| 1 | SUBROUTINE ZTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) |
|---|
| 2 | * .. Scalar Arguments .. |
|---|
| 3 | INTEGER INCX,LDA,N |
|---|
| 4 | CHARACTER DIAG,TRANS,UPLO |
|---|
| 5 | * .. |
|---|
| 6 | * .. Array Arguments .. |
|---|
| 7 | DOUBLE COMPLEX A(LDA,*),X(*) |
|---|
| 8 | * .. |
|---|
| 9 | * |
|---|
| 10 | * Purpose |
|---|
| 11 | * ======= |
|---|
| 12 | * |
|---|
| 13 | * ZTRSV 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. |
|---|
| 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 | * A - COMPLEX*16 array of DIMENSION ( LDA, n ). |
|---|
| 65 | * Before entry with UPLO = 'U' or 'u', the leading n by n |
|---|
| 66 | * upper triangular part of the array A must contain the upper |
|---|
| 67 | * triangular matrix and the strictly lower triangular part of |
|---|
| 68 | * A is not referenced. |
|---|
| 69 | * Before entry with UPLO = 'L' or 'l', the leading n by n |
|---|
| 70 | * lower triangular part of the array A must contain the lower |
|---|
| 71 | * triangular matrix and the strictly upper triangular part of |
|---|
| 72 | * A is not referenced. |
|---|
| 73 | * Note that when DIAG = 'U' or 'u', the diagonal elements of |
|---|
| 74 | * A are not referenced either, but are assumed to be unity. |
|---|
| 75 | * Unchanged on exit. |
|---|
| 76 | * |
|---|
| 77 | * LDA - INTEGER. |
|---|
| 78 | * On entry, LDA specifies the first dimension of A as declared |
|---|
| 79 | * in the calling (sub) program. LDA must be at least |
|---|
| 80 | * max( 1, n ). |
|---|
| 81 | * Unchanged on exit. |
|---|
| 82 | * |
|---|
| 83 | * X - COMPLEX*16 array of dimension at least |
|---|
| 84 | * ( 1 + ( n - 1 )*abs( INCX ) ). |
|---|
| 85 | * Before entry, the incremented array X must contain the n |
|---|
| 86 | * element right-hand side vector b. On exit, X is overwritten |
|---|
| 87 | * with the solution vector x. |
|---|
| 88 | * |
|---|
| 89 | * INCX - INTEGER. |
|---|
| 90 | * On entry, INCX specifies the increment for the elements of |
|---|
| 91 | * X. INCX must not be zero. |
|---|
| 92 | * Unchanged on exit. |
|---|
| 93 | * |
|---|
| 94 | * |
|---|
| 95 | * Level 2 Blas routine. |
|---|
| 96 | * |
|---|
| 97 | * -- Written on 22-October-1986. |
|---|
| 98 | * Jack Dongarra, Argonne National Lab. |
|---|
| 99 | * Jeremy Du Croz, Nag Central Office. |
|---|
| 100 | * Sven Hammarling, Nag Central Office. |
|---|
| 101 | * Richard Hanson, Sandia National Labs. |
|---|
| 102 | * |
|---|
| 103 | * |
|---|
| 104 | * .. Parameters .. |
|---|
| 105 | DOUBLE COMPLEX ZERO |
|---|
| 106 | PARAMETER (ZERO= (0.0D+0,0.0D+0)) |
|---|
| 107 | * .. |
|---|
| 108 | * .. Local Scalars .. |
|---|
| 109 | DOUBLE COMPLEX TEMP |
|---|
| 110 | INTEGER I,INFO,IX,J,JX,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 DCONJG,MAX |
|---|
| 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 (LDA.LT.MAX(1,N)) THEN |
|---|
| 137 | INFO = 6 |
|---|
| 138 | ELSE IF (INCX.EQ.0) THEN |
|---|
| 139 | INFO = 8 |
|---|
| 140 | END IF |
|---|
| 141 | IF (INFO.NE.0) THEN |
|---|
| 142 | CALL XERBLA('ZTRSV ',INFO) |
|---|
| 143 | RETURN |
|---|
| 144 | END IF |
|---|
| 145 | * |
|---|
| 146 | * Quick return if possible. |
|---|
| 147 | * |
|---|
| 148 | IF (N.EQ.0) RETURN |
|---|
| 149 | * |
|---|
| 150 | NOCONJ = LSAME(TRANS,'T') |
|---|
| 151 | NOUNIT = LSAME(DIAG,'N') |
|---|
| 152 | * |
|---|
| 153 | * Set up the start point in X if the increment is not unity. This |
|---|
| 154 | * will be ( N - 1 )*INCX too small for descending loops. |
|---|
| 155 | * |
|---|
| 156 | IF (INCX.LE.0) THEN |
|---|
| 157 | KX = 1 - (N-1)*INCX |
|---|
| 158 | ELSE IF (INCX.NE.1) THEN |
|---|
| 159 | KX = 1 |
|---|
| 160 | END IF |
|---|
| 161 | * |
|---|
| 162 | * Start the operations. In this version the elements of A are |
|---|
| 163 | * accessed sequentially with one pass through A. |
|---|
| 164 | * |
|---|
| 165 | IF (LSAME(TRANS,'N')) THEN |
|---|
| 166 | * |
|---|
| 167 | * Form x := inv( A )*x. |
|---|
| 168 | * |
|---|
| 169 | IF (LSAME(UPLO,'U')) THEN |
|---|
| 170 | IF (INCX.EQ.1) THEN |
|---|
| 171 | DO 20 J = N,1,-1 |
|---|
| 172 | IF (X(J).NE.ZERO) THEN |
|---|
| 173 | IF (NOUNIT) X(J) = X(J)/A(J,J) |
|---|
| 174 | TEMP = X(J) |
|---|
| 175 | DO 10 I = J - 1,1,-1 |
|---|
| 176 | X(I) = X(I) - TEMP*A(I,J) |
|---|
| 177 | 10 CONTINUE |
|---|
| 178 | END IF |
|---|
| 179 | 20 CONTINUE |
|---|
| 180 | ELSE |
|---|
| 181 | JX = KX + (N-1)*INCX |
|---|
| 182 | DO 40 J = N,1,-1 |
|---|
| 183 | IF (X(JX).NE.ZERO) THEN |
|---|
| 184 | IF (NOUNIT) X(JX) = X(JX)/A(J,J) |
|---|
| 185 | TEMP = X(JX) |
|---|
| 186 | IX = JX |
|---|
| 187 | DO 30 I = J - 1,1,-1 |
|---|
| 188 | IX = IX - INCX |
|---|
| 189 | X(IX) = X(IX) - TEMP*A(I,J) |
|---|
| 190 | 30 CONTINUE |
|---|
| 191 | END IF |
|---|
| 192 | JX = JX - INCX |
|---|
| 193 | 40 CONTINUE |
|---|
| 194 | END IF |
|---|
| 195 | ELSE |
|---|
| 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)/A(J,J) |
|---|
| 200 | TEMP = X(J) |
|---|
| 201 | DO 50 I = J + 1,N |
|---|
| 202 | X(I) = X(I) - TEMP*A(I,J) |
|---|
| 203 | 50 CONTINUE |
|---|
| 204 | END IF |
|---|
| 205 | 60 CONTINUE |
|---|
| 206 | ELSE |
|---|
| 207 | JX = KX |
|---|
| 208 | DO 80 J = 1,N |
|---|
| 209 | IF (X(JX).NE.ZERO) THEN |
|---|
| 210 | IF (NOUNIT) X(JX) = X(JX)/A(J,J) |
|---|
| 211 | TEMP = X(JX) |
|---|
| 212 | IX = JX |
|---|
| 213 | DO 70 I = J + 1,N |
|---|
| 214 | IX = IX + INCX |
|---|
| 215 | X(IX) = X(IX) - TEMP*A(I,J) |
|---|
| 216 | 70 CONTINUE |
|---|
| 217 | END IF |
|---|
| 218 | JX = JX + INCX |
|---|
| 219 | 80 CONTINUE |
|---|
| 220 | END IF |
|---|
| 221 | END IF |
|---|
| 222 | ELSE |
|---|
| 223 | * |
|---|
| 224 | * Form x := inv( A' )*x or x := inv( conjg( A' ) )*x. |
|---|
| 225 | * |
|---|
| 226 | IF (LSAME(UPLO,'U')) THEN |
|---|
| 227 | IF (INCX.EQ.1) THEN |
|---|
| 228 | DO 110 J = 1,N |
|---|
| 229 | TEMP = X(J) |
|---|
| 230 | IF (NOCONJ) THEN |
|---|
| 231 | DO 90 I = 1,J - 1 |
|---|
| 232 | TEMP = TEMP - A(I,J)*X(I) |
|---|
| 233 | 90 CONTINUE |
|---|
| 234 | IF (NOUNIT) TEMP = TEMP/A(J,J) |
|---|
| 235 | ELSE |
|---|
| 236 | DO 100 I = 1,J - 1 |
|---|
| 237 | TEMP = TEMP - DCONJG(A(I,J))*X(I) |
|---|
| 238 | 100 CONTINUE |
|---|
| 239 | IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J)) |
|---|
| 240 | END IF |
|---|
| 241 | X(J) = TEMP |
|---|
| 242 | 110 CONTINUE |
|---|
| 243 | ELSE |
|---|
| 244 | JX = KX |
|---|
| 245 | DO 140 J = 1,N |
|---|
| 246 | IX = KX |
|---|
| 247 | TEMP = X(JX) |
|---|
| 248 | IF (NOCONJ) THEN |
|---|
| 249 | DO 120 I = 1,J - 1 |
|---|
| 250 | TEMP = TEMP - A(I,J)*X(IX) |
|---|
| 251 | IX = IX + INCX |
|---|
| 252 | 120 CONTINUE |
|---|
| 253 | IF (NOUNIT) TEMP = TEMP/A(J,J) |
|---|
| 254 | ELSE |
|---|
| 255 | DO 130 I = 1,J - 1 |
|---|
| 256 | TEMP = TEMP - DCONJG(A(I,J))*X(IX) |
|---|
| 257 | IX = IX + INCX |
|---|
| 258 | 130 CONTINUE |
|---|
| 259 | IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J)) |
|---|
| 260 | END IF |
|---|
| 261 | X(JX) = TEMP |
|---|
| 262 | JX = JX + INCX |
|---|
| 263 | 140 CONTINUE |
|---|
| 264 | END IF |
|---|
| 265 | ELSE |
|---|
| 266 | IF (INCX.EQ.1) THEN |
|---|
| 267 | DO 170 J = N,1,-1 |
|---|
| 268 | TEMP = X(J) |
|---|
| 269 | IF (NOCONJ) THEN |
|---|
| 270 | DO 150 I = N,J + 1,-1 |
|---|
| 271 | TEMP = TEMP - A(I,J)*X(I) |
|---|
| 272 | 150 CONTINUE |
|---|
| 273 | IF (NOUNIT) TEMP = TEMP/A(J,J) |
|---|
| 274 | ELSE |
|---|
| 275 | DO 160 I = N,J + 1,-1 |
|---|
| 276 | TEMP = TEMP - DCONJG(A(I,J))*X(I) |
|---|
| 277 | 160 CONTINUE |
|---|
| 278 | IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J)) |
|---|
| 279 | END IF |
|---|
| 280 | X(J) = TEMP |
|---|
| 281 | 170 CONTINUE |
|---|
| 282 | ELSE |
|---|
| 283 | KX = KX + (N-1)*INCX |
|---|
| 284 | JX = KX |
|---|
| 285 | DO 200 J = N,1,-1 |
|---|
| 286 | IX = KX |
|---|
| 287 | TEMP = X(JX) |
|---|
| 288 | IF (NOCONJ) THEN |
|---|
| 289 | DO 180 I = N,J + 1,-1 |
|---|
| 290 | TEMP = TEMP - A(I,J)*X(IX) |
|---|
| 291 | IX = IX - INCX |
|---|
| 292 | 180 CONTINUE |
|---|
| 293 | IF (NOUNIT) TEMP = TEMP/A(J,J) |
|---|
| 294 | ELSE |
|---|
| 295 | DO 190 I = N,J + 1,-1 |
|---|
| 296 | TEMP = TEMP - DCONJG(A(I,J))*X(IX) |
|---|
| 297 | IX = IX - INCX |
|---|
| 298 | 190 CONTINUE |
|---|
| 299 | IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J)) |
|---|
| 300 | END IF |
|---|
| 301 | X(JX) = TEMP |
|---|
| 302 | JX = JX - INCX |
|---|
| 303 | 200 CONTINUE |
|---|
| 304 | END IF |
|---|
| 305 | END IF |
|---|
| 306 | END IF |
|---|
| 307 | * |
|---|
| 308 | RETURN |
|---|
| 309 | * |
|---|
| 310 | * End of ZTRSV . |
|---|
| 311 | * |
|---|
| 312 | END |
|---|
