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 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).

Definition at line 154 of file ctrsyl3.f.

  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).

Definition at line 155 of file ztrsyl3.f.

Author

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