1 SUBROUTINE DTPSV(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 * DTPSV solves one of the systems of equations 14 * 15 * A*x = b, or 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' 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION 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 DOUBLE PRECISION ZERO 106 PARAMETER (ZERO=0.0D+0) 107 * .. 108 * .. Local Scalars .. 109 DOUBLE PRECISION TEMP 110 INTEGER I,INFO,IX,J,JX,K,KK,KX 111 LOGICAL NOUNIT 112 * .. 113 * .. External Functions .. 114 LOGICAL LSAME 115 EXTERNAL LSAME 116 * .. 117 * .. External Subroutines .. 118 EXTERNAL XERBLA 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('DTPSV ',INFO) 138 RETURN 139 END IF 140 * 141 * Quick return if possible. 142 * 143 IF (N.EQ.0) RETURN 144 * 145 NOUNIT = LSAME(DIAG,'N') 146 * 147 * Set up the start point in X if the increment is not unity. This 148 * will be ( N - 1 )*INCX too small for descending loops. 149 * 150 IF (INCX.LE.0) THEN 151 KX = 1 - (N-1)*INCX 152 ELSE IF (INCX.NE.1) THEN 153 KX = 1 154 END IF 155 * 156 * Start the operations. In this version the elements of AP are 157 * accessed sequentially with one pass through AP. 158 * 159 IF (LSAME(TRANS,'N')) THEN 160 * 161 * Form x := inv( A )*x. 162 * 163 IF (LSAME(UPLO,'U')) THEN 164 KK = (N* (N+1))/2 165 IF (INCX.EQ.1) THEN 166 DO 20 J = N,1,-1 167 IF (X(J).NE.ZERO) THEN 168 IF (NOUNIT) X(J) = X(J)/AP(KK) 169 TEMP = X(J) 170 K = KK - 1 171 DO 10 I = J - 1,1,-1 172 X(I) = X(I) - TEMP*AP(K) 173 K = K - 1 174 10 CONTINUE 175 END IF 176 KK = KK - J 177 20 CONTINUE 178 ELSE 179 JX = KX + (N-1)*INCX 180 DO 40 J = N,1,-1 181 IF (X(JX).NE.ZERO) THEN 182 IF (NOUNIT) X(JX) = X(JX)/AP(KK) 183 TEMP = X(JX) 184 IX = JX 185 DO 30 K = KK - 1,KK - J + 1,-1 186 IX = IX - INCX 187 X(IX) = X(IX) - TEMP*AP(K) 188 30 CONTINUE 189 END IF 190 JX = JX - INCX 191 KK = KK - J 192 40 CONTINUE 193 END IF 194 ELSE 195 KK = 1 196 IF (INCX.EQ.1) THEN 197 DO 60 J = 1,N 198 IF (X(J).NE.ZERO) THEN 199 IF (NOUNIT) X(J) = X(J)/AP(KK) 200 TEMP = X(J) 201 K = KK + 1 202 DO 50 I = J + 1,N 203 X(I) = X(I) - TEMP*AP(K) 204 K = K + 1 205 50 CONTINUE 206 END IF 207 KK = KK + (N-J+1) 208 60 CONTINUE 209 ELSE 210 JX = KX 211 DO 80 J = 1,N 212 IF (X(JX).NE.ZERO) THEN 213 IF (NOUNIT) X(JX) = X(JX)/AP(KK) 214 TEMP = X(JX) 215 IX = JX 216 DO 70 K = KK + 1,KK + N - J 217 IX = IX + INCX 218 X(IX) = X(IX) - TEMP*AP(K) 219 70 CONTINUE 220 END IF 221 JX = JX + INCX 222 KK = KK + (N-J+1) 223 80 CONTINUE 224 END IF 225 END IF 226 ELSE 227 * 228 * Form x := inv( A' )*x. 229 * 230 IF (LSAME(UPLO,'U')) THEN 231 KK = 1 232 IF (INCX.EQ.1) THEN 233 DO 100 J = 1,N 234 TEMP = X(J) 235 K = KK 236 DO 90 I = 1,J - 1 237 TEMP = TEMP - AP(K)*X(I) 238 K = K + 1 239 90 CONTINUE 240 IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) 241 X(J) = TEMP 242 KK = KK + J 243 100 CONTINUE 244 ELSE 245 JX = KX 246 DO 120 J = 1,N 247 TEMP = X(JX) 248 IX = KX 249 DO 110 K = KK,KK + J - 2 250 TEMP = TEMP - AP(K)*X(IX) 251 IX = IX + INCX 252 110 CONTINUE 253 IF (NOUNIT) TEMP = TEMP/AP(KK+J-1) 254 X(JX) = TEMP 255 JX = JX + INCX 256 KK = KK + J 257 120 CONTINUE 258 END IF 259 ELSE 260 KK = (N* (N+1))/2 261 IF (INCX.EQ.1) THEN 262 DO 140 J = N,1,-1 263 TEMP = X(J) 264 K = KK 265 DO 130 I = N,J + 1,-1 266 TEMP = TEMP - AP(K)*X(I) 267 K = K - 1 268 130 CONTINUE 269 IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) 270 X(J) = TEMP 271 KK = KK - (N-J+1) 272 140 CONTINUE 273 ELSE 274 KX = KX + (N-1)*INCX 275 JX = KX 276 DO 160 J = N,1,-1 277 TEMP = X(JX) 278 IX = KX 279 DO 150 K = KK,KK - (N- (J+1)),-1 280 TEMP = TEMP - AP(K)*X(IX) 281 IX = IX - INCX 282 150 CONTINUE 283 IF (NOUNIT) TEMP = TEMP/AP(KK-N+J) 284 X(JX) = TEMP 285 JX = JX - INCX 286 KK = KK - (N-J+1) 287 160 CONTINUE 288 END IF 289 END IF 290 END IF 291 * 292 RETURN 293 * 294 * End of DTPSV . 295 * 296 END 297
