.TH "TESTING/MATGEN/clatm5.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
TESTING/MATGEN/clatm5.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBclatm5\fP (prtype, m, n, a, lda, b, ldb, c, ldc, d, ldd, e, \fBlde\fP, f, ldf, r, ldr, l, ldl, alpha, qblcka, qblckb)"
.br
.RI "\fBCLATM5\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "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( \fBlde\fP, * ) 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)"

.PP
\fBCLATM5\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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 ] )
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIPRTYPE\fP 
.PP
.nf
          PRTYPE is INTEGER
          'Points' to a certain type of the matrices to generate
          (see further details)\&.
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          Specifies the order of A and D and the number of rows in
          C, F,  R and L\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          Specifies the order of B and E and the number of columns in
          C, F, R and L\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX array, dimension (LDA, M)\&.
          On exit A M-by-M is initialized according to PRTYPE\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of A\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is COMPLEX array, dimension (LDB, N)\&.
          On exit B N-by-N is initialized according to PRTYPE\&.
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
          LDB is INTEGER
          The leading dimension of B\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is COMPLEX array, dimension (LDC, N)\&.
          On exit C M-by-N is initialized according to PRTYPE\&.
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
          LDC is INTEGER
          The leading dimension of C\&.
.fi
.PP
.br
\fID\fP 
.PP
.nf
          D is COMPLEX array, dimension (LDD, M)\&.
          On exit D M-by-M is initialized according to PRTYPE\&.
.fi
.PP
.br
\fILDD\fP 
.PP
.nf
          LDD is INTEGER
          The leading dimension of D\&.
.fi
.PP
.br
\fIE\fP 
.PP
.nf
          E is COMPLEX array, dimension (LDE, N)\&.
          On exit E N-by-N is initialized according to PRTYPE\&.
.fi
.PP
.br
\fILDE\fP 
.PP
.nf
          LDE is INTEGER
          The leading dimension of E\&.
.fi
.PP
.br
\fIF\fP 
.PP
.nf
          F is COMPLEX array, dimension (LDF, N)\&.
          On exit F M-by-N is initialized according to PRTYPE\&.
.fi
.PP
.br
\fILDF\fP 
.PP
.nf
          LDF is INTEGER
          The leading dimension of F\&.
.fi
.PP
.br
\fIR\fP 
.PP
.nf
          R is COMPLEX array, dimension (LDR, N)\&.
          On exit R M-by-N is initialized according to PRTYPE\&.
.fi
.PP
.br
\fILDR\fP 
.PP
.nf
          LDR is INTEGER
          The leading dimension of R\&.
.fi
.PP
.br
\fIL\fP 
.PP
.nf
          L is COMPLEX array, dimension (LDL, N)\&.
          On exit L M-by-N is initialized according to PRTYPE\&.
.fi
.PP
.br
\fILDL\fP 
.PP
.nf
          LDL is INTEGER
          The leading dimension of L\&.
.fi
.PP
.br
\fIALPHA\fP 
.PP
.nf
          ALPHA is REAL
          Parameter used in generating PRTYPE = 1 and 5 matrices\&.
.fi
.PP
.br
\fIQBLCKA\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIQBLCKB\fP 
.PP
.nf
          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\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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\&.
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB265\fP of file \fBclatm5\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.