| 1 | !-------------------------------------------------------------- |
|---|
| 2 | ! |
|---|
| 3 | ! BLAS/LAPACK-like subroutines used by the integration algorithms |
|---|
| 4 | ! It is recommended to replace them by calls to the optimized |
|---|
| 5 | ! BLAS/LAPACK library for your machine |
|---|
| 6 | ! |
|---|
| 7 | ! (C) Adrian Sandu, Aug. 2004 |
|---|
| 8 | ! Virginia Polytechnic Institute and State University |
|---|
| 9 | !-------------------------------------------------------------- |
|---|
| 10 | |
|---|
| 11 | |
|---|
| 12 | !-------------------------------------------------------------- |
|---|
| 13 | SUBROUTINE WCOPY(N,X,incX,Y,incY) |
|---|
| 14 | !-------------------------------------------------------------- |
|---|
| 15 | ! copies a vector, x, to a vector, y: y <- x |
|---|
| 16 | ! only for incX=incY=1 |
|---|
| 17 | ! after BLAS |
|---|
| 18 | ! replace this by the function from the optimized BLAS implementation: |
|---|
| 19 | ! CALL SCOPY(N,X,1,Y,1) or CALL DCOPY(N,X,1,Y,1) |
|---|
| 20 | !-------------------------------------------------------------- |
|---|
| 21 | |
|---|
| 22 | INTEGER i,incX,incY,M,MP1,N |
|---|
| 23 | KPP_REAL X(N),Y(N) |
|---|
| 24 | |
|---|
| 25 | IF (N.LE.0) RETURN |
|---|
| 26 | |
|---|
| 27 | M = MOD(N,8) |
|---|
| 28 | IF( M .NE. 0 ) THEN |
|---|
| 29 | DO i = 1,M |
|---|
| 30 | Y(i) = X(i) |
|---|
| 31 | END DO |
|---|
| 32 | IF( N .LT. 8 ) RETURN |
|---|
| 33 | END IF |
|---|
| 34 | MP1 = M+1 |
|---|
| 35 | DO i = MP1,N,8 |
|---|
| 36 | Y(i) = X(i) |
|---|
| 37 | Y(i + 1) = X(i + 1) |
|---|
| 38 | Y(i + 2) = X(i + 2) |
|---|
| 39 | Y(i + 3) = X(i + 3) |
|---|
| 40 | Y(i + 4) = X(i + 4) |
|---|
| 41 | Y(i + 5) = X(i + 5) |
|---|
| 42 | Y(i + 6) = X(i + 6) |
|---|
| 43 | Y(i + 7) = X(i + 7) |
|---|
| 44 | END DO |
|---|
| 45 | RETURN |
|---|
| 46 | END |
|---|
| 47 | |
|---|
| 48 | |
|---|
| 49 | !-------------------------------------------------------------- |
|---|
| 50 | SUBROUTINE WAXPY(N,Alpha,X,incX,Y,incY) |
|---|
| 51 | !-------------------------------------------------------------- |
|---|
| 52 | ! constant times a vector plus a vector: y <- y + Alpha*x |
|---|
| 53 | ! only for incX=incY=1 |
|---|
| 54 | ! after BLAS |
|---|
| 55 | ! replace this by the function from the optimized BLAS implementation: |
|---|
| 56 | ! CALL SAXPY(N,Alpha,X,1,Y,1) or CALL DAXPY(N,Alpha,X,1,Y,1) |
|---|
| 57 | !-------------------------------------------------------------- |
|---|
| 58 | |
|---|
| 59 | INTEGER i,incX,incY,M,MP1,N |
|---|
| 60 | KPP_REAL X(N),Y(N),Alpha |
|---|
| 61 | KPP_REAL ZERO |
|---|
| 62 | PARAMETER( ZERO = 0.0d0 ) |
|---|
| 63 | |
|---|
| 64 | IF (Alpha .EQ. ZERO) RETURN |
|---|
| 65 | IF (N .LE. 0) RETURN |
|---|
| 66 | |
|---|
| 67 | M = MOD(N,4) |
|---|
| 68 | IF( M .NE. 0 ) THEN |
|---|
| 69 | DO i = 1,M |
|---|
| 70 | Y(i) = Y(i) + Alpha*X(i) |
|---|
| 71 | END DO |
|---|
| 72 | IF( N .LT. 4 ) RETURN |
|---|
| 73 | END IF |
|---|
| 74 | MP1 = M + 1 |
|---|
| 75 | DO i = MP1,N,4 |
|---|
| 76 | Y(i) = Y(i) + Alpha*X(i) |
|---|
| 77 | Y(i + 1) = Y(i + 1) + Alpha*X(i + 1) |
|---|
| 78 | Y(i + 2) = Y(i + 2) + Alpha*X(i + 2) |
|---|
| 79 | Y(i + 3) = Y(i + 3) + Alpha*X(i + 3) |
|---|
| 80 | END DO |
|---|
| 81 | RETURN |
|---|
| 82 | END |
|---|
| 83 | |
|---|
| 84 | |
|---|
| 85 | |
|---|
| 86 | !-------------------------------------------------------------- |
|---|
| 87 | SUBROUTINE WSCAL(N,Alpha,X,incX) |
|---|
| 88 | !-------------------------------------------------------------- |
|---|
| 89 | ! constant times a vector: x(1:N) <- Alpha*x(1:N) |
|---|
| 90 | ! only for incX=incY=1 |
|---|
| 91 | ! after BLAS |
|---|
| 92 | ! replace this by the function from the optimized BLAS implementation: |
|---|
| 93 | ! CALL SSCAL(N,Alpha,X,1) or CALL DSCAL(N,Alpha,X,1) |
|---|
| 94 | !-------------------------------------------------------------- |
|---|
| 95 | |
|---|
| 96 | INTEGER i,incX,M,MP1,N |
|---|
| 97 | KPP_REAL X(N),Alpha |
|---|
| 98 | KPP_REAL ZERO, ONE |
|---|
| 99 | PARAMETER( ZERO = 0.0d0 ) |
|---|
| 100 | PARAMETER( ONE = 1.0d0 ) |
|---|
| 101 | |
|---|
| 102 | IF (Alpha .EQ. ONE) RETURN |
|---|
| 103 | IF (N .LE. 0) RETURN |
|---|
| 104 | |
|---|
| 105 | M = MOD(N,5) |
|---|
| 106 | IF( M .NE. 0 ) THEN |
|---|
| 107 | IF (Alpha .EQ. (-ONE)) THEN |
|---|
| 108 | DO i = 1,M |
|---|
| 109 | X(i) = -X(i) |
|---|
| 110 | END DO |
|---|
| 111 | ELSEIF (Alpha .EQ. ZERO) THEN |
|---|
| 112 | DO i = 1,M |
|---|
| 113 | X(i) = ZERO |
|---|
| 114 | END DO |
|---|
| 115 | ELSE |
|---|
| 116 | DO i = 1,M |
|---|
| 117 | X(i) = Alpha*X(i) |
|---|
| 118 | END DO |
|---|
| 119 | END IF |
|---|
| 120 | IF( N .LT. 5 ) RETURN |
|---|
| 121 | END IF |
|---|
| 122 | MP1 = M + 1 |
|---|
| 123 | IF (Alpha .EQ. (-ONE)) THEN |
|---|
| 124 | DO i = MP1,N,5 |
|---|
| 125 | X(i) = -X(i) |
|---|
| 126 | X(i + 1) = -X(i + 1) |
|---|
| 127 | X(i + 2) = -X(i + 2) |
|---|
| 128 | X(i + 3) = -X(i + 3) |
|---|
| 129 | X(i + 4) = -X(i + 4) |
|---|
| 130 | END DO |
|---|
| 131 | ELSEIF (Alpha .EQ. ZERO) THEN |
|---|
| 132 | DO i = MP1,N,5 |
|---|
| 133 | X(i) = ZERO |
|---|
| 134 | X(i + 1) = ZERO |
|---|
| 135 | X(i + 2) = ZERO |
|---|
| 136 | X(i + 3) = ZERO |
|---|
| 137 | X(i + 4) = ZERO |
|---|
| 138 | END DO |
|---|
| 139 | ELSE |
|---|
| 140 | DO i = MP1,N,5 |
|---|
| 141 | X(i) = Alpha*X(i) |
|---|
| 142 | X(i + 1) = Alpha*X(i + 1) |
|---|
| 143 | X(i + 2) = Alpha*X(i + 2) |
|---|
| 144 | X(i + 3) = Alpha*X(i + 3) |
|---|
| 145 | X(i + 4) = Alpha*X(i + 4) |
|---|
| 146 | END DO |
|---|
| 147 | END IF |
|---|
| 148 | RETURN |
|---|
| 149 | END |
|---|
| 150 | |
|---|
| 151 | !-------------------------------------------------------------- |
|---|
| 152 | KPP_REAL FUNCTION WLAMCH( C ) |
|---|
| 153 | !-------------------------------------------------------------- |
|---|
| 154 | ! returns epsilon machine |
|---|
| 155 | ! after LAPACK |
|---|
| 156 | ! replace this by the function from the optimized LAPACK implementation: |
|---|
| 157 | ! CALL SLAMCH('E') or CALL DLAMCH('E') |
|---|
| 158 | !-------------------------------------------------------------- |
|---|
| 159 | |
|---|
| 160 | CHARACTER C |
|---|
| 161 | INTEGER i |
|---|
| 162 | KPP_REAL ONE, HALF, Eps, Suma |
|---|
| 163 | PARAMETER (ONE = 1.0d0) |
|---|
| 164 | PARAMETER (HALF = 0.5d0) |
|---|
| 165 | LOGICAL First |
|---|
| 166 | SAVE First, Eps |
|---|
| 167 | DATA First /.TRUE./ |
|---|
| 168 | |
|---|
| 169 | IF (First) THEN |
|---|
| 170 | First = .FALSE. |
|---|
| 171 | Eps = HALF**(16) |
|---|
| 172 | DO i = 17, 80 |
|---|
| 173 | Eps = Eps*HALF |
|---|
| 174 | CALL WLAMCH_ADD(ONE,Eps,Suma) |
|---|
| 175 | IF (Suma.LE.ONE) GOTO 10 |
|---|
| 176 | END DO |
|---|
| 177 | PRINT*,'ERROR IN WLAMCH. EPS < ',Eps |
|---|
| 178 | RETURN |
|---|
| 179 | 10 Eps = Eps*2 |
|---|
| 180 | i = i-1 |
|---|
| 181 | END IF |
|---|
| 182 | |
|---|
| 183 | WLAMCH = Eps |
|---|
| 184 | |
|---|
| 185 | RETURN |
|---|
| 186 | END |
|---|
| 187 | |
|---|
| 188 | SUBROUTINE WLAMCH_ADD( A, B, Suma ) |
|---|
| 189 | KPP_REAL A, B, Suma |
|---|
| 190 | Suma = A + B |
|---|
| 191 | RETURN |
|---|
| 192 | END |
|---|
| 193 | |
|---|
| 194 | !-------------------------------------------------------------- |
|---|
| 195 | SUBROUTINE SET2ZERO(N,Y) |
|---|
| 196 | !-------------------------------------------------------------- |
|---|
| 197 | ! copies zeros into the vector y: y <- 0 |
|---|
| 198 | ! after BLAS |
|---|
| 199 | !-------------------------------------------------------------- |
|---|
| 200 | |
|---|
| 201 | INTEGER i,M,MP1,N |
|---|
| 202 | KPP_REAL Y(N) |
|---|
| 203 | |
|---|
| 204 | IF (N.LE.0) RETURN |
|---|
| 205 | |
|---|
| 206 | M = MOD(N,8) |
|---|
| 207 | IF( M .NE. 0 ) THEN |
|---|
| 208 | DO i = 1,M |
|---|
| 209 | Y(i) = 0.0d0 |
|---|
| 210 | END DO |
|---|
| 211 | IF( N .LT. 8 ) RETURN |
|---|
| 212 | END IF |
|---|
| 213 | MP1 = M+1 |
|---|
| 214 | DO i = MP1,N,8 |
|---|
| 215 | Y(i) = 0.0d0 |
|---|
| 216 | Y(i + 1) = 0.0d0 |
|---|
| 217 | Y(i + 2) = 0.0d0 |
|---|
| 218 | Y(i + 3) = 0.0d0 |
|---|
| 219 | Y(i + 4) = 0.0d0 |
|---|
| 220 | Y(i + 5) = 0.0d0 |
|---|
| 221 | Y(i + 6) = 0.0d0 |
|---|
| 222 | Y(i + 7) = 0.0d0 |
|---|
| 223 | END DO |
|---|
| 224 | |
|---|
| 225 | END SUBROUTINE SET2ZERO |
|---|
| 226 | |
|---|
| 227 | |
|---|
| 228 | !-------------------------------------------------------------- |
|---|
| 229 | KPP_REAL FUNCTION WDOT (N, DX, incX, DY, incY) |
|---|
| 230 | !-------------------------------------------------------------- |
|---|
| 231 | ! dot produce: wdot = x(1:N)*y(1:N) |
|---|
| 232 | ! only for incX=incY=1 |
|---|
| 233 | ! after BLAS |
|---|
| 234 | ! replace this by the function from the optimized BLAS implementation: |
|---|
| 235 | ! CALL SDOT(N,X,1,Y,1) or CALL DDOT(N,X,1,Y,1) |
|---|
| 236 | !-------------------------------------------------------------- |
|---|
| 237 | ! USE messy_mecca_kpp_Precision |
|---|
| 238 | !-------------------------------------------------------------- |
|---|
| 239 | IMPLICIT NONE |
|---|
| 240 | INTEGER N, incX, incY |
|---|
| 241 | KPP_REAL DX(N), DY(N) |
|---|
| 242 | |
|---|
| 243 | INTEGER i, IX, IY, M, MP1, NS |
|---|
| 244 | |
|---|
| 245 | WDOT = 0.0D0 |
|---|
| 246 | IF (N .LE. 0) RETURN |
|---|
| 247 | IF (incX .EQ. incY) IF (incX-1) 5,20,60 |
|---|
| 248 | ! |
|---|
| 249 | ! Code for unequal or nonpositive increments. |
|---|
| 250 | ! |
|---|
| 251 | 5 IX = 1 |
|---|
| 252 | IY = 1 |
|---|
| 253 | IF (incX .LT. 0) IX = (-N+1)*incX + 1 |
|---|
| 254 | IF (incY .LT. 0) IY = (-N+1)*incY + 1 |
|---|
| 255 | DO i = 1,N |
|---|
| 256 | WDOT = WDOT + DX(IX)*DY(IY) |
|---|
| 257 | IX = IX + incX |
|---|
| 258 | IY = IY + incY |
|---|
| 259 | END DO |
|---|
| 260 | RETURN |
|---|
| 261 | ! |
|---|
| 262 | ! Code for both increments equal to 1. |
|---|
| 263 | ! |
|---|
| 264 | ! Clean-up loop so remaining vector length is a multiple of 5. |
|---|
| 265 | ! |
|---|
| 266 | 20 M = MOD(N,5) |
|---|
| 267 | IF (M .EQ. 0) GO TO 40 |
|---|
| 268 | DO i = 1,M |
|---|
| 269 | WDOT = WDOT + DX(i)*DY(i) |
|---|
| 270 | END DO |
|---|
| 271 | IF (N .LT. 5) RETURN |
|---|
| 272 | 40 MP1 = M + 1 |
|---|
| 273 | DO i = MP1,N,5 |
|---|
| 274 | WDOT = WDOT + DX(i)*DY(i) |
|---|
| 275 | & + DX(i+1)*DY(i+1) + DX(i+2)*DY(i+2) |
|---|
| 276 | & + DX(i+3)*DY(i+3) + DX(i+4)*DY(i+4) |
|---|
| 277 | END DO |
|---|
| 278 | RETURN |
|---|
| 279 | ! |
|---|
| 280 | ! Code for equal, positive, non-unit increments. |
|---|
| 281 | ! |
|---|
| 282 | 60 NS = N*incX |
|---|
| 283 | DO i = 1,NS,incX |
|---|
| 284 | WDOT = WDOT + DX(i)*DY(i) |
|---|
| 285 | END DO |
|---|
| 286 | |
|---|
| 287 | END FUNCTION WDOT |
|---|
| 288 | |
|---|
| 289 | |
|---|
| 290 | !-------------------------------------------------------------- |
|---|
| 291 | SUBROUTINE WADD(N,X,Y,Z) |
|---|
| 292 | !-------------------------------------------------------------- |
|---|
| 293 | ! adds two vectors: z <- x + y |
|---|
| 294 | ! BLAS - like |
|---|
| 295 | !-------------------------------------------------------------- |
|---|
| 296 | |
|---|
| 297 | INTEGER i, M, MP1, N |
|---|
| 298 | KPP_REAL X(N),Y(N),Z(N) |
|---|
| 299 | |
|---|
| 300 | IF (N.LE.0) RETURN |
|---|
| 301 | |
|---|
| 302 | M = MOD(N,5) |
|---|
| 303 | IF( M .NE. 0 ) THEN |
|---|
| 304 | DO i = 1,M |
|---|
| 305 | Z(i) = X(i) + Y(i) |
|---|
| 306 | END DO |
|---|
| 307 | IF( N .LT. 5 ) RETURN |
|---|
| 308 | END IF |
|---|
| 309 | MP1 = M+1 |
|---|
| 310 | DO i = MP1,N,5 |
|---|
| 311 | Z(i) = X(i) + Y(i) |
|---|
| 312 | Z(i + 1) = X(i + 1) + Y(i + 1) |
|---|
| 313 | Z(i + 2) = X(i + 2) + Y(i + 2) |
|---|
| 314 | Z(i + 3) = X(i + 3) + Y(i + 3) |
|---|
| 315 | Z(i + 4) = X(i + 4) + Y(i + 4) |
|---|
| 316 | END DO |
|---|
| 317 | |
|---|
| 318 | END SUBROUTINE WADD |
|---|
| 319 | !-------------------------------------------------------------- |
|---|
