);
Include Files
- mkl.h
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
- Specifies the type of matrices to generate.
- If,prtype= 1AandBare Jordan blocks,DandEare identity matrices.A:If(theni==j)Ai,j= 1.0.If(thenj==i+ 1)Ai,j= -1.0.OtherwiseAi,j= 0.0,i,j= 1...mB:If(theni==j)Bi,j= 1.0 -.alphaIf(thenj==i+ 1)Bi,j= 1.0.OtherwiseBi,j= 0.0,.i,j= 1...nD:If(theni==j)Di,j= 1.0.OtherwiseDi,j= 0.0,.i,j= 1...mE:If(theni==j)Ei,j= 1.0OtherwiseEi,j= 0.0,.i,j= 1...nL=Rare chosen from [-10...10], which specifies the right hand sides (C,F).
- If: Triangular and/or quasi- triangular.prtype= 2 or 3A:If(theni≤j)Ai,j= [-1...1].OtherwiseAi,j= 0.0,.i,j= 1...MIf (prtype= 3) thenA=k+ 1,k+ 1A;k,kAk+ 1,k= [-1...1];sign(.A) = -(sign(k,k+ 1A)k+ 1,kk= 1,m- 1,qblckaB:If(theni≤j)Bi,j= [-1...1].OtherwiseBi,j= 0.0,.i,j= 1...nIf (prtype= 3) thenB=k+ 1,k+ 1Bk,kBk+ 1,k= [-1...1]sign(B)k,k+ 1= -(sign(B)k+ 1,kk= 1,n- 1,qblckb.D:If(theni≤j)Di,j= [-1...1].OtherwiseDi,j= 0.0,.i,j= 1...mE:If(i <= j)thenEi,j= [-1...1].OtherwiseEi,j= 0.0, i, j = 1...N.L,Rare chosen from [-10...10], which specifies the right hand sides (C,F).
- Ifprtype= 4 FullAi,j= [-10...10]Di,j= [-1...1]i,j= 1...mBi,j= [-10...10]Ei,j= [-1...1]i,j= 1...nRi,j= [-10...10]Li,j= [-1...1]i= 1..m,j= 1...nLandRspecifies the right hand sides (C,F).
- Ifprtype= 5 special case common and/or close eigs.
- m
- Specifies the order ofAandDand the number of rows inC,F,RandL.
- n
- Specifies the order ofBandEand the number of columns inC,F,RandL.
- lda
- The leading dimension ofa.
- ldb
- The leading dimension ofb.
- ldc
- The leading dimension ofc.
- ldd
- The leading dimension ofd.
- lde
- The leading dimension ofe.
- ldf
- The leading dimension off.
- ldr
- The leading dimension ofr.
- ldl
- The leading dimension ofl.
- alpha
- Parameter used in generatingprtype= 1 and 5 matrices.
- qblcka
- Whenprtype= 3, specifies the distance between 2-by-2 blocks on the diagonal inA. Otherwise,qblckais not referenced.qblcka> 1.
- qblckb
- Whenprtype= 3, specifies the distance between 2-by-2 blocks on the diagonal inB. Otherwise,qblckbis not referenced.qblckb> 1.
Output Parameters
- a
- Array, size. On exitlda*macontains them-by-marrayAinitialized according toprtype.
- b
- Array, size. On exitldb*nbcontains then-by-narrayBinitialized according toprtype.
- c
- Array, size. On exitldc*nccontains them-by-narrayCinitialized according toprtype.
- d
- Array, size. On exitldd*mdcontains them-by-marrayDinitialized according toprtype.
- e
- Array, size. On exitlde*necontains then-by-narrayEinitialized according toprtype.
- f
- Array, size. On exitldf*nfcontains them-by-narrayFinitialized according toprtype.
- r
- Array, size. On exitldr*nRcontains them-by-narrayRinitialized according toprtype.
- l
- Array, size. On exitldl*nlcontains them-by-narrayLinitialized according toprtype.