LAPACK  3.4.1
LAPACK: Linear Algebra PACKage
ztrsyl.f
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00001 *> \brief \b ZTRSYL
00002 *
00003 *  =========== DOCUMENTATION ===========
00004 *
00005 * Online html documentation available at 
00006 *            http://www.netlib.org/lapack/explore-html/ 
00007 *
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00009 *> Download ZTRSYL + dependencies 
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00015 *> [TXT]</a>
00016 *> \endhtmlonly 
00017 *
00018 *  Definition:
00019 *  ===========
00020 *
00021 *       SUBROUTINE ZTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C,
00022 *                          LDC, SCALE, INFO )
00023 * 
00024 *       .. Scalar Arguments ..
00025 *       CHARACTER          TRANA, TRANB
00026 *       INTEGER            INFO, ISGN, LDA, LDB, LDC, M, N
00027 *       DOUBLE PRECISION   SCALE
00028 *       ..
00029 *       .. Array Arguments ..
00030 *       COMPLEX*16         A( LDA, * ), B( LDB, * ), C( LDC, * )
00031 *       ..
00032 *  
00033 *
00034 *> \par Purpose:
00035 *  =============
00036 *>
00037 *> \verbatim
00038 *>
00039 *> ZTRSYL solves the complex Sylvester matrix equation:
00040 *>
00041 *>    op(A)*X + X*op(B) = scale*C or
00042 *>    op(A)*X - X*op(B) = scale*C,
00043 *>
00044 *> where op(A) = A or A**H, and A and B are both upper triangular. A is
00045 *> M-by-M and B is N-by-N; the right hand side C and the solution X are
00046 *> M-by-N; and scale is an output scale factor, set <= 1 to avoid
00047 *> overflow in X.
00048 *> \endverbatim
00049 *
00050 *  Arguments:
00051 *  ==========
00052 *
00053 *> \param[in] TRANA
00054 *> \verbatim
00055 *>          TRANA is CHARACTER*1
00056 *>          Specifies the option op(A):
00057 *>          = 'N': op(A) = A    (No transpose)
00058 *>          = 'C': op(A) = A**H (Conjugate transpose)
00059 *> \endverbatim
00060 *>
00061 *> \param[in] TRANB
00062 *> \verbatim
00063 *>          TRANB is CHARACTER*1
00064 *>          Specifies the option op(B):
00065 *>          = 'N': op(B) = B    (No transpose)
00066 *>          = 'C': op(B) = B**H (Conjugate transpose)
00067 *> \endverbatim
00068 *>
00069 *> \param[in] ISGN
00070 *> \verbatim
00071 *>          ISGN is INTEGER
00072 *>          Specifies the sign in the equation:
00073 *>          = +1: solve op(A)*X + X*op(B) = scale*C
00074 *>          = -1: solve op(A)*X - X*op(B) = scale*C
00075 *> \endverbatim
00076 *>
00077 *> \param[in] M
00078 *> \verbatim
00079 *>          M is INTEGER
00080 *>          The order of the matrix A, and the number of rows in the
00081 *>          matrices X and C. M >= 0.
00082 *> \endverbatim
00083 *>
00084 *> \param[in] N
00085 *> \verbatim
00086 *>          N is INTEGER
00087 *>          The order of the matrix B, and the number of columns in the
00088 *>          matrices X and C. N >= 0.
00089 *> \endverbatim
00090 *>
00091 *> \param[in] A
00092 *> \verbatim
00093 *>          A is COMPLEX*16 array, dimension (LDA,M)
00094 *>          The upper triangular matrix A.
00095 *> \endverbatim
00096 *>
00097 *> \param[in] LDA
00098 *> \verbatim
00099 *>          LDA is INTEGER
00100 *>          The leading dimension of the array A. LDA >= max(1,M).
00101 *> \endverbatim
00102 *>
00103 *> \param[in] B
00104 *> \verbatim
00105 *>          B is COMPLEX*16 array, dimension (LDB,N)
00106 *>          The upper triangular matrix B.
00107 *> \endverbatim
00108 *>
00109 *> \param[in] LDB
00110 *> \verbatim
00111 *>          LDB is INTEGER
00112 *>          The leading dimension of the array B. LDB >= max(1,N).
00113 *> \endverbatim
00114 *>
00115 *> \param[in,out] C
00116 *> \verbatim
00117 *>          C is COMPLEX*16 array, dimension (LDC,N)
00118 *>          On entry, the M-by-N right hand side matrix C.
00119 *>          On exit, C is overwritten by the solution matrix X.
00120 *> \endverbatim
00121 *>
00122 *> \param[in] LDC
00123 *> \verbatim
00124 *>          LDC is INTEGER
00125 *>          The leading dimension of the array C. LDC >= max(1,M)
00126 *> \endverbatim
00127 *>
00128 *> \param[out] SCALE
00129 *> \verbatim
00130 *>          SCALE is DOUBLE PRECISION
00131 *>          The scale factor, scale, set <= 1 to avoid overflow in X.
00132 *> \endverbatim
00133 *>
00134 *> \param[out] INFO
00135 *> \verbatim
00136 *>          INFO is INTEGER
00137 *>          = 0: successful exit
00138 *>          < 0: if INFO = -i, the i-th argument had an illegal value
00139 *>          = 1: A and B have common or very close eigenvalues; perturbed
00140 *>               values were used to solve the equation (but the matrices
00141 *>               A and B are unchanged).
00142 *> \endverbatim
00143 *
00144 *  Authors:
00145 *  ========
00146 *
00147 *> \author Univ. of Tennessee 
00148 *> \author Univ. of California Berkeley 
00149 *> \author Univ. of Colorado Denver 
00150 *> \author NAG Ltd. 
00151 *
00152 *> \date November 2011
00153 *
00154 *> \ingroup complex16SYcomputational
00155 *
00156 *  =====================================================================
00157       SUBROUTINE ZTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C,
00158      $                   LDC, SCALE, INFO )
00159 *
00160 *  -- LAPACK computational routine (version 3.4.0) --
00161 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00162 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00163 *     November 2011
00164 *
00165 *     .. Scalar Arguments ..
00166       CHARACTER          TRANA, TRANB
00167       INTEGER            INFO, ISGN, LDA, LDB, LDC, M, N
00168       DOUBLE PRECISION   SCALE
00169 *     ..
00170 *     .. Array Arguments ..
00171       COMPLEX*16         A( LDA, * ), B( LDB, * ), C( LDC, * )
00172 *     ..
00173 *
00174 *  =====================================================================
00175 *
00176 *     .. Parameters ..
00177       DOUBLE PRECISION   ONE
00178       PARAMETER          ( ONE = 1.0D+0 )
00179 *     ..
00180 *     .. Local Scalars ..
00181       LOGICAL            NOTRNA, NOTRNB
00182       INTEGER            J, K, L
00183       DOUBLE PRECISION   BIGNUM, DA11, DB, EPS, SCALOC, SGN, SMIN,
00184      $                   SMLNUM
00185       COMPLEX*16         A11, SUML, SUMR, VEC, X11
00186 *     ..
00187 *     .. Local Arrays ..
00188       DOUBLE PRECISION   DUM( 1 )
00189 *     ..
00190 *     .. External Functions ..
00191       LOGICAL            LSAME
00192       DOUBLE PRECISION   DLAMCH, ZLANGE
00193       COMPLEX*16         ZDOTC, ZDOTU, ZLADIV
00194       EXTERNAL           LSAME, DLAMCH, ZLANGE, ZDOTC, ZDOTU, ZLADIV
00195 *     ..
00196 *     .. External Subroutines ..
00197       EXTERNAL           DLABAD, XERBLA, ZDSCAL
00198 *     ..
00199 *     .. Intrinsic Functions ..
00200       INTRINSIC          ABS, DBLE, DCMPLX, DCONJG, DIMAG, MAX, MIN
00201 *     ..
00202 *     .. Executable Statements ..
00203 *
00204 *     Decode and Test input parameters
00205 *
00206       NOTRNA = LSAME( TRANA, 'N' )
00207       NOTRNB = LSAME( TRANB, 'N' )
00208 *
00209       INFO = 0
00210       IF( .NOT.NOTRNA .AND. .NOT.LSAME( TRANA, 'C' ) ) THEN
00211          INFO = -1
00212       ELSE IF( .NOT.NOTRNB .AND. .NOT.LSAME( TRANB, 'C' ) ) THEN
00213          INFO = -2
00214       ELSE IF( ISGN.NE.1 .AND. ISGN.NE.-1 ) THEN
00215          INFO = -3
00216       ELSE IF( M.LT.0 ) THEN
00217          INFO = -4
00218       ELSE IF( N.LT.0 ) THEN
00219          INFO = -5
00220       ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
00221          INFO = -7
00222       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00223          INFO = -9
00224       ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
00225          INFO = -11
00226       END IF
00227       IF( INFO.NE.0 ) THEN
00228          CALL XERBLA( 'ZTRSYL', -INFO )
00229          RETURN
00230       END IF
00231 *
00232 *     Quick return if possible
00233 *
00234       SCALE = ONE
00235       IF( M.EQ.0 .OR. N.EQ.0 )
00236      $   RETURN
00237 *
00238 *     Set constants to control overflow
00239 *
00240       EPS = DLAMCH( 'P' )
00241       SMLNUM = DLAMCH( 'S' )
00242       BIGNUM = ONE / SMLNUM
00243       CALL DLABAD( SMLNUM, BIGNUM )
00244       SMLNUM = SMLNUM*DBLE( M*N ) / EPS
00245       BIGNUM = ONE / SMLNUM
00246       SMIN = MAX( SMLNUM, EPS*ZLANGE( 'M', M, M, A, LDA, DUM ),
00247      $       EPS*ZLANGE( 'M', N, N, B, LDB, DUM ) )
00248       SGN = ISGN
00249 *
00250       IF( NOTRNA .AND. NOTRNB ) THEN
00251 *
00252 *        Solve    A*X + ISGN*X*B = scale*C.
00253 *
00254 *        The (K,L)th block of X is determined starting from
00255 *        bottom-left corner column by column by
00256 *
00257 *            A(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
00258 *
00259 *        Where
00260 *                    M                        L-1
00261 *          R(K,L) = SUM [A(K,I)*X(I,L)] +ISGN*SUM [X(K,J)*B(J,L)].
00262 *                  I=K+1                      J=1
00263 *
00264          DO 30 L = 1, N
00265             DO 20 K = M, 1, -1
00266 *
00267                SUML = ZDOTU( M-K, A( K, MIN( K+1, M ) ), LDA,
00268      $                C( MIN( K+1, M ), L ), 1 )
00269                SUMR = ZDOTU( L-1, C( K, 1 ), LDC, B( 1, L ), 1 )
00270                VEC = C( K, L ) - ( SUML+SGN*SUMR )
00271 *
00272                SCALOC = ONE
00273                A11 = A( K, K ) + SGN*B( L, L )
00274                DA11 = ABS( DBLE( A11 ) ) + ABS( DIMAG( A11 ) )
00275                IF( DA11.LE.SMIN ) THEN
00276                   A11 = SMIN
00277                   DA11 = SMIN
00278                   INFO = 1
00279                END IF
00280                DB = ABS( DBLE( VEC ) ) + ABS( DIMAG( VEC ) )
00281                IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
00282                   IF( DB.GT.BIGNUM*DA11 )
00283      $               SCALOC = ONE / DB
00284                END IF
00285                X11 = ZLADIV( VEC*DCMPLX( SCALOC ), A11 )
00286 *
00287                IF( SCALOC.NE.ONE ) THEN
00288                   DO 10 J = 1, N
00289                      CALL ZDSCAL( M, SCALOC, C( 1, J ), 1 )
00290    10             CONTINUE
00291                   SCALE = SCALE*SCALOC
00292                END IF
00293                C( K, L ) = X11
00294 *
00295    20       CONTINUE
00296    30    CONTINUE
00297 *
00298       ELSE IF( .NOT.NOTRNA .AND. NOTRNB ) THEN
00299 *
00300 *        Solve    A**H *X + ISGN*X*B = scale*C.
00301 *
00302 *        The (K,L)th block of X is determined starting from
00303 *        upper-left corner column by column by
00304 *
00305 *            A**H(K,K)*X(K,L) + ISGN*X(K,L)*B(L,L) = C(K,L) - R(K,L)
00306 *
00307 *        Where
00308 *                   K-1                           L-1
00309 *          R(K,L) = SUM [A**H(I,K)*X(I,L)] + ISGN*SUM [X(K,J)*B(J,L)]
00310 *                   I=1                           J=1
00311 *
00312          DO 60 L = 1, N
00313             DO 50 K = 1, M
00314 *
00315                SUML = ZDOTC( K-1, A( 1, K ), 1, C( 1, L ), 1 )
00316                SUMR = ZDOTU( L-1, C( K, 1 ), LDC, B( 1, L ), 1 )
00317                VEC = C( K, L ) - ( SUML+SGN*SUMR )
00318 *
00319                SCALOC = ONE
00320                A11 = DCONJG( A( K, K ) ) + SGN*B( L, L )
00321                DA11 = ABS( DBLE( A11 ) ) + ABS( DIMAG( A11 ) )
00322                IF( DA11.LE.SMIN ) THEN
00323                   A11 = SMIN
00324                   DA11 = SMIN
00325                   INFO = 1
00326                END IF
00327                DB = ABS( DBLE( VEC ) ) + ABS( DIMAG( VEC ) )
00328                IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
00329                   IF( DB.GT.BIGNUM*DA11 )
00330      $               SCALOC = ONE / DB
00331                END IF
00332 *
00333                X11 = ZLADIV( VEC*DCMPLX( SCALOC ), A11 )
00334 *
00335                IF( SCALOC.NE.ONE ) THEN
00336                   DO 40 J = 1, N
00337                      CALL ZDSCAL( M, SCALOC, C( 1, J ), 1 )
00338    40             CONTINUE
00339                   SCALE = SCALE*SCALOC
00340                END IF
00341                C( K, L ) = X11
00342 *
00343    50       CONTINUE
00344    60    CONTINUE
00345 *
00346       ELSE IF( .NOT.NOTRNA .AND. .NOT.NOTRNB ) THEN
00347 *
00348 *        Solve    A**H*X + ISGN*X*B**H = C.
00349 *
00350 *        The (K,L)th block of X is determined starting from
00351 *        upper-right corner column by column by
00352 *
00353 *            A**H(K,K)*X(K,L) + ISGN*X(K,L)*B**H(L,L) = C(K,L) - R(K,L)
00354 *
00355 *        Where
00356 *                    K-1
00357 *           R(K,L) = SUM [A**H(I,K)*X(I,L)] +
00358 *                    I=1
00359 *                           N
00360 *                     ISGN*SUM [X(K,J)*B**H(L,J)].
00361 *                          J=L+1
00362 *
00363          DO 90 L = N, 1, -1
00364             DO 80 K = 1, M
00365 *
00366                SUML = ZDOTC( K-1, A( 1, K ), 1, C( 1, L ), 1 )
00367                SUMR = ZDOTC( N-L, C( K, MIN( L+1, N ) ), LDC,
00368      $                B( L, MIN( L+1, N ) ), LDB )
00369                VEC = C( K, L ) - ( SUML+SGN*DCONJG( SUMR ) )
00370 *
00371                SCALOC = ONE
00372                A11 = DCONJG( A( K, K )+SGN*B( L, L ) )
00373                DA11 = ABS( DBLE( A11 ) ) + ABS( DIMAG( A11 ) )
00374                IF( DA11.LE.SMIN ) THEN
00375                   A11 = SMIN
00376                   DA11 = SMIN
00377                   INFO = 1
00378                END IF
00379                DB = ABS( DBLE( VEC ) ) + ABS( DIMAG( VEC ) )
00380                IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
00381                   IF( DB.GT.BIGNUM*DA11 )
00382      $               SCALOC = ONE / DB
00383                END IF
00384 *
00385                X11 = ZLADIV( VEC*DCMPLX( SCALOC ), A11 )
00386 *
00387                IF( SCALOC.NE.ONE ) THEN
00388                   DO 70 J = 1, N
00389                      CALL ZDSCAL( M, SCALOC, C( 1, J ), 1 )
00390    70             CONTINUE
00391                   SCALE = SCALE*SCALOC
00392                END IF
00393                C( K, L ) = X11
00394 *
00395    80       CONTINUE
00396    90    CONTINUE
00397 *
00398       ELSE IF( NOTRNA .AND. .NOT.NOTRNB ) THEN
00399 *
00400 *        Solve    A*X + ISGN*X*B**H = C.
00401 *
00402 *        The (K,L)th block of X is determined starting from
00403 *        bottom-left corner column by column by
00404 *
00405 *           A(K,K)*X(K,L) + ISGN*X(K,L)*B**H(L,L) = C(K,L) - R(K,L)
00406 *
00407 *        Where
00408 *                    M                          N
00409 *          R(K,L) = SUM [A(K,I)*X(I,L)] + ISGN*SUM [X(K,J)*B**H(L,J)]
00410 *                  I=K+1                      J=L+1
00411 *
00412          DO 120 L = N, 1, -1
00413             DO 110 K = M, 1, -1
00414 *
00415                SUML = ZDOTU( M-K, A( K, MIN( K+1, M ) ), LDA,
00416      $                C( MIN( K+1, M ), L ), 1 )
00417                SUMR = ZDOTC( N-L, C( K, MIN( L+1, N ) ), LDC,
00418      $                B( L, MIN( L+1, N ) ), LDB )
00419                VEC = C( K, L ) - ( SUML+SGN*DCONJG( SUMR ) )
00420 *
00421                SCALOC = ONE
00422                A11 = A( K, K ) + SGN*DCONJG( B( L, L ) )
00423                DA11 = ABS( DBLE( A11 ) ) + ABS( DIMAG( A11 ) )
00424                IF( DA11.LE.SMIN ) THEN
00425                   A11 = SMIN
00426                   DA11 = SMIN
00427                   INFO = 1
00428                END IF
00429                DB = ABS( DBLE( VEC ) ) + ABS( DIMAG( VEC ) )
00430                IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN
00431                   IF( DB.GT.BIGNUM*DA11 )
00432      $               SCALOC = ONE / DB
00433                END IF
00434 *
00435                X11 = ZLADIV( VEC*DCMPLX( SCALOC ), A11 )
00436 *
00437                IF( SCALOC.NE.ONE ) THEN
00438                   DO 100 J = 1, N
00439                      CALL ZDSCAL( M, SCALOC, C( 1, J ), 1 )
00440   100             CONTINUE
00441                   SCALE = SCALE*SCALOC
00442                END IF
00443                C( K, L ) = X11
00444 *
00445   110       CONTINUE
00446   120    CONTINUE
00447 *
00448       END IF
00449 *
00450       RETURN
00451 *
00452 *     End of ZTRSYL
00453 *
00454       END
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