trsyl(3)

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

    !>          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.

  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.

  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.

  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.

Author

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