.TH "trsyl3" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
trsyl3 \- trsyl3: Sylvester equation, level 3
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBctrsyl3\fP (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, swork, ldswork, info)"
.br
.RI "\fBCTRSYL3\fP "
.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 "
.ti -1c
.RI "subroutine \fBstrsyl3\fP (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, iwork, liwork, swork, ldswork, info)"
.br
.RI "\fBSTRSYL3\fP "
.ti -1c
.RI "subroutine \fBztrsyl3\fP (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, swork, ldswork, info)"
.br
.RI "\fBZTRSYL3\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine ctrsyl3 (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, real, dimension( ldswork, * ) swork, integer ldswork, integer info)"

.PP
\fBCTRSYL3\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!>  CTRSYL3 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\&.
!>
!>  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)
!>          = '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
\fISWORK\fP 
.PP
.nf
!>          SWORK is REAL 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 \fB167\fP of file \fBctrsyl3\&.f\fP\&.
.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 \fB197\fP of file \fBdtrsyl3\&.f\fP\&.
.SS "subroutine strsyl3 (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, dimension( * ) iwork, integer liwork, real, dimension( ldswork, * ) swork, integer ldswork, integer info)"

.PP
\fBSTRSYL3\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!>  STRSYL3 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\&.
!>
!>  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 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
\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 REAL 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 \fB196\fP of file \fBstrsyl3\&.f\fP\&.
.SS "subroutine ztrsyl3 (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, double precision, dimension( ldswork, * ) swork, integer ldswork, integer info)"

.PP
\fBZTRSYL3\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!>  ZTRSYL3 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\&.
!>
!>  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)
!>          = '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
\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
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.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
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.RE
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.PP
Definition at line \fB168\fP of file \fBztrsyl3\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.