trsyl3(3)

NAME
trsyl3 - trsyl3: Sylvester equation, level 3

SYNOPSIS

  Functions

subroutine ctrsyl3 (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, swork, ldswork, info)
CTRSYL3
subroutine dtrsyl3 (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, iwork, liwork, swork, ldswork, info)
DTRSYL3
subroutine strsyl3 (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, iwork, liwork, swork, ldswork, info)
STRSYL3
subroutine ztrsyl3 (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, swork, ldswork, info)
ZTRSYL3

Detailed Description

Function Documentation

  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)

CTRSYL3

Purpose:

    !>
    !>  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.
    !>

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.
    !>

    SWORK

    !>          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.
    !>

    LDSWORK

    !>          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.
    !>

    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).
    !>

  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)

DTRSYL3

Purpose:

    !>
    !>  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.
    !>

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.
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
    !>          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
    !>

    LIWORK

    !>          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.
    !>

    SWORK

    !>          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.
    !>

    LDSWORK

    !>          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.
    !>

    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).
    !>

  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)

STRSYL3

Purpose:

    !>
    !>  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.
    !>

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.
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
    !>          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
    !>

    LIWORK

    !>          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.
    !>

    SWORK

    !>          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.
    !>

    LDSWORK

    !>          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.
    !>

    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).
    !>

  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)

ZTRSYL3

Purpose:

    !>
    !>  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.
    !>

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.
    !>

    SWORK

    !>          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.
    !>

    LDSWORK

    !>          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.
    !>

    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

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