Gael Guennebaud | a6f483e | 2010-11-22 18:05:09 +0100 | [diff] [blame] | 1 | SUBROUTINE STPSV(UPLO,TRANS,DIAG,N,AP,X,INCX) |
| 2 | * .. Scalar Arguments .. |
| 3 | INTEGER INCX,N |
| 4 | CHARACTER DIAG,TRANS,UPLO |
| 5 | * .. |
| 6 | * .. Array Arguments .. |
| 7 | REAL AP(*),X(*) |
| 8 | * .. |
| 9 | * |
| 10 | * Purpose |
| 11 | * ======= |
| 12 | * |
| 13 | * STPSV 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 - REAL 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 - REAL 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 | REAL ZERO |
| 106 | PARAMETER (ZERO=0.0E+0) |
| 107 | * .. |
| 108 | * .. Local Scalars .. |
| 109 | REAL 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('STPSV ',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 STPSV . |
| 295 | * |
| 296 | END |