1 SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX) 2 * .. Scalar Arguments .. 3 INTEGER INCX,N 4 CHARACTER DIAG,TRANS,UPLO 5 * .. 6 * .. Array Arguments .. 7 DOUBLE COMPLEX AP(*),X(*) 8 * .. 9 * 10 * Purpose 11 * ======= 12 * 13 * ZTPMV performs one of the matrix-vector operations 14 * 15 * x := A*x, or x := A'*x, or x := conjg( A' )*x, 16 * 17 * where x is an n element vector and A is an n by n unit, or non-unit, 18 * upper or lower triangular matrix, supplied in packed form. 19 * 20 * Arguments 21 * ========== 22 * 23 * UPLO - CHARACTER*1. 24 * On entry, UPLO specifies whether the matrix is an upper or 25 * lower triangular matrix as follows: 26 * 27 * UPLO = 'U' or 'u' A is an upper triangular matrix. 28 * 29 * UPLO = 'L' or 'l' A is a lower triangular matrix. 30 * 31 * Unchanged on exit. 32 * 33 * TRANS - CHARACTER*1. 34 * On entry, TRANS specifies the operation to be performed as 35 * follows: 36 * 37 * TRANS = 'N' or 'n' x := A*x. 38 * 39 * TRANS = 'T' or 't' x := A'*x. 40 * 41 * TRANS = 'C' or 'c' x := conjg( A' )*x. 42 * 43 * Unchanged on exit. 44 * 45 * DIAG - CHARACTER*1. 46 * On entry, DIAG specifies whether or not A is unit 47 * triangular as follows: 48 * 49 * DIAG = 'U' or 'u' A is assumed to be unit triangular. 50 * 51 * DIAG = 'N' or 'n' A is not assumed to be unit 52 * triangular. 53 * 54 * Unchanged on exit. 55 * 56 * N - INTEGER. 57 * On entry, N specifies the order of the matrix A. 58 * N must be at least zero. 59 * Unchanged on exit. 60 * 61 * AP - COMPLEX*16 array of DIMENSION at least 62 * ( ( n*( n + 1 ) )/2 ). 63 * Before entry with UPLO = 'U' or 'u', the array AP must 64 * contain the upper triangular matrix packed sequentially, 65 * column by column, so that AP( 1 ) contains a( 1, 1 ), 66 * AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) 67 * respectively, and so on. 68 * Before entry with UPLO = 'L' or 'l', the array AP must 69 * contain the lower triangular matrix packed sequentially, 70 * column by column, so that AP( 1 ) contains a( 1, 1 ), 71 * AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) 72 * respectively, and so on. 73 * Note that when DIAG = 'U' or 'u', the diagonal elements of 74 * A are not referenced, but are assumed to be unity. 75 * Unchanged on exit. 76 * 77 * X - COMPLEX*16 array of dimension at least 78 * ( 1 + ( n - 1 )*abs( INCX ) ). 79 * Before entry, the incremented array X must contain the n 80 * element vector x. On exit, X is overwritten with the 81 * tranformed vector x. 82 * 83 * INCX - INTEGER. 84 * On entry, INCX specifies the increment for the elements of 85 * X. INCX must not be zero. 86 * Unchanged on exit. 87 * 88 * Further Details 89 * =============== 90 * 91 * Level 2 Blas routine. 92 * 93 * -- Written on 22-October-1986. 94 * Jack Dongarra, Argonne National Lab. 95 * Jeremy Du Croz, Nag Central Office. 96 * Sven Hammarling, Nag Central Office. 97 * Richard Hanson, Sandia National Labs. 98 * 99 * ===================================================================== 100 * 101 * .. Parameters .. 102 DOUBLE COMPLEX ZERO 103 PARAMETER (ZERO= (0.0D+0,0.0D+0)) 104 * .. 105 * .. Local Scalars .. 106 DOUBLE COMPLEX TEMP 107 INTEGER I,INFO,IX,J,JX,K,KK,KX 108 LOGICAL NOCONJ,NOUNIT 109 * .. 110 * .. External Functions .. 111 LOGICAL LSAME 112 EXTERNAL LSAME 113 * .. 114 * .. External Subroutines .. 115 EXTERNAL XERBLA 116 * .. 117 * .. Intrinsic Functions .. 118 INTRINSIC DCONJG 119 * .. 120 * 121 * Test the input parameters. 122 * 123 INFO = 0 124 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 125 INFO = 1 126 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 127 + .NOT.LSAME(TRANS,'C')) THEN 128 INFO = 2 129 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 130 INFO = 3 131 ELSE IF (N.LT.0) THEN 132 INFO = 4 133 ELSE IF (INCX.EQ.0) THEN 134 INFO = 7 135 END IF 136 IF (INFO.NE.0) THEN 137 CALL XERBLA('ZTPMV ',INFO) 138 RETURN 139 END IF 140 * 141 * Quick return if possible. 142 * 143 IF (N.EQ.0) RETURN 144 * 145 NOCONJ = LSAME(TRANS,'T') 146 NOUNIT = LSAME(DIAG,'N') 147 * 148 * Set up the start point in X if the increment is not unity. This 149 * will be ( N - 1 )*INCX too small for descending loops. 150 * 151 IF (INCX.LE.0) THEN 152 KX = 1 - (N-1)*INCX 153 ELSE IF (INCX.NE.1) THEN 154 KX = 1 155 END IF 156 * 157 * Start the operations. In this version the elements of AP are 158 * accessed sequentially with one pass through AP. 159 * 160 IF (LSAME(TRANS,'N')) THEN 161 * 162 * Form x:= A*x. 163 * 164 IF (LSAME(UPLO,'U')) THEN 165 KK = 1 166 IF (INCX.EQ.1) THEN 167 DO 20 J = 1,N 168 IF (X(J).NE.ZERO) THEN 169 TEMP = X(J) 170 K = KK 171 DO 10 I = 1,J - 1 172 X(I) = X(I) + TEMP*AP(K) 173 K = K + 1 174 10 CONTINUE 175 IF (NOUNIT) X(J) = X(J)*AP(KK+J-1) 176 END IF 177 KK = KK + J 178 20 CONTINUE 179 ELSE 180 JX = KX 181 DO 40 J = 1,N 182 IF (X(JX).NE.ZERO) THEN 183 TEMP = X(JX) 184 IX = KX 185 DO 30 K = KK,KK + J - 2 186 X(IX) = X(IX) + TEMP*AP(K) 187 IX = IX + INCX 188 30 CONTINUE 189 IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1) 190 END IF 191 JX = JX + INCX 192 KK = KK + J 193 40 CONTINUE 194 END IF 195 ELSE 196 KK = (N* (N+1))/2 197 IF (INCX.EQ.1) THEN 198 DO 60 J = N,1,-1 199 IF (X(J).NE.ZERO) THEN 200 TEMP = X(J) 201 K = KK 202 DO 50 I = N,J + 1,-1 203 X(I) = X(I) + TEMP*AP(K) 204 K = K - 1 205 50 CONTINUE 206 IF (NOUNIT) X(J) = X(J)*AP(KK-N+J) 207 END IF 208 KK = KK - (N-J+1) 209 60 CONTINUE 210 ELSE 211 KX = KX + (N-1)*INCX 212 JX = KX 213 DO 80 J = N,1,-1 214 IF (X(JX).NE.ZERO) THEN 215 TEMP = X(JX) 216 IX = KX 217 DO 70 K = KK,KK - (N- (J+1)),-1 218 X(IX) = X(IX) + TEMP*AP(K) 219 IX = IX - INCX 220 70 CONTINUE 221 IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J) 222 END IF 223 JX = JX - INCX 224 KK = KK - (N-J+1) 225 80 CONTINUE 226 END IF 227 END IF 228 ELSE 229 * 230 * Form x := A'*x or x := conjg( A' )*x. 231 * 232 IF (LSAME(UPLO,'U')) THEN 233 KK = (N* (N+1))/2 234 IF (INCX.EQ.1) THEN 235 DO 110 J = N,1,-1 236 TEMP = X(J) 237 K = KK - 1 238 IF (NOCONJ) THEN 239 IF (NOUNIT) TEMP = TEMP*AP(KK) 240 DO 90 I = J - 1,1,-1 241 TEMP = TEMP + AP(K)*X(I) 242 K = K - 1 243 90 CONTINUE 244 ELSE 245 IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK)) 246 DO 100 I = J - 1,1,-1 247 TEMP = TEMP + DCONJG(AP(K))*X(I) 248 K = K - 1 249 100 CONTINUE 250 END IF 251 X(J) = TEMP 252 KK = KK - J 253 110 CONTINUE 254 ELSE 255 JX = KX + (N-1)*INCX 256 DO 140 J = N,1,-1 257 TEMP = X(JX) 258 IX = JX 259 IF (NOCONJ) THEN 260 IF (NOUNIT) TEMP = TEMP*AP(KK) 261 DO 120 K = KK - 1,KK - J + 1,-1 262 IX = IX - INCX 263 TEMP = TEMP + AP(K)*X(IX) 264 120 CONTINUE 265 ELSE 266 IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK)) 267 DO 130 K = KK - 1,KK - J + 1,-1 268 IX = IX - INCX 269 TEMP = TEMP + DCONJG(AP(K))*X(IX) 270 130 CONTINUE 271 END IF 272 X(JX) = TEMP 273 JX = JX - INCX 274 KK = KK - J 275 140 CONTINUE 276 END IF 277 ELSE 278 KK = 1 279 IF (INCX.EQ.1) THEN 280 DO 170 J = 1,N 281 TEMP = X(J) 282 K = KK + 1 283 IF (NOCONJ) THEN 284 IF (NOUNIT) TEMP = TEMP*AP(KK) 285 DO 150 I = J + 1,N 286 TEMP = TEMP + AP(K)*X(I) 287 K = K + 1 288 150 CONTINUE 289 ELSE 290 IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK)) 291 DO 160 I = J + 1,N 292 TEMP = TEMP + DCONJG(AP(K))*X(I) 293 K = K + 1 294 160 CONTINUE 295 END IF 296 X(J) = TEMP 297 KK = KK + (N-J+1) 298 170 CONTINUE 299 ELSE 300 JX = KX 301 DO 200 J = 1,N 302 TEMP = X(JX) 303 IX = JX 304 IF (NOCONJ) THEN 305 IF (NOUNIT) TEMP = TEMP*AP(KK) 306 DO 180 K = KK + 1,KK + N - J 307 IX = IX + INCX 308 TEMP = TEMP + AP(K)*X(IX) 309 180 CONTINUE 310 ELSE 311 IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK)) 312 DO 190 K = KK + 1,KK + N - J 313 IX = IX + INCX 314 TEMP = TEMP + DCONJG(AP(K))*X(IX) 315 190 CONTINUE 316 END IF 317 X(JX) = TEMP 318 JX = JX + INCX 319 KK = KK + (N-J+1) 320 200 CONTINUE 321 END IF 322 END IF 323 END IF 324 * 325 RETURN 326 * 327 * End of ZTPMV . 328 * 329 END 330
