.TH "trsyl" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
trsyl \- trsyl: Sylvester equation
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBctrsyl\fP (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info)"
.br
.RI "\fBCTRSYL\fP "
.ti -1c
.RI "subroutine \fBdtrsyl\fP (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info)"
.br
.RI "\fBDTRSYL\fP "
.ti -1c
.RI "subroutine \fBstrsyl\fP (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info)"
.br
.RI "\fBSTRSYL\fP "
.ti -1c
.RI "subroutine \fBztrsyl\fP (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info)"
.br
.RI "\fBZTRSYL\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine ctrsyl (character trana, character tranb, integer isgn, integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldc, * ) c, integer ldc, real scale, integer info)"

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

.PP
.nf
 CTRSYL solves the complex 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**H, and A and B are both upper 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\&.
.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)
          = 'C': op(A) = A**H (Conjugate transpose)
.fi
.PP
.br
\fITRANB\fP 
.PP
.nf
          TRANB is CHARACTER*1
          Specifies the option op(B):
          = 'N': op(B) = B    (No transpose)
          = 'C': op(B) = B**H (Conjugate 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 COMPLEX array, dimension (LDA,M)
          The upper triangular matrix A\&.
.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 COMPLEX array, dimension (LDB,N)
          The upper triangular matrix B\&.
.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 COMPLEX 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 REAL
          The scale factor, scale, set <= 1 to avoid overflow in X\&.
.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
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB155\fP of file \fBctrsyl\&.f\fP\&.
.SS "subroutine dtrsyl (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 info)"

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

.PP
.nf
 DTRSYL 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\&.
.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
\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
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB162\fP of file \fBdtrsyl\&.f\fP\&.
.SS "subroutine strsyl (character trana, character tranb, integer isgn, integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldc, * ) c, integer ldc, real scale, integer info)"

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

.PP
.nf
 STRSYL 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 SHSEQR), 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\&.
.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 REAL 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 REAL 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 REAL 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 REAL
          The scale factor, scale, set <= 1 to avoid overflow in X\&.
.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
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB162\fP of file \fBstrsyl\&.f\fP\&.
.SS "subroutine ztrsyl (character trana, character tranb, integer isgn, 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, double precision scale, integer info)"

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

.PP
.nf
 ZTRSYL solves the complex 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**H, and A and B are both upper 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\&.
.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)
          = 'C': op(A) = A**H (Conjugate transpose)
.fi
.PP
.br
\fITRANB\fP 
.PP
.nf
          TRANB is CHARACTER*1
          Specifies the option op(B):
          = 'N': op(B) = B    (No transpose)
          = 'C': op(B) = B**H (Conjugate 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 COMPLEX*16 array, dimension (LDA,M)
          The upper triangular matrix A\&.
.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 COMPLEX*16 array, dimension (LDB,N)
          The upper triangular matrix B\&.
.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 COMPLEX*16 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
\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
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB155\fP of file \fBztrsyl\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.