.TH "SRC/dtrsyl3.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/dtrsyl3.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdtrsyl3\fP (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, iwork, liwork, swork, ldswork, info)"
.br
.RI "\fBDTRSYL3\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dtrsyl3 (character trana, character tranb, integer isgn, integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldc, * ) c, integer ldc, double precision scale, integer, dimension( * ) iwork, integer liwork, double precision, dimension( ldswork, * ) swork, integer ldswork, integer info)"

.PP
\fBDTRSYL3\fP 
.PP
\fBPurpose\fP
.RS 4

.PP
.nf
  DTRSYL3 solves the real Sylvester matrix equation:

     op(A)*X + X*op(B) = scale*C or
     op(A)*X - X*op(B) = scale*C,

  where op(A) = A or A**T, and  A and B are both upper quasi-
  triangular\&. A is M-by-M and B is N-by-N; the right hand side C and
  the solution X are M-by-N; and scale is an output scale factor, set
  <= 1 to avoid overflow in X\&.

  A and B must be in Schur canonical form (as returned by DHSEQR), that
  is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks;
  each 2-by-2 diagonal block has its diagonal elements equal and its
  off-diagonal elements of opposite sign\&.

  This is the block version of the algorithm\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fITRANA\fP 
.PP
.nf
          TRANA is CHARACTER*1
          Specifies the option op(A):
          = 'N': op(A) = A    (No transpose)
          = 'T': op(A) = A**T (Transpose)
          = 'C': op(A) = A**H (Conjugate transpose = Transpose)
.fi
.PP
.br
\fITRANB\fP 
.PP
.nf
          TRANB is CHARACTER*1
          Specifies the option op(B):
          = 'N': op(B) = B    (No transpose)
          = 'T': op(B) = B**T (Transpose)
          = 'C': op(B) = B**H (Conjugate transpose = Transpose)
.fi
.PP
.br
\fIISGN\fP 
.PP
.nf
          ISGN is INTEGER
          Specifies the sign in the equation:
          = +1: solve op(A)*X + X*op(B) = scale*C
          = -1: solve op(A)*X - X*op(B) = scale*C
.fi
.PP
.br
\fIM\fP 
.PP
.nf
          M is INTEGER
          The order of the matrix A, and the number of rows in the
          matrices X and C\&. M >= 0\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix B, and the number of columns in the
          matrices X and C\&. N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is DOUBLE PRECISION array, dimension (LDA,M)
          The upper quasi-triangular matrix A, in Schur canonical form\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&. LDA >= max(1,M)\&.
.fi
.PP
.br
\fIB\fP 
.PP
.nf
          B is DOUBLE PRECISION array, dimension (LDB,N)
          The upper quasi-triangular matrix B, in Schur canonical form\&.
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
          LDB is INTEGER
          The leading dimension of the array B\&. LDB >= max(1,N)\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is DOUBLE PRECISION array, dimension (LDC,N)
          On entry, the M-by-N right hand side matrix C\&.
          On exit, C is overwritten by the solution matrix X\&.
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
          LDC is INTEGER
          The leading dimension of the array C\&. LDC >= max(1,M)
.fi
.PP
.br
\fISCALE\fP 
.PP
.nf
          SCALE is DOUBLE PRECISION
          The scale factor, scale, set <= 1 to avoid overflow in X\&.
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK\&.
.fi
.PP
.br
\fILIWORK\fP 
.PP
.nf
          IWORK is INTEGER
          The dimension of the array IWORK\&. LIWORK >=  ((M + NB - 1) / NB + 1)
          + ((N + NB - 1) / NB + 1), where NB is the optimal block size\&.

          If LIWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal dimension of the IWORK array,
          returns this value as the first entry of the IWORK array, and
          no error message related to LIWORK is issued by XERBLA\&.
.fi
.PP
.br
\fISWORK\fP 
.PP
.nf
          SWORK is DOUBLE PRECISION array, dimension (MAX(2, ROWS),
          MAX(1,COLS))\&.
          On exit, if INFO = 0, SWORK(1) returns the optimal value ROWS
          and SWORK(2) returns the optimal COLS\&.
.fi
.PP
.br
\fILDSWORK\fP 
.PP
.nf
          LDSWORK is INTEGER
          LDSWORK >= MAX(2,ROWS), where ROWS = ((M + NB - 1) / NB + 1)
          and NB is the optimal block size\&.

          If LDSWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal dimensions of the SWORK matrix,
          returns these values as the first and second entry of the SWORK
          matrix, and no error message related LWORK is issued by XERBLA\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
          = 1: A and B have common or very close eigenvalues; perturbed
               values were used to solve the equation (but the matrices
               A and B are unchanged)\&.
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB178\fP of file \fBdtrsyl3\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.