trsyl - Man Page

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

          M is INTEGER
          The order of the matrix A, and the number of rows in the
          matrices X and C. M >= 0.

N

          N is INTEGER
          The order of the matrix B, and the number of columns in the
          matrices X and C. N >= 0.

A

          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

          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

          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

          M is INTEGER
          The order of the matrix A, and the number of rows in the
          matrices X and C. M >= 0.

N

          N is INTEGER
          The order of the matrix B, and the number of columns in the
          matrices X and C. N >= 0.

A

          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

          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

          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

          M is INTEGER
          The order of the matrix A, and the number of rows in the
          matrices X and C. M >= 0.

N

          N is INTEGER
          The order of the matrix B, and the number of columns in the
          matrices X and C. N >= 0.

A

          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

          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

          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, 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)

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

          M is INTEGER
          The order of the matrix A, and the number of rows in the
          matrices X and C. M >= 0.

N

          N is INTEGER
          The order of the matrix B, and the number of columns in the
          matrices X and C. N >= 0.

A

          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

          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

          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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Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK