NAME

trsyl - trsyl: Sylvester equation

SYNOPSIS

Functions

subroutine ctrsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info)
CTRSYL subroutine dtrsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info)
DTRSYL subroutine strsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info)
STRSYL subroutine ztrsyl (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info)
ZTRSYL

Detailed Description

Function Documentation

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)

CTRSYL

Purpose:



 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.

Parameters

TRANA



          TRANA is CHARACTER*1


          Specifies the option op(A):


          = 'N': op(A) = A    (No transpose)


          = 'C': op(A) = A**H (Conjugate transpose)

TRANB



          TRANB is CHARACTER*1


          Specifies the option op(B):


          = 'N': op(B) = B    (No transpose)


          = 'C': op(B) = B**H (Conjugate transpose)

ISGN



          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



          M is INTEGER


          The order of the matrix A, and the number of rows in the


          matrices X and C. M >= 0.



          N is INTEGER


          The order of the matrix B, and the number of columns in the


          matrices X and C. N >= 0.



          A is COMPLEX array, dimension (LDA,M)


          The upper triangular matrix A.

LDA



          LDA is INTEGER


          The leading dimension of the array A. LDA >= max(1,M).



          B is COMPLEX array, dimension (LDB,N)


          The upper triangular matrix B.

LDB



          LDB is INTEGER


          The leading dimension of the array B. LDB >= max(1,N).



          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.

LDC



          LDC is INTEGER


          The leading dimension of the array C. LDC >= max(1,M)

SCALE



          SCALE is REAL


          The scale factor, scale, set <= 1 to avoid overflow in X.

INFO



          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).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 155 of file ctrsyl.f.

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)

DTRSYL

Purpose:



 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.

Parameters

TRANA



          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)

TRANB



          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)

ISGN



          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



          M is INTEGER


          The order of the matrix A, and the number of rows in the


          matrices X and C. M >= 0.



          N is INTEGER


          The order of the matrix B, and the number of columns in the


          matrices X and C. N >= 0.



          A is DOUBLE PRECISION array, dimension (LDA,M)


          The upper quasi-triangular matrix A, in Schur canonical form.

LDA



          LDA is INTEGER


          The leading dimension of the array A. LDA >= max(1,M).



          B is DOUBLE PRECISION array, dimension (LDB,N)


          The upper quasi-triangular matrix B, in Schur canonical form.

LDB



          LDB is INTEGER


          The leading dimension of the array B. LDB >= max(1,N).



          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.

LDC



          LDC is INTEGER


          The leading dimension of the array C. LDC >= max(1,M)

SCALE



          SCALE is DOUBLE PRECISION


          The scale factor, scale, set <= 1 to avoid overflow in X.

INFO



          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).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 162 of file dtrsyl.f.

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)

STRSYL

Purpose:



 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.

Parameters

TRANA



          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)

TRANB



          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)

ISGN



          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



          M is INTEGER


          The order of the matrix A, and the number of rows in the


          matrices X and C. M >= 0.



          N is INTEGER


          The order of the matrix B, and the number of columns in the


          matrices X and C. N >= 0.



          A is REAL array, dimension (LDA,M)


          The upper quasi-triangular matrix A, in Schur canonical form.

LDA



          LDA is INTEGER


          The leading dimension of the array A. LDA >= max(1,M).



          B is REAL array, dimension (LDB,N)


          The upper quasi-triangular matrix B, in Schur canonical form.

LDB



          LDB is INTEGER


          The leading dimension of the array B. LDB >= max(1,N).



          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.

LDC



          LDC is INTEGER


          The leading dimension of the array C. LDC >= max(1,M)

SCALE



          SCALE is REAL


          The scale factor, scale, set <= 1 to avoid overflow in X.

INFO



          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).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 162 of file strsyl.f.

subroutine ztrsyl (character trana, character tranb, integer isgn, integer m, integer n, complex16, dimension( lda, ) a, integer lda, complex16, dimension( ldb, ) b, integer ldb, complex16, dimension( ldc, ) c, integer ldc, double precision scale, integer info)

ZTRSYL

Purpose:



 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.

Parameters

TRANA



          TRANA is CHARACTER*1


          Specifies the option op(A):


          = 'N': op(A) = A    (No transpose)


          = 'C': op(A) = A**H (Conjugate transpose)

TRANB



          TRANB is CHARACTER*1


          Specifies the option op(B):


          = 'N': op(B) = B    (No transpose)


          = 'C': op(B) = B**H (Conjugate transpose)

ISGN



          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



          M is INTEGER


          The order of the matrix A, and the number of rows in the


          matrices X and C. M >= 0.



          N is INTEGER


          The order of the matrix B, and the number of columns in the


          matrices X and C. N >= 0.



          A is COMPLEX*16 array, dimension (LDA,M)


          The upper triangular matrix A.

LDA



          LDA is INTEGER


          The leading dimension of the array A. LDA >= max(1,M).



          B is COMPLEX*16 array, dimension (LDB,N)


          The upper triangular matrix B.

LDB



          LDB is INTEGER


          The leading dimension of the array B. LDB >= max(1,N).



          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.

LDC



          LDC is INTEGER


          The leading dimension of the array C. LDC >= max(1,M)

SCALE



          SCALE is DOUBLE PRECISION


          The scale factor, scale, set <= 1 to avoid overflow in X.

INFO



          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).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 155 of file ztrsyl.f.

Author

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