1 SUBROUTINE DTPMV(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 PRECISION AP(*),X(*) 8 * .. 9 * 10 * Purpose 11 * ======= 12 * 13 * DTPMV performs one of the matrix-vector operations 14 * 15 * x := A*x, or x := 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 := 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION 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 PRECISION ZERO 103 PARAMETER (ZERO=0.0D+0) 104 * .. 105 * .. Local Scalars .. 106 DOUBLE PRECISION TEMP 107 INTEGER I,INFO,IX,J,JX,K,KK,KX 108 LOGICAL NOUNIT 109 * .. 110 * .. External Functions .. 111 LOGICAL LSAME 112 EXTERNAL LSAME 113 * .. 114 * .. External Subroutines .. 115 EXTERNAL XERBLA 116 * .. 117 * 118 * Test the input parameters. 119 * 120 INFO = 0 121 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 122 INFO = 1 123 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. 124 + .NOT.LSAME(TRANS,'C')) THEN 125 INFO = 2 126 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN 127 INFO = 3 128 ELSE IF (N.LT.0) THEN 129 INFO = 4 130 ELSE IF (INCX.EQ.0) THEN 131 INFO = 7 132 END IF 133 IF (INFO.NE.0) THEN 134 CALL XERBLA('DTPMV ',INFO) 135 RETURN 136 END IF 137 * 138 * Quick return if possible. 139 * 140 IF (N.EQ.0) RETURN 141 * 142 NOUNIT = LSAME(DIAG,'N') 143 * 144 * Set up the start point in X if the increment is not unity. This 145 * will be ( N - 1 )*INCX too small for descending loops. 146 * 147 IF (INCX.LE.0) THEN 148 KX = 1 - (N-1)*INCX 149 ELSE IF (INCX.NE.1) THEN 150 KX = 1 151 END IF 152 * 153 * Start the operations. In this version the elements of AP are 154 * accessed sequentially with one pass through AP. 155 * 156 IF (LSAME(TRANS,'N')) THEN 157 * 158 * Form x:= A*x. 159 * 160 IF (LSAME(UPLO,'U')) THEN 161 KK = 1 162 IF (INCX.EQ.1) THEN 163 DO 20 J = 1,N 164 IF (X(J).NE.ZERO) THEN 165 TEMP = X(J) 166 K = KK 167 DO 10 I = 1,J - 1 168 X(I) = X(I) + TEMP*AP(K) 169 K = K + 1 170 10 CONTINUE 171 IF (NOUNIT) X(J) = X(J)*AP(KK+J-1) 172 END IF 173 KK = KK + J 174 20 CONTINUE 175 ELSE 176 JX = KX 177 DO 40 J = 1,N 178 IF (X(JX).NE.ZERO) THEN 179 TEMP = X(JX) 180 IX = KX 181 DO 30 K = KK,KK + J - 2 182 X(IX) = X(IX) + TEMP*AP(K) 183 IX = IX + INCX 184 30 CONTINUE 185 IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1) 186 END IF 187 JX = JX + INCX 188 KK = KK + J 189 40 CONTINUE 190 END IF 191 ELSE 192 KK = (N* (N+1))/2 193 IF (INCX.EQ.1) THEN 194 DO 60 J = N,1,-1 195 IF (X(J).NE.ZERO) THEN 196 TEMP = X(J) 197 K = KK 198 DO 50 I = N,J + 1,-1 199 X(I) = X(I) + TEMP*AP(K) 200 K = K - 1 201 50 CONTINUE 202 IF (NOUNIT) X(J) = X(J)*AP(KK-N+J) 203 END IF 204 KK = KK - (N-J+1) 205 60 CONTINUE 206 ELSE 207 KX = KX + (N-1)*INCX 208 JX = KX 209 DO 80 J = N,1,-1 210 IF (X(JX).NE.ZERO) THEN 211 TEMP = X(JX) 212 IX = KX 213 DO 70 K = KK,KK - (N- (J+1)),-1 214 X(IX) = X(IX) + TEMP*AP(K) 215 IX = IX - INCX 216 70 CONTINUE 217 IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J) 218 END IF 219 JX = JX - INCX 220 KK = KK - (N-J+1) 221 80 CONTINUE 222 END IF 223 END IF 224 ELSE 225 * 226 * Form x := A'*x. 227 * 228 IF (LSAME(UPLO,'U')) THEN 229 KK = (N* (N+1))/2 230 IF (INCX.EQ.1) THEN 231 DO 100 J = N,1,-1 232 TEMP = X(J) 233 IF (NOUNIT) TEMP = TEMP*AP(KK) 234 K = KK - 1 235 DO 90 I = J - 1,1,-1 236 TEMP = TEMP + AP(K)*X(I) 237 K = K - 1 238 90 CONTINUE 239 X(J) = TEMP 240 KK = KK - J 241 100 CONTINUE 242 ELSE 243 JX = KX + (N-1)*INCX 244 DO 120 J = N,1,-1 245 TEMP = X(JX) 246 IX = JX 247 IF (NOUNIT) TEMP = TEMP*AP(KK) 248 DO 110 K = KK - 1,KK - J + 1,-1 249 IX = IX - INCX 250 TEMP = TEMP + AP(K)*X(IX) 251 110 CONTINUE 252 X(JX) = TEMP 253 JX = JX - INCX 254 KK = KK - J 255 120 CONTINUE 256 END IF 257 ELSE 258 KK = 1 259 IF (INCX.EQ.1) THEN 260 DO 140 J = 1,N 261 TEMP = X(J) 262 IF (NOUNIT) TEMP = TEMP*AP(KK) 263 K = KK + 1 264 DO 130 I = J + 1,N 265 TEMP = TEMP + AP(K)*X(I) 266 K = K + 1 267 130 CONTINUE 268 X(J) = TEMP 269 KK = KK + (N-J+1) 270 140 CONTINUE 271 ELSE 272 JX = KX 273 DO 160 J = 1,N 274 TEMP = X(JX) 275 IX = JX 276 IF (NOUNIT) TEMP = TEMP*AP(KK) 277 DO 150 K = KK + 1,KK + N - J 278 IX = IX + INCX 279 TEMP = TEMP + AP(K)*X(IX) 280 150 CONTINUE 281 X(JX) = TEMP 282 JX = JX + INCX 283 KK = KK + (N-J+1) 284 160 CONTINUE 285 END IF 286 END IF 287 END IF 288 * 289 RETURN 290 * 291 * End of DTPMV . 292 * 293 END 294
