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dtrsyl.f

      SUBROUTINE DTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C,
     $                   LDC, SCALE, INFO )
*
*  -- LAPACK routine (version 2.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
*     Courant Institute, Argonne National Lab, and Rice University
*     March 31, 1993
*
*     .. Scalar Arguments ..
      CHARACTER          TRANA, TRANB
      INTEGER            INFO, ISGN, LDA, LDB, LDC, M, N
      DOUBLE PRECISION   SCALE
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), C( LDC, * )
*     ..
*
*  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.
*
*  Arguments
*  =========
*
*  TRANA   (input) 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   (input) 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    (input) 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       (input) INTEGER
*          The order of the matrix A, and the number of rows in the
*          matrices X and C. M >= 0.
*
*  N       (input) INTEGER
*          The order of the matrix B, and the number of columns in the
*          matrices X and C. N >= 0.
*
*  A       (input) DOUBLE PRECISION array, dimension (LDA,M)
*          The upper quasi-triangular matrix A, in Schur canonical form.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A. LDA >= max(1,M).
*
*  B       (input) DOUBLE PRECISION array, dimension (LDB,N)
*          The upper quasi-triangular matrix B, in Schur canonical form.
*
*  LDB     (input) INTEGER
*          The leading dimension of the array B. LDB >= max(1,N).
*
*  C       (input/output) 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     (input) INTEGER
*          The leading dimension of the array C. LDC >= max(1,M)
*
*  SCALE   (output) DOUBLE PRECISION
*          The scale factor, scale, set <= 1 to avoid overflow in X.
*
*  INFO    (output) 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).
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            NOTRNA, NOTRNB
      INTEGER            IERR, J, K, K1, K2, KNEXT, L, L1, L2, LNEXT
      DOUBLE PRECISION   A11, BIGNUM, DA11, DB, EPS, SCALOC, SGN, SMIN,
     $                   SMLNUM, SUML, SUMR, XNORM
*     ..
*     .. Local Arrays ..
      DOUBLE PRECISION   DUM( 1 ), VEC( 2, 2 ), X( 2, 2 )
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DDOT, DLAMCH, DLANGE
      EXTERNAL           LSAME, DDOT, DLAMCH, DLANGE
*     ..
*     .. External Subroutines ..
      EXTERNAL           DLABAD, DLALN2, DLASY2, DSCAL, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, DBLE, MAX, MIN
*     ..
*     .. Executable Statements ..
*
*     Decode and Test input parameters
*
      NOTRNA = LSAME( TRANA, 'N' )
      NOTRNB = LSAME( TRANB, 'N' )
*
      INFO = 0
      IF( .NOT.NOTRNA .AND. .NOT.LSAME( TRANA, 'T' ) .AND. .NOT.
     $    LSAME( TRANA, 'C' ) ) THEN
         INFO = -1
      ELSE IF( .NOT.NOTRNB .AND. .NOT.LSAME( TRANB, 'T' ) .AND. .NOT.
     $         LSAME( TRANB, 'C' ) ) THEN
         INFO = -2
      ELSE IF( ISGN.NE.1 .AND. ISGN.NE.-1 ) THEN
         INFO = -3
      ELSE IF( M.LT.0 ) THEN
         INFO = -4
      ELSE IF( N.LT.0 ) THEN
         INFO = -5
      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
         INFO = -7
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -9
      ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
         INFO = -11
      END IF
      IF( INFO.NE.0 ) THEN
         CALL XERBLA( 'DTRSYL', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( M.EQ.0 .OR. N.EQ.0 )
     $   RETURN
*
*     Set constants to control overflow
*
      EPS = DLAMCH( 'P' )
      SMLNUM = DLAMCH( 'S' )
      BIGNUM = ONE / SMLNUM
      CALL DLABAD( SMLNUM, BIGNUM )
      SMLNUM = SMLNUM*DBLE( M*N ) / EPS
      BIGNUM = ONE / SMLNUM
*
      SMIN = MAX( SMLNUM, EPS*DLANGE( 'M', M, M, A, LDA, DUM ),
     $       EPS*DLANGE( 'M', N, N, B, LDB, DUM ) )
*
      SCALE = ONE
      SGN = ISGN
*
      IF( NOTRNA .AND. NOTRNB ) THEN
*
*        Solve    A*X + ISGN*X*B = scale*C.
*
*        The (K,L)th block of X is determined starting from
*        bottom-left corner column by column by
*
*         A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
*
*        Where
*                  M                         L-1
*        R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B(J,L)].
*                I=K+1                       J=1
*
*        Start column loop (index = L)
*        L1 (L2) : column index of the first (first) row of X(K,L).
*
         LNEXT = 1
         DO 60 L = 1, N
            IF( L.LT.LNEXT )
     $         GO TO 60
            IF( L.EQ.N ) THEN
               L1 = L
               L2 = L
            ELSE
               IF( B( L+1, L ).NE.ZERO ) THEN
                  L1 = L
                  L2 = L + 1
                  LNEXT = L + 2
               ELSE
                  L1 = L
                  L2 = L
                  LNEXT = L + 1
               END IF
            END IF
*
*           Start row loop (index = K)
*           K1 (K2): row index of the first (last) row of X(K,L).
*
            KNEXT = M
            DO 50 K = M, 1, -1
               IF( K.GT.KNEXT )
     $            GO TO 50
               IF( K.EQ.1 ) THEN
                  K1 = K
                  K2 = K
               ELSE
                  IF( A( K, K-1 ).NE.ZERO ) THEN
                     K1 = K - 1
                     K2 = K
                     KNEXT = K - 2
                  ELSE
                     K1 = K
                     K2 = K
                     KNEXT = K - 1
                  END IF
               END IF
*
               IF( L1.EQ.L2 .AND. K1.EQ.K2 ) THEN
                  SUML = DDOT( M-K1, A( K1, MIN( K1+1, M ) ), LDA,
     $                   C( MIN( K1+1, M ), L1 ), 1 )
                  SUMR = DDOT( L1-1, C( K1, 1 ), LDC, B( 1, L1 ), 1 )
                  VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )
                  SCALOC = ONE
*
                  A11 = A( K1, K1 ) + SGN*B( L1, L1 )
                  DA11 = ABS( A11 )
                  IF( DA11.LE.SMIN ) THEN
                     A11 = SMIN
                     DA11 = SMIN
                     INFO = 1
                  END IF
                  DB = ABS( VEC( 1, 1 ) )
                  IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
                     IF( DB.GT.BIGNUM*DA11 )
     $                  SCALOC = ONE / DB
                  END IF
                  X( 1, 1 ) = ( VEC( 1, 1 )*SCALOC ) / A11
*
                  IF( SCALOC.NE.ONE ) THEN
                     DO 10 J = 1, N
                        CALL DSCAL( M, SCALOC, C( 1, J ), 1 )
   10                CONTINUE
                     SCALE = SCALE*SCALOC
                  END IF
                  C( K1, L1 ) = X( 1, 1 )
*
               ELSE IF( L1.EQ.L2 .AND. K1.NE.K2 ) THEN
*
                  SUML = DDOT( M-K2, A( K1, MIN( K2+1, M ) ), LDA,
     $                   C( MIN( K2+1, M ), L1 ), 1 )
                  SUMR = DDOT( L1-1, C( K1, 1 ), LDC, B( 1, L1 ), 1 )
                  VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )
*
                  SUML = DDOT( M-K2, A( K2, MIN( K2+1, M ) ), LDA,
     $                   C( MIN( K2+1, M ), L1 ), 1 )
                  SUMR = DDOT( L1-1, C( K2, 1 ), LDC, B( 1, L1 ), 1 )
                  VEC( 2, 1 ) = C( K2, L1 ) - ( SUML+SGN*SUMR )
*
                  CALL DLALN2( .FALSE., 2, 1, SMIN, ONE, A( K1, K1 ),
     $                         LDA, ONE, ONE, VEC, 2, -SGN*B( L1, L1 ),
     $                         ZERO, X, 2, SCALOC, XNORM, IERR )
                  IF( IERR.NE.0 )
     $               INFO = 1
*
                  IF( SCALOC.NE.ONE ) THEN
                     DO 20 J = 1, N
                        CALL DSCAL( M, SCALOC, C( 1, J ), 1 )
   20                CONTINUE
                     SCALE = SCALE*SCALOC
                  END IF
                  C( K1, L1 ) = X( 1, 1 )
                  C( K2, L1 ) = X( 2, 1 )
*
               ELSE IF( L1.NE.L2 .AND. K1.EQ.K2 ) THEN
*
                  SUML = DDOT( M-K1, A( K1, MIN( K1+1, M ) ), LDA,
     $                   C( MIN( K1+1, M ), L1 ), 1 )
                  SUMR = DDOT( L1-1, C( K1, 1 ), LDC, B( 1, L1 ), 1 )
                  VEC( 1, 1 ) = SGN*( C( K1, L1 )-( SUML+SGN*SUMR ) )
*
                  SUML = DDOT( M-K1, A( K1, MIN( K1+1, M ) ), LDA,
     $                   C( MIN( K1+1, M ), L2 ), 1 )
                  SUMR = DDOT( L1-1, C( K1, 1 ), LDC, B( 1, L2 ), 1 )
                  VEC( 2, 1 ) = SGN*( C( K1, L2 )-( SUML+SGN*SUMR ) )
*
                  CALL DLALN2( .TRUE., 2, 1, SMIN, ONE, B( L1, L1 ),
     $                         LDB, ONE, ONE, VEC, 2, -SGN*A( K1, K1 ),
     $                         ZERO, X, 2, SCALOC, XNORM, IERR )
                  IF( IERR.NE.0 )
     $               INFO = 1
*
                  IF( SCALOC.NE.ONE ) THEN
                     DO 30 J = 1, N
                        CALL DSCAL( M, SCALOC, C( 1, J ), 1 )
   30                CONTINUE
                     SCALE = SCALE*SCALOC
                  END IF
                  C( K1, L1 ) = X( 1, 1 )
                  C( K1, L2 ) = X( 2, 1 )
*
               ELSE IF( L1.NE.L2 .AND. K1.NE.K2 ) THEN
*
                  SUML = DDOT( M-K2, A( K1, MIN( K2+1, M ) ), LDA,
     $                   C( MIN( K2+1, M ), L1 ), 1 )
                  SUMR = DDOT( L1-1, C( K1, 1 ), LDC, B( 1, L1 ), 1 )
                  VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )
*
                  SUML = DDOT( M-K2, A( K1, MIN( K2+1, M ) ), LDA,
     $                   C( MIN( K2+1, M ), L2 ), 1 )
                  SUMR = DDOT( L1-1, C( K1, 1 ), LDC, B( 1, L2 ), 1 )
                  VEC( 1, 2 ) = C( K1, L2 ) - ( SUML+SGN*SUMR )
*
                  SUML = DDOT( M-K2, A( K2, MIN( K2+1, M ) ), LDA,
     $                   C( MIN( K2+1, M ), L1 ), 1 )
                  SUMR = DDOT( L1-1, C( K2, 1 ), LDC, B( 1, L1 ), 1 )
                  VEC( 2, 1 ) = C( K2, L1 ) - ( SUML+SGN*SUMR )
*
                  SUML = DDOT( M-K2, A( K2, MIN( K2+1, M ) ), LDA,
     $                   C( MIN( K2+1, M ), L2 ), 1 )
                  SUMR = DDOT( L1-1, C( K2, 1 ), LDC, B( 1, L2 ), 1 )
                  VEC( 2, 2 ) = C( K2, L2 ) - ( SUML+SGN*SUMR )
*
                  CALL DLASY2( .FALSE., .FALSE., ISGN, 2, 2,
     $                         A( K1, K1 ), LDA, B( L1, L1 ), LDB, VEC,
     $                         2, SCALOC, X, 2, XNORM, IERR )
                  IF( IERR.NE.0 )
     $               INFO = 1
*
                  IF( SCALOC.NE.ONE ) THEN
                     DO 40 J = 1, N
                        CALL DSCAL( M, SCALOC, C( 1, J ), 1 )
   40                CONTINUE
                     SCALE = SCALE*SCALOC
                  END IF
                  C( K1, L1 ) = X( 1, 1 )
                  C( K1, L2 ) = X( 1, 2 )
                  C( K2, L1 ) = X( 2, 1 )
                  C( K2, L2 ) = X( 2, 2 )
               END IF
*
   50       CONTINUE
*
   60    CONTINUE
*
      ELSE IF( .NOT.NOTRNA .AND. NOTRNB ) THEN
*
*        Solve    A




' *X + ISGN*X*B = scale*C.**        The (K,L)th block of X is determined starting from*        upper-left corner column by column by**          A(K,K)'*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
*
*        Where
*                   K-1                        L-1
*          R(K,L) = SUM [A(I,K)





































































































































































'*X(I,L)] +ISGN*SUM [X(K,J)*B(J,L)]*                   I=1                        J=1**        Start column loop (index = L)*        L1 (L2): column index of the first (last) row of X(K,L)*         LNEXT = 1         DO 120 L = 1, N            IF( L.LT.LNEXT )     $         GO TO 120            IF( L.EQ.N ) THEN               L1 = L               L2 = L            ELSE               IF( B( L+1, L ).NE.ZERO ) THEN                  L1 = L                  L2 = L + 1                  LNEXT = L + 2               ELSE                  L1 = L                  L2 = L                  LNEXT = L + 1               END IF            END IF**           Start row loop (index = K)*           K1 (K2): row index of the first (last) row of X(K,L)*            KNEXT = 1            DO 110 K = 1, M               IF( K.LT.KNEXT )     $            GO TO 110               IF( K.EQ.M ) THEN                  K1 = K                  K2 = K               ELSE                  IF( A( K+1, K ).NE.ZERO ) THEN                     K1 = K                     K2 = K + 1                     KNEXT = K + 2                  ELSE                     K1 = K                     K2 = K                     KNEXT = K + 1                  END IF               END IF*               IF( L1.EQ.L2 .AND. K1.EQ.K2 ) THEN                  SUML = DDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 )                  SUMR = DDOT( L1-1, C( K1, 1 ), LDC, B( 1, L1 ), 1 )                  VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )                  SCALOC = ONE*                  A11 = A( K1, K1 ) + SGN*B( L1, L1 )                  DA11 = ABS( A11 )                  IF( DA11.LE.SMIN ) THEN                     A11 = SMIN                     DA11 = SMIN                     INFO = 1                  END IF                  DB = ABS( VEC( 1, 1 ) )                  IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN                     IF( DB.GT.BIGNUM*DA11 )     $                  SCALOC = ONE / DB                  END IF                  X( 1, 1 ) = ( VEC( 1, 1 )*SCALOC ) / A11*                  IF( SCALOC.NE.ONE ) THEN                     DO 70 J = 1, N                        CALL DSCAL( M, SCALOC, C( 1, J ), 1 )   70                CONTINUE                     SCALE = SCALE*SCALOC                  END IF                  C( K1, L1 ) = X( 1, 1 )*               ELSE IF( L1.EQ.L2 .AND. K1.NE.K2 ) THEN*                  SUML = DDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 )                  SUMR = DDOT( L1-1, C( K1, 1 ), LDC, B( 1, L1 ), 1 )                  VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )*                  SUML = DDOT( K1-1, A( 1, K2 ), 1, C( 1, L1 ), 1 )                  SUMR = DDOT( L1-1, C( K2, 1 ), LDC, B( 1, L1 ), 1 )                  VEC( 2, 1 ) = C( K2, L1 ) - ( SUML+SGN*SUMR )*                  CALL DLALN2( .TRUE., 2, 1, SMIN, ONE, A( K1, K1 ),     $                         LDA, ONE, ONE, VEC, 2, -SGN*B( L1, L1 ),     $                         ZERO, X, 2, SCALOC, XNORM, IERR )                  IF( IERR.NE.0 )     $               INFO = 1*                  IF( SCALOC.NE.ONE ) THEN                     DO 80 J = 1, N                        CALL DSCAL( M, SCALOC, C( 1, J ), 1 )   80                CONTINUE                     SCALE = SCALE*SCALOC                  END IF                  C( K1, L1 ) = X( 1, 1 )                  C( K2, L1 ) = X( 2, 1 )*               ELSE IF( L1.NE.L2 .AND. K1.EQ.K2 ) THEN*                  SUML = DDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 )                  SUMR = DDOT( L1-1, C( K1, 1 ), LDC, B( 1, L1 ), 1 )                  VEC( 1, 1 ) = SGN*( C( K1, L1 )-( SUML+SGN*SUMR ) )*                  SUML = DDOT( K1-1, A( 1, K1 ), 1, C( 1, L2 ), 1 )                  SUMR = DDOT( L1-1, C( K1, 1 ), LDC, B( 1, L2 ), 1 )                  VEC( 2, 1 ) = SGN*( C( K1, L2 )-( SUML+SGN*SUMR ) )*                  CALL DLALN2( .TRUE., 2, 1, SMIN, ONE, B( L1, L1 ),     $                         LDB, ONE, ONE, VEC, 2, -SGN*A( K1, K1 ),     $                         ZERO, X, 2, SCALOC, XNORM, IERR )                  IF( IERR.NE.0 )     $               INFO = 1*                  IF( SCALOC.NE.ONE ) THEN                     DO 90 J = 1, N                        CALL DSCAL( M, SCALOC, C( 1, J ), 1 )   90                CONTINUE                     SCALE = SCALE*SCALOC                  END IF                  C( K1, L1 ) = X( 1, 1 )                  C( K1, L2 ) = X( 2, 1 )*               ELSE IF( L1.NE.L2 .AND. K1.NE.K2 ) THEN*                  SUML = DDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 )                  SUMR = DDOT( L1-1, C( K1, 1 ), LDC, B( 1, L1 ), 1 )                  VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )*                  SUML = DDOT( K1-1, A( 1, K1 ), 1, C( 1, L2 ), 1 )                  SUMR = DDOT( L1-1, C( K1, 1 ), LDC, B( 1, L2 ), 1 )                  VEC( 1, 2 ) = C( K1, L2 ) - ( SUML+SGN*SUMR )*                  SUML = DDOT( K1-1, A( 1, K2 ), 1, C( 1, L1 ), 1 )                  SUMR = DDOT( L1-1, C( K2, 1 ), LDC, B( 1, L1 ), 1 )                  VEC( 2, 1 ) = C( K2, L1 ) - ( SUML+SGN*SUMR )*                  SUML = DDOT( K1-1, A( 1, K2 ), 1, C( 1, L2 ), 1 )                  SUMR = DDOT( L1-1, C( K2, 1 ), LDC, B( 1, L2 ), 1 )                  VEC( 2, 2 ) = C( K2, L2 ) - ( SUML+SGN*SUMR )*                  CALL DLASY2( .TRUE., .FALSE., ISGN, 2, 2, A( K1, K1 ),     $                         LDA, B( L1, L1 ), LDB, VEC, 2, SCALOC, X,     $                         2, XNORM, IERR )                  IF( IERR.NE.0 )     $               INFO = 1*                  IF( SCALOC.NE.ONE ) THEN                     DO 100 J = 1, N                        CALL DSCAL( M, SCALOC, C( 1, J ), 1 )  100                CONTINUE                     SCALE = SCALE*SCALOC                  END IF                  C( K1, L1 ) = X( 1, 1 )                  C( K1, L2 ) = X( 1, 2 )                  C( K2, L1 ) = X( 2, 1 )                  C( K2, L2 ) = X( 2, 2 )               END IF*  110       CONTINUE  120    CONTINUE*      ELSE IF( .NOT.NOTRNA .AND. .NOT.NOTRNB ) THEN**        Solve    A'*X + ISGN*X*B




' = scale*C.**        The (K,L)th block of X is determined starting from*        top-right corner column by column by**           A(K,K)'*X(K,L) + ISGN*X(K,L)*B(L,L)



' = C(K,L) - R(K,L)**        Where*                     K-1                          N*            R(K,L) = SUM [A(I,K)'*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)














































































































































































'].*                     I=1                        J=L+1**        Start column loop (index = L)*        L1 (L2): column index of the first (last) row of X(K,L)*         LNEXT = N         DO 180 L = N, 1, -1            IF( L.GT.LNEXT )     $         GO TO 180            IF( L.EQ.1 ) THEN               L1 = L               L2 = L            ELSE               IF( B( L, L-1 ).NE.ZERO ) THEN                  L1 = L - 1                  L2 = L                  LNEXT = L - 2               ELSE                  L1 = L                  L2 = L                  LNEXT = L - 1               END IF            END IF**           Start row loop (index = K)*           K1 (K2): row index of the first (last) row of X(K,L)*            KNEXT = 1            DO 170 K = 1, M               IF( K.LT.KNEXT )     $            GO TO 170               IF( K.EQ.M ) THEN                  K1 = K                  K2 = K               ELSE                  IF( A( K+1, K ).NE.ZERO ) THEN                     K1 = K                     K2 = K + 1                     KNEXT = K + 2                  ELSE                     K1 = K                     K2 = K                     KNEXT = K + 1                  END IF               END IF*               IF( L1.EQ.L2 .AND. K1.EQ.K2 ) THEN                  SUML = DDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 )                  SUMR = DDOT( N-L1, C( K1, MIN( L1+1, N ) ), LDC,     $                   B( L1, MIN( L1+1, N ) ), LDB )                  VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )                  SCALOC = ONE*                  A11 = A( K1, K1 ) + SGN*B( L1, L1 )                  DA11 = ABS( A11 )                  IF( DA11.LE.SMIN ) THEN                     A11 = SMIN                     DA11 = SMIN                     INFO = 1                  END IF                  DB = ABS( VEC( 1, 1 ) )                  IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN                     IF( DB.GT.BIGNUM*DA11 )     $                  SCALOC = ONE / DB                  END IF                  X( 1, 1 ) = ( VEC( 1, 1 )*SCALOC ) / A11*                  IF( SCALOC.NE.ONE ) THEN                     DO 130 J = 1, N                        CALL DSCAL( M, SCALOC, C( 1, J ), 1 )  130                CONTINUE                     SCALE = SCALE*SCALOC                  END IF                  C( K1, L1 ) = X( 1, 1 )*               ELSE IF( L1.EQ.L2 .AND. K1.NE.K2 ) THEN*                  SUML = DDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 )                  SUMR = DDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,     $                   B( L1, MIN( L2+1, N ) ), LDB )                  VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )*                  SUML = DDOT( K1-1, A( 1, K2 ), 1, C( 1, L1 ), 1 )                  SUMR = DDOT( N-L2, C( K2, MIN( L2+1, N ) ), LDC,     $                   B( L1, MIN( L2+1, N ) ), LDB )                  VEC( 2, 1 ) = C( K2, L1 ) - ( SUML+SGN*SUMR )*                  CALL DLALN2( .TRUE., 2, 1, SMIN, ONE, A( K1, K1 ),     $                         LDA, ONE, ONE, VEC, 2, -SGN*B( L1, L1 ),     $                         ZERO, X, 2, SCALOC, XNORM, IERR )                  IF( IERR.NE.0 )     $               INFO = 1*                  IF( SCALOC.NE.ONE ) THEN                     DO 140 J = 1, N                        CALL DSCAL( M, SCALOC, C( 1, J ), 1 )  140                CONTINUE                     SCALE = SCALE*SCALOC                  END IF                  C( K1, L1 ) = X( 1, 1 )                  C( K2, L1 ) = X( 2, 1 )*               ELSE IF( L1.NE.L2 .AND. K1.EQ.K2 ) THEN*                  SUML = DDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 )                  SUMR = DDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,     $                   B( L1, MIN( L2+1, N ) ), LDB )                  VEC( 1, 1 ) = SGN*( C( K1, L1 )-( SUML+SGN*SUMR ) )*                  SUML = DDOT( K1-1, A( 1, K1 ), 1, C( 1, L2 ), 1 )                  SUMR = DDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,     $                   B( L2, MIN( L2+1, N ) ), LDB )                  VEC( 2, 1 ) = SGN*( C( K1, L2 )-( SUML+SGN*SUMR ) )*                  CALL DLALN2( .FALSE., 2, 1, SMIN, ONE, B( L1, L1 ),     $                         LDB, ONE, ONE, VEC, 2, -SGN*A( K1, K1 ),     $                         ZERO, X, 2, SCALOC, XNORM, IERR )                  IF( IERR.NE.0 )     $               INFO = 1*                  IF( SCALOC.NE.ONE ) THEN                     DO 150 J = 1, N                        CALL DSCAL( M, SCALOC, C( 1, J ), 1 )  150                CONTINUE                     SCALE = SCALE*SCALOC                  END IF                  C( K1, L1 ) = X( 1, 1 )                  C( K1, L2 ) = X( 2, 1 )*               ELSE IF( L1.NE.L2 .AND. K1.NE.K2 ) THEN*                  SUML = DDOT( K1-1, A( 1, K1 ), 1, C( 1, L1 ), 1 )                  SUMR = DDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,     $                   B( L1, MIN( L2+1, N ) ), LDB )                  VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )*                  SUML = DDOT( K1-1, A( 1, K1 ), 1, C( 1, L2 ), 1 )                  SUMR = DDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,     $                   B( L2, MIN( L2+1, N ) ), LDB )                  VEC( 1, 2 ) = C( K1, L2 ) - ( SUML+SGN*SUMR )*                  SUML = DDOT( K1-1, A( 1, K2 ), 1, C( 1, L1 ), 1 )                  SUMR = DDOT( N-L2, C( K2, MIN( L2+1, N ) ), LDC,     $                   B( L1, MIN( L2+1, N ) ), LDB )                  VEC( 2, 1 ) = C( K2, L1 ) - ( SUML+SGN*SUMR )*                  SUML = DDOT( K1-1, A( 1, K2 ), 1, C( 1, L2 ), 1 )                  SUMR = DDOT( N-L2, C( K2, MIN( L2+1, N ) ), LDC,     $                   B( L2, MIN( L2+1, N ) ), LDB )                  VEC( 2, 2 ) = C( K2, L2 ) - ( SUML+SGN*SUMR )*                  CALL DLASY2( .TRUE., .TRUE., ISGN, 2, 2, A( K1, K1 ),     $                         LDA, B( L1, L1 ), LDB, VEC, 2, SCALOC, X,     $                         2, XNORM, IERR )                  IF( IERR.NE.0 )     $               INFO = 1*                  IF( SCALOC.NE.ONE ) THEN                     DO 160 J = 1, N                        CALL DSCAL( M, SCALOC, C( 1, J ), 1 )  160                CONTINUE                     SCALE = SCALE*SCALOC                  END IF                  C( K1, L1 ) = X( 1, 1 )                  C( K1, L2 ) = X( 1, 2 )                  C( K2, L1 ) = X( 2, 1 )                  C( K2, L2 ) = X( 2, 2 )               END IF*  170       CONTINUE  180    CONTINUE*      ELSE IF( NOTRNA .AND. .NOT.NOTRNB ) THEN**        Solve    A*X + ISGN*X*B' = scale*C.
*
*        The (K,L)th block of X is determined starting from
*        bottom-right corner column by column by
*
*            A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L)



' = C(K,L) - R(K,L)**        Where*                      M                          N*            R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B(L,J)'].
*                    I=K+1                      J=L+1
*
*        Start column loop (index = L)
*        L1 (L2): column index of the first (last) row of X(K,L)
*
         LNEXT = N
         DO 240 L = N, 1, -1
            IF( L.GT.LNEXT )
     $         GO TO 240
            IF( L.EQ.1 ) THEN
               L1 = L
               L2 = L
            ELSE
               IF( B( L, L-1 ).NE.ZERO ) THEN
                  L1 = L - 1
                  L2 = L
                  LNEXT = L - 2
               ELSE
                  L1 = L
                  L2 = L
                  LNEXT = L - 1
               END IF
            END IF
*
*           Start row loop (index = K)
*           K1 (K2): row index of the first (last) row of X(K,L)
*
            KNEXT = M
            DO 230 K = M, 1, -1
               IF( K.GT.KNEXT )
     $            GO TO 230
               IF( K.EQ.1 ) THEN
                  K1 = K
                  K2 = K
               ELSE
                  IF( A( K, K-1 ).NE.ZERO ) THEN
                     K1 = K - 1
                     K2 = K
                     KNEXT = K - 2
                  ELSE
                     K1 = K
                     K2 = K
                     KNEXT = K - 1
                  END IF
               END IF
*
               IF( L1.EQ.L2 .AND. K1.EQ.K2 ) THEN
                  SUML = DDOT( M-K1, A( K1, MIN( K1+1, M ) ), LDA,
     $                   C( MIN( K1+1, M ), L1 ), 1 )
                  SUMR = DDOT( N-L1, C( K1, MIN( L1+1, N ) ), LDC,
     $                   B( L1, MIN( L1+1, N ) ), LDB )
                  VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )
                  SCALOC = ONE
*
                  A11 = A( K1, K1 ) + SGN*B( L1, L1 )
                  DA11 = ABS( A11 )
                  IF( DA11.LE.SMIN ) THEN
                     A11 = SMIN
                     DA11 = SMIN
                     INFO = 1
                  END IF
                  DB = ABS( VEC( 1, 1 ) )
                  IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
                     IF( DB.GT.BIGNUM*DA11 )
     $                  SCALOC = ONE / DB
                  END IF
                  X( 1, 1 ) = ( VEC( 1, 1 )*SCALOC ) / A11
*
                  IF( SCALOC.NE.ONE ) THEN
                     DO 190 J = 1, N
                        CALL DSCAL( M, SCALOC, C( 1, J ), 1 )
  190                CONTINUE
                     SCALE = SCALE*SCALOC
                  END IF
                  C( K1, L1 ) = X( 1, 1 )
*
               ELSE IF( L1.EQ.L2 .AND. K1.NE.K2 ) THEN
*
                  SUML = DDOT( M-K2, A( K1, MIN( K2+1, M ) ), LDA,
     $                   C( MIN( K2+1, M ), L1 ), 1 )
                  SUMR = DDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,
     $                   B( L1, MIN( L2+1, N ) ), LDB )
                  VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )
*
                  SUML = DDOT( M-K2, A( K2, MIN( K2+1, M ) ), LDA,
     $                   C( MIN( K2+1, M ), L1 ), 1 )
                  SUMR = DDOT( N-L2, C( K2, MIN( L2+1, N ) ), LDC,
     $                   B( L1, MIN( L2+1, N ) ), LDB )
                  VEC( 2, 1 ) = C( K2, L1 ) - ( SUML+SGN*SUMR )
*
                  CALL DLALN2( .FALSE., 2, 1, SMIN, ONE, A( K1, K1 ),
     $                         LDA, ONE, ONE, VEC, 2, -SGN*B( L1, L1 ),
     $                         ZERO, X, 2, SCALOC, XNORM, IERR )
                  IF( IERR.NE.0 )
     $               INFO = 1
*
                  IF( SCALOC.NE.ONE ) THEN
                     DO 200 J = 1, N
                        CALL DSCAL( M, SCALOC, C( 1, J ), 1 )
  200                CONTINUE
                     SCALE = SCALE*SCALOC
                  END IF
                  C( K1, L1 ) = X( 1, 1 )
                  C( K2, L1 ) = X( 2, 1 )
*
               ELSE IF( L1.NE.L2 .AND. K1.EQ.K2 ) THEN
*
                  SUML = DDOT( M-K1, A( K1, MIN( K1+1, M ) ), LDA,
     $                   C( MIN( K1+1, M ), L1 ), 1 )
                  SUMR = DDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,
     $                   B( L1, MIN( L2+1, N ) ), LDB )
                  VEC( 1, 1 ) = SGN*( C( K1, L1 )-( SUML+SGN*SUMR ) )
*
                  SUML = DDOT( M-K1, A( K1, MIN( K1+1, M ) ), LDA,
     $                   C( MIN( K1+1, M ), L2 ), 1 )
                  SUMR = DDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,
     $                   B( L2, MIN( L2+1, N ) ), LDB )
                  VEC( 2, 1 ) = SGN*( C( K1, L2 )-( SUML+SGN*SUMR ) )
*
                  CALL DLALN2( .FALSE., 2, 1, SMIN, ONE, B( L1, L1 ),
     $                         LDB, ONE, ONE, VEC, 2, -SGN*A( K1, K1 ),
     $                         ZERO, X, 2, SCALOC, XNORM, IERR )
                  IF( IERR.NE.0 )
     $               INFO = 1
*
                  IF( SCALOC.NE.ONE ) THEN
                     DO 210 J = 1, N
                        CALL DSCAL( M, SCALOC, C( 1, J ), 1 )
  210                CONTINUE
                     SCALE = SCALE*SCALOC
                  END IF
                  C( K1, L1 ) = X( 1, 1 )
                  C( K1, L2 ) = X( 2, 1 )
*
               ELSE IF( L1.NE.L2 .AND. K1.NE.K2 ) THEN
*
                  SUML = DDOT( M-K2, A( K1, MIN( K2+1, M ) ), LDA,
     $                   C( MIN( K2+1, M ), L1 ), 1 )
                  SUMR = DDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,
     $                   B( L1, MIN( L2+1, N ) ), LDB )
                  VEC( 1, 1 ) = C( K1, L1 ) - ( SUML+SGN*SUMR )
*
                  SUML = DDOT( M-K2, A( K1, MIN( K2+1, M ) ), LDA,
     $                   C( MIN( K2+1, M ), L2 ), 1 )
                  SUMR = DDOT( N-L2, C( K1, MIN( L2+1, N ) ), LDC,
     $                   B( L2, MIN( L2+1, N ) ), LDB )
                  VEC( 1, 2 ) = C( K1, L2 ) - ( SUML+SGN*SUMR )
*
                  SUML = DDOT( M-K2, A( K2, MIN( K2+1, M ) ), LDA,
     $                   C( MIN( K2+1, M ), L1 ), 1 )
                  SUMR = DDOT( N-L2, C( K2, MIN( L2+1, N ) ), LDC,
     $                   B( L1, MIN( L2+1, N ) ), LDB )
                  VEC( 2, 1 ) = C( K2, L1 ) - ( SUML+SGN*SUMR )
*
                  SUML = DDOT( M-K2, A( K2, MIN( K2+1, M ) ), LDA,
     $                   C( MIN( K2+1, M ), L2 ), 1 )
                  SUMR = DDOT( N-L2, C( K2, MIN( L2+1, N ) ), LDC,
     $                   B( L2, MIN( L2+1, N ) ), LDB )
                  VEC( 2, 2 ) = C( K2, L2 ) - ( SUML+SGN*SUMR )
*
                  CALL DLASY2( .FALSE., .TRUE., ISGN, 2, 2, A( K1, K1 ),
     $                         LDA, B( L1, L1 ), LDB, VEC, 2, SCALOC, X,
     $                         2, XNORM, IERR )
                  IF( IERR.NE.0 )
     $               INFO = 1
*
                  IF( SCALOC.NE.ONE ) THEN
                     DO 220 J = 1, N
                        CALL DSCAL( M, SCALOC, C( 1, J ), 1 )
  220                CONTINUE
                     SCALE = SCALE*SCALOC
                  END IF
                  C( K1, L1 ) = X( 1, 1 )
                  C( K1, L2 ) = X( 1, 2 )
                  C( K2, L1 ) = X( 2, 1 )
                  C( K2, L2 ) = X( 2, 2 )
               END IF
*
  230       CONTINUE
  240    CONTINUE
*
      END IF
*
      RETURN
*
*     End of DTRSYL
*
      END

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