Library Functions Manual

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 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.
!>

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, complex16, dimension( lda, ) a, integer lda, complex16, dimension( ldb, ) b, integer ldb, complex16, dimension( ldc, ) c, integer ldc, double precision scale, double precision, dimension( ldswork, * ) swork, integer ldswork, integer info)¶

ZTRSYL3