1 SUBROUTINE CTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) 2* .. Scalar Arguments .. 3 INTEGER INCX,N 4 CHARACTER DIAG,TRANS,UPLO 5* .. 6* .. Array Arguments .. 7 COMPLEX AP(*),X(*) 8* .. 9* 10* Purpose 11* ======= 12* 13* CTPSV solves one of the systems of equations 14* 15* A*x = b, or A'*x = b, or conjg( A' )*x = b, 16* 17* where b and x are n element vectors and A is an n by n unit, or 18* non-unit, upper or lower triangular matrix, supplied in packed form. 19* 20* No test for singularity or near-singularity is included in this 21* routine. Such tests must be performed before calling this routine. 22* 23* Arguments 24* ========== 25* 26* UPLO - CHARACTER*1. 27* On entry, UPLO specifies whether the matrix is an upper or 28* lower triangular matrix as follows: 29* 30* UPLO = 'U' or 'u' A is an upper triangular matrix. 31* 32* UPLO = 'L' or 'l' A is a lower triangular matrix. 33* 34* Unchanged on exit. 35* 36* TRANS - CHARACTER*1. 37* On entry, TRANS specifies the equations to be solved as 38* follows: 39* 40* TRANS = 'N' or 'n' A*x = b. 41* 42* TRANS = 'T' or 't' A'*x = b. 43* 44* TRANS = 'C' or 'c' conjg( A' )*x = b. 45* 46* Unchanged on exit. 47* 48* DIAG - CHARACTER*1. 49* On entry, DIAG specifies whether or not A is unit 50* triangular as follows: 51* 52* DIAG = 'U' or 'u' A is assumed to be unit triangular. 53* 54* DIAG = 'N' or 'n' A is not assumed to be unit 55* triangular. 56* 57* Unchanged on exit. 58* 59* N - INTEGER. 60* On entry, N specifies the order of the matrix A. 61* N must be at least zero. 62* Unchanged on exit. 63* 64* AP - COMPLEX array of DIMENSION at least 65* ( ( n*( n + 1 ) )/2 ). 66* Before entry with UPLO = 'U' or 'u', the array AP must 67* contain the upper triangular matrix packed sequentially, 68* column by column, so that AP( 1 ) contains a( 1, 1 ), 69* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) 70* respectively, and so on. 71* Before entry with UPLO = 'L' or 'l', the array AP must 72* contain the lower triangular matrix packed sequentially, 73* column by column, so that AP( 1 ) contains a( 1, 1 ), 74* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) 75* respectively, and so on. 76* Note that when DIAG = 'U' or 'u', the diagonal elements of 77* A are not referenced, but are assumed to be unity. 78* Unchanged on exit. 79* 80* X - COMPLEX array of dimension at least 81* ( 1 + ( n - 1 )*abs( INCX ) ). 82* Before entry, the incremented array X must contain the n 83* element right-hand side vector b. On exit, X is overwritten 84* with the solution vector x. 85* 86* INCX - INTEGER. 87* On entry, INCX specifies the increment for the elements of 88* X. INCX must not be zero. 89* Unchanged on exit. 90* 91* Further Details 92* =============== 93* 94* Level 2 Blas routine. 95* 96* -- Written on 22-October-1986. 97* Jack Dongarra, Argonne National Lab. 98* Jeremy Du Croz, Nag Central Office. 99* Sven Hammarling, Nag Central Office. 100* Richard Hanson, Sandia National Labs. 101* 102* ===================================================================== 103* 104* .. Parameters .. 105 COMPLEX ZERO 106 PARAMETER (ZERO= (0.0E+0,0.0E+0)) 107* .. 108* .. Local Scalars .. 109 COMPLEX TEMP 110 INTEGER I,INFO,IX,J,JX,K,KK,KX 111 LOGICAL NOCONJ,NOUNIT 112* .. 113* .. External Functions .. 114 LOGICAL LSAME 115 EXTERNAL LSAME 116* .. 117* .. External Subroutines .. 118 EXTERNAL XERBLA 119* .. 120* .. Intrinsic Functions .. 121 INTRINSIC CONJG 122* .. 123* 124* Test the input parameters. 125* 126 INFO = 0 127 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 128 INFO = 1 129 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 130 + .NOT.LSAME(TRANS,'C')) THEN 131 INFO = 2 132 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 133 INFO = 3 134 ELSE IF (N.LT.0) THEN 135 INFO = 4 136 ELSE IF (INCX.EQ.0) THEN 137 INFO = 7 138 END IF 139 IF (INFO.NE.0) THEN 140 CALL XERBLA('CTPSV ',INFO) 141 RETURN 142 END IF 143* 144* Quick return if possible. 145* 146 IF (N.EQ.0) RETURN 147* 148 NOCONJ = LSAME(TRANS,'T') 149 NOUNIT = LSAME(DIAG,'N') 150* 151* Set up the start point in X if the increment is not unity. This 152* will be ( N - 1 )*INCX too small for descending loops. 153* 154 IF (INCX.LE.0) THEN 155 KX = 1 - (N-1)*INCX 156 ELSE IF (INCX.NE.1) THEN 157 KX = 1 158 END IF 159* 160* Start the operations. In this version the elements of AP are 161* accessed sequentially with one pass through AP. 162* 163 IF (LSAME(TRANS,'N')) THEN 164* 165* Form x := inv( A )*x. 166* 167 IF (LSAME(UPLO,'U')) THEN 168 KK = (N* (N+1))/2 169 IF (INCX.EQ.1) THEN 170 DO 20 J = N,1,-1 171 IF (X(J).NE.ZERO) THEN 172 IF (NOUNIT) X(J) = X(J)/AP(KK) 173 TEMP = X(J) 174 K = KK - 1 175 DO 10 I = J - 1,1,-1 176 X(I) = X(I) - TEMP*AP(K) 177 K = K - 1 178 10 CONTINUE 179 END IF 180 KK = KK - J 181 20 CONTINUE 182 ELSE 183 JX = KX + (N-1)*INCX 184 DO 40 J = N,1,-1 185 IF (X(JX).NE.ZERO) THEN 186 IF (NOUNIT) X(JX) = X(JX)/AP(KK) 187 TEMP = X(JX) 188 IX = JX 189 DO 30 K = KK - 1,KK - J + 1,-1 190 IX = IX - INCX 191 X(IX) = X(IX) - TEMP*AP(K) 192 30 CONTINUE 193 END IF 194 JX = JX - INCX 195 KK = KK - J 196 40 CONTINUE 197 END IF 198 ELSE 199 KK = 1 200 IF (INCX.EQ.1) THEN 201 DO 60 J = 1,N 202 IF (X(J).NE.ZERO) THEN 203 IF (NOUNIT) X(J) = X(J)/AP(KK) 204 TEMP = X(J) 205 K = KK + 1 206 DO 50 I = J + 1,N 207 X(I) = X(I) - TEMP*AP(K) 208 K = K + 1 209 50 CONTINUE 210 END IF 211 KK = KK + (N-J+1) 212 60 CONTINUE 213 ELSE 214 JX = KX 215 DO 80 J = 1,N 216 IF (X(JX).NE.ZERO) THEN 217 IF (NOUNIT) X(JX) = X(JX)/AP(KK) 218 TEMP = X(JX) 219 IX = JX 220 DO 70 K = KK + 1,KK + N - J 221 IX = IX + INCX 222 X(IX) = X(IX) - TEMP*AP(K) 223 70 CONTINUE 224 END IF 225 JX = JX + INCX 226 KK = KK + (N-J+1) 227 80 CONTINUE 228 END IF 229 END IF 230 ELSE 231* 232* Form x := inv( A' )*x or x := inv( conjg( A' ) )*x. 233* 234 IF (LSAME(UPLO,'U')) THEN 235 KK = 1 236 IF (INCX.EQ.1) THEN 237 DO 110 J = 1,N 238 TEMP = X(J) 239 K = KK 240 IF (NOCONJ) THEN 241 DO 90 I = 1,J - 1 242 TEMP = TEMP - AP(K)*X(I) 243 K = K + 1 244 90 CONTINUE 245 IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) 246 ELSE 247 DO 100 I = 1,J - 1 248 TEMP = TEMP - CONJG(AP(K))*X(I) 249 K = K + 1 250 100 CONTINUE 251 IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK+J-1)) 252 END IF 253 X(J) = TEMP 254 KK = KK + J 255 110 CONTINUE 256 ELSE 257 JX = KX 258 DO 140 J = 1,N 259 TEMP = X(JX) 260 IX = KX 261 IF (NOCONJ) THEN 262 DO 120 K = KK,KK + J - 2 263 TEMP = TEMP - AP(K)*X(IX) 264 IX = IX + INCX 265 120 CONTINUE 266 IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) 267 ELSE 268 DO 130 K = KK,KK + J - 2 269 TEMP = TEMP - CONJG(AP(K))*X(IX) 270 IX = IX + INCX 271 130 CONTINUE 272 IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK+J-1)) 273 END IF 274 X(JX) = TEMP 275 JX = JX + INCX 276 KK = KK + J 277 140 CONTINUE 278 END IF 279 ELSE 280 KK = (N* (N+1))/2 281 IF (INCX.EQ.1) THEN 282 DO 170 J = N,1,-1 283 TEMP = X(J) 284 K = KK 285 IF (NOCONJ) THEN 286 DO 150 I = N,J + 1,-1 287 TEMP = TEMP - AP(K)*X(I) 288 K = K - 1 289 150 CONTINUE 290 IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) 291 ELSE 292 DO 160 I = N,J + 1,-1 293 TEMP = TEMP - CONJG(AP(K))*X(I) 294 K = K - 1 295 160 CONTINUE 296 IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK-N+J)) 297 END IF 298 X(J) = TEMP 299 KK = KK - (N-J+1) 300 170 CONTINUE 301 ELSE 302 KX = KX + (N-1)*INCX 303 JX = KX 304 DO 200 J = N,1,-1 305 TEMP = X(JX) 306 IX = KX 307 IF (NOCONJ) THEN 308 DO 180 K = KK,KK - (N- (J+1)),-1 309 TEMP = TEMP - AP(K)*X(IX) 310 IX = IX - INCX 311 180 CONTINUE 312 IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) 313 ELSE 314 DO 190 K = KK,KK - (N- (J+1)),-1 315 TEMP = TEMP - CONJG(AP(K))*X(IX) 316 IX = IX - INCX 317 190 CONTINUE 318 IF (NOUNIT) TEMP = TEMP/CONJG(AP(KK-N+J)) 319 END IF 320 X(JX) = TEMP 321 JX = JX - INCX 322 KK = KK - (N-J+1) 323 200 CONTINUE 324 END IF 325 END IF 326 END IF 327* 328 RETURN 329* 330* End of CTPSV . 331* 332 END 333