|
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 |
SUBROUTINE ZTRSYL( TRANA, TRANB, ISGN, M, N, A, LDA, B, LDB, C,
$ LDC, SCALE, INFO ) * * -- LAPACK routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2011 -- * * .. Scalar Arguments .. CHARACTER TRANA, TRANB INTEGER INFO, ISGN, LDA, LDB, LDC, M, N DOUBLE PRECISION SCALE * .. * .. Array Arguments .. COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * ) * .. * * Purpose * ======= * * ZTRSYL 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. * * Arguments * ========= * * TRANA (input) CHARACTER*1 * Specifies the option op(A): * = 'N': op(A) = A (No transpose) * = 'C': op(A) = A**H (Conjugate transpose) * * TRANB (input) CHARACTER*1 * Specifies the option op(B): * = 'N': op(B) = B (No transpose) * = 'C': op(B) = B**H (Conjugate 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) COMPLEX*16 array, dimension (LDA,M) * The upper triangular matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,M). * * B (input) COMPLEX*16 array, dimension (LDB,N) * The upper triangular matrix B. * * LDB (input) INTEGER * The leading dimension of the array B. LDB >= max(1,N). * * C (input/output) 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 (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 ONE PARAMETER ( ONE = 1.0D+0 ) * .. * .. Local Scalars .. LOGICAL NOTRNA, NOTRNB INTEGER J, K, L DOUBLE PRECISION BIGNUM, DA11, DB, EPS, SCALOC, SGN, SMIN, $ SMLNUM COMPLEX*16 A11, SUML, SUMR, VEC, X11 * .. * .. Local Arrays .. DOUBLE PRECISION DUM( 1 ) * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, ZLANGE COMPLEX*16 ZDOTC, ZDOTU, ZLADIV EXTERNAL LSAME, DLAMCH, ZLANGE, ZDOTC, ZDOTU, ZLADIV * .. * .. External Subroutines .. EXTERNAL DLABAD, XERBLA, ZDSCAL * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, 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, 'C' ) ) THEN INFO = -1 ELSE IF( .NOT.NOTRNB .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( 'ZTRSYL', -INFO ) RETURN END IF * * Quick return if possible * SCALE = ONE 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*ZLANGE( 'M', M, M, A, LDA, DUM ), $ EPS*ZLANGE( 'M', N, N, B, LDB, DUM ) ) 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 * DO 30 L = 1, N DO 20 K = M, 1, -1 * SUML = ZDOTU( M-K, A( K, MIN( K+1, M ) ), LDA, $ C( MIN( K+1, M ), L ), 1 ) SUMR = ZDOTU( L-1, C( K, 1 ), LDC, B( 1, L ), 1 ) VEC = C( K, L ) - ( SUML+SGN*SUMR ) * SCALOC = ONE A11 = A( K, K ) + SGN*B( L, L ) DA11 = ABS( DBLE( A11 ) ) + ABS( DIMAG( A11 ) ) IF( DA11.LE.SMIN ) THEN A11 = SMIN DA11 = SMIN INFO = 1 END IF DB = ABS( DBLE( VEC ) ) + ABS( DIMAG( VEC ) ) IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN IF( DB.GT.BIGNUM*DA11 ) $ SCALOC = ONE / DB END IF X11 = ZLADIV( VEC*DCMPLX( SCALOC ), A11 ) * IF( SCALOC.NE.ONE ) THEN DO 10 J = 1, N CALL ZDSCAL( M, SCALOC, C( 1, J ), 1 ) 10 CONTINUE SCALE = SCALE*SCALOC END IF C( K, L ) = X11 * 20 CONTINUE 30 CONTINUE * ELSE IF( .NOT.NOTRNA .AND. NOTRNB ) THEN * * Solve A**H *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**H(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**H(I,K)*X(I,L)] + ISGN*SUM [X(K,J)*B(J,L)] * I=1 J=1 * DO 60 L = 1, N DO 50 K = 1, M * SUML = ZDOTC( K-1, A( 1, K ), 1, C( 1, L ), 1 ) SUMR = ZDOTU( L-1, C( K, 1 ), LDC, B( 1, L ), 1 ) VEC = C( K, L ) - ( SUML+SGN*SUMR ) * SCALOC = ONE A11 = DCONJG( A( K, K ) ) + SGN*B( L, L ) DA11 = ABS( DBLE( A11 ) ) + ABS( DIMAG( A11 ) ) IF( DA11.LE.SMIN ) THEN A11 = SMIN DA11 = SMIN INFO = 1 END IF DB = ABS( DBLE( VEC ) ) + ABS( DIMAG( VEC ) ) IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN IF( DB.GT.BIGNUM*DA11 ) $ SCALOC = ONE / DB END IF * X11 = ZLADIV( VEC*DCMPLX( SCALOC ), A11 ) * IF( SCALOC.NE.ONE ) THEN DO 40 J = 1, N CALL ZDSCAL( M, SCALOC, C( 1, J ), 1 ) 40 CONTINUE SCALE = SCALE*SCALOC END IF C( K, L ) = X11 * 50 CONTINUE 60 CONTINUE * ELSE IF( .NOT.NOTRNA .AND. .NOT.NOTRNB ) THEN * * Solve A**H*X + ISGN*X*B**H = C. * * The (K,L)th block of X is determined starting from * upper-right corner column by column by * * A**H(K,K)*X(K,L) + ISGN*X(K,L)*B**H(L,L) = C(K,L) - R(K,L) * * Where * K-1 * R(K,L) = SUM [A**H(I,K)*X(I,L)] + * I=1 * N * ISGN*SUM [X(K,J)*B**H(L,J)]. * J=L+1 * DO 90 L = N, 1, -1 DO 80 K = 1, M * SUML = ZDOTC( K-1, A( 1, K ), 1, C( 1, L ), 1 ) SUMR = ZDOTC( N-L, C( K, MIN( L+1, N ) ), LDC, $ B( L, MIN( L+1, N ) ), LDB ) VEC = C( K, L ) - ( SUML+SGN*DCONJG( SUMR ) ) * SCALOC = ONE A11 = DCONJG( A( K, K )+SGN*B( L, L ) ) DA11 = ABS( DBLE( A11 ) ) + ABS( DIMAG( A11 ) ) IF( DA11.LE.SMIN ) THEN A11 = SMIN DA11 = SMIN INFO = 1 END IF DB = ABS( DBLE( VEC ) ) + ABS( DIMAG( VEC ) ) IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN IF( DB.GT.BIGNUM*DA11 ) $ SCALOC = ONE / DB END IF * X11 = ZLADIV( VEC*DCMPLX( SCALOC ), A11 ) * IF( SCALOC.NE.ONE ) THEN DO 70 J = 1, N CALL ZDSCAL( M, SCALOC, C( 1, J ), 1 ) 70 CONTINUE SCALE = SCALE*SCALOC END IF C( K, L ) = X11 * 80 CONTINUE 90 CONTINUE * ELSE IF( NOTRNA .AND. .NOT.NOTRNB ) THEN * * Solve A*X + ISGN*X*B**H = 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**H(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**H(L,J)] * I=K+1 J=L+1 * DO 120 L = N, 1, -1 DO 110 K = M, 1, -1 * SUML = ZDOTU( M-K, A( K, MIN( K+1, M ) ), LDA, $ C( MIN( K+1, M ), L ), 1 ) SUMR = ZDOTC( N-L, C( K, MIN( L+1, N ) ), LDC, $ B( L, MIN( L+1, N ) ), LDB ) VEC = C( K, L ) - ( SUML+SGN*DCONJG( SUMR ) ) * SCALOC = ONE A11 = A( K, K ) + SGN*DCONJG( B( L, L ) ) DA11 = ABS( DBLE( A11 ) ) + ABS( DIMAG( A11 ) ) IF( DA11.LE.SMIN ) THEN A11 = SMIN DA11 = SMIN INFO = 1 END IF DB = ABS( DBLE( VEC ) ) + ABS( DIMAG( VEC ) ) IF( DA11.LT.ONE .AND. DB.GT.ONE ) THEN IF( DB.GT.BIGNUM*DA11 ) $ SCALOC = ONE / DB END IF * X11 = ZLADIV( VEC*DCMPLX( SCALOC ), A11 ) * IF( SCALOC.NE.ONE ) THEN DO 100 J = 1, N CALL ZDSCAL( M, SCALOC, C( 1, J ), 1 ) 100 CONTINUE SCALE = SCALE*SCALOC END IF C( K, L ) = X11 * 110 CONTINUE 120 CONTINUE * END IF * RETURN * * End of ZTRSYL * END |