[15457] | 1 | SUBROUTINE DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) |
---|
| 2 | * .. Scalar Arguments .. |
---|
| 3 | DOUBLE PRECISION ALPHA,BETA |
---|
| 4 | INTEGER INCX,INCY,LDA,N |
---|
| 5 | CHARACTER UPLO |
---|
| 6 | * .. |
---|
| 7 | * .. Array Arguments .. |
---|
| 8 | DOUBLE PRECISION A(LDA,*),X(*),Y(*) |
---|
| 9 | * .. |
---|
| 10 | * |
---|
| 11 | * Purpose |
---|
| 12 | * ======= |
---|
| 13 | * |
---|
| 14 | * DSYMV performs the matrix-vector operation |
---|
| 15 | * |
---|
| 16 | * y := alpha*A*x + beta*y, |
---|
| 17 | * |
---|
| 18 | * where alpha and beta are scalars, x and y are n element vectors and |
---|
| 19 | * A is an n by n symmetric matrix. |
---|
| 20 | * |
---|
| 21 | * Arguments |
---|
| 22 | * ========== |
---|
| 23 | * |
---|
| 24 | * UPLO - CHARACTER*1. |
---|
| 25 | * On entry, UPLO specifies whether the upper or lower |
---|
| 26 | * triangular part of the array A is to be referenced as |
---|
| 27 | * follows: |
---|
| 28 | * |
---|
| 29 | * UPLO = 'U' or 'u' Only the upper triangular part of A |
---|
| 30 | * is to be referenced. |
---|
| 31 | * |
---|
| 32 | * UPLO = 'L' or 'l' Only the lower triangular part of A |
---|
| 33 | * is to be referenced. |
---|
| 34 | * |
---|
| 35 | * Unchanged on exit. |
---|
| 36 | * |
---|
| 37 | * N - INTEGER. |
---|
| 38 | * On entry, N specifies the order of the matrix A. |
---|
| 39 | * N must be at least zero. |
---|
| 40 | * Unchanged on exit. |
---|
| 41 | * |
---|
| 42 | * ALPHA - DOUBLE PRECISION. |
---|
| 43 | * On entry, ALPHA specifies the scalar alpha. |
---|
| 44 | * Unchanged on exit. |
---|
| 45 | * |
---|
| 46 | * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). |
---|
| 47 | * Before entry with UPLO = 'U' or 'u', the leading n by n |
---|
| 48 | * upper triangular part of the array A must contain the upper |
---|
| 49 | * triangular part of the symmetric matrix and the strictly |
---|
| 50 | * lower triangular part of A is not referenced. |
---|
| 51 | * Before entry with UPLO = 'L' or 'l', the leading n by n |
---|
| 52 | * lower triangular part of the array A must contain the lower |
---|
| 53 | * triangular part of the symmetric matrix and the strictly |
---|
| 54 | * upper triangular part of A is not referenced. |
---|
| 55 | * Unchanged on exit. |
---|
| 56 | * |
---|
| 57 | * LDA - INTEGER. |
---|
| 58 | * On entry, LDA specifies the first dimension of A as declared |
---|
| 59 | * in the calling (sub) program. LDA must be at least |
---|
| 60 | * max( 1, n ). |
---|
| 61 | * Unchanged on exit. |
---|
| 62 | * |
---|
| 63 | * X - DOUBLE PRECISION array of dimension at least |
---|
| 64 | * ( 1 + ( n - 1 )*abs( INCX ) ). |
---|
| 65 | * Before entry, the incremented array X must contain the n |
---|
| 66 | * element vector x. |
---|
| 67 | * Unchanged on exit. |
---|
| 68 | * |
---|
| 69 | * INCX - INTEGER. |
---|
| 70 | * On entry, INCX specifies the increment for the elements of |
---|
| 71 | * X. INCX must not be zero. |
---|
| 72 | * Unchanged on exit. |
---|
| 73 | * |
---|
| 74 | * BETA - DOUBLE PRECISION. |
---|
| 75 | * On entry, BETA specifies the scalar beta. When BETA is |
---|
| 76 | * supplied as zero then Y need not be set on input. |
---|
| 77 | * Unchanged on exit. |
---|
| 78 | * |
---|
| 79 | * Y - DOUBLE PRECISION array of dimension at least |
---|
| 80 | * ( 1 + ( n - 1 )*abs( INCY ) ). |
---|
| 81 | * Before entry, the incremented array Y must contain the n |
---|
| 82 | * element vector y. On exit, Y is overwritten by the updated |
---|
| 83 | * vector y. |
---|
| 84 | * |
---|
| 85 | * INCY - INTEGER. |
---|
| 86 | * On entry, INCY specifies the increment for the elements of |
---|
| 87 | * Y. INCY must not be zero. |
---|
| 88 | * Unchanged on exit. |
---|
| 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 | * .. Parameters .. |
---|
| 101 | DOUBLE PRECISION ONE,ZERO |
---|
| 102 | PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) |
---|
| 103 | * .. |
---|
| 104 | * .. Local Scalars .. |
---|
| 105 | DOUBLE PRECISION TEMP1,TEMP2 |
---|
| 106 | INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY |
---|
| 107 | * .. |
---|
| 108 | * .. External Functions .. |
---|
| 109 | LOGICAL LSAME |
---|
| 110 | EXTERNAL LSAME |
---|
| 111 | * .. |
---|
| 112 | * .. External Subroutines .. |
---|
| 113 | EXTERNAL XERBLA |
---|
| 114 | * .. |
---|
| 115 | * .. Intrinsic Functions .. |
---|
| 116 | INTRINSIC MAX |
---|
| 117 | * .. |
---|
| 118 | * |
---|
| 119 | * Test the input parameters. |
---|
| 120 | * |
---|
| 121 | INFO = 0 |
---|
| 122 | IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN |
---|
| 123 | INFO = 1 |
---|
| 124 | ELSE IF (N.LT.0) THEN |
---|
| 125 | INFO = 2 |
---|
| 126 | ELSE IF (LDA.LT.MAX(1,N)) THEN |
---|
| 127 | INFO = 5 |
---|
| 128 | ELSE IF (INCX.EQ.0) THEN |
---|
| 129 | INFO = 7 |
---|
| 130 | ELSE IF (INCY.EQ.0) THEN |
---|
| 131 | INFO = 10 |
---|
| 132 | END IF |
---|
| 133 | IF (INFO.NE.0) THEN |
---|
| 134 | CALL XERBLA('DSYMV ',INFO) |
---|
| 135 | RETURN |
---|
| 136 | END IF |
---|
| 137 | * |
---|
| 138 | * Quick return if possible. |
---|
| 139 | * |
---|
| 140 | IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN |
---|
| 141 | * |
---|
| 142 | * Set up the start points in X and Y. |
---|
| 143 | * |
---|
| 144 | IF (INCX.GT.0) THEN |
---|
| 145 | KX = 1 |
---|
| 146 | ELSE |
---|
| 147 | KX = 1 - (N-1)*INCX |
---|
| 148 | END IF |
---|
| 149 | IF (INCY.GT.0) THEN |
---|
| 150 | KY = 1 |
---|
| 151 | ELSE |
---|
| 152 | KY = 1 - (N-1)*INCY |
---|
| 153 | END IF |
---|
| 154 | * |
---|
| 155 | * Start the operations. In this version the elements of A are |
---|
| 156 | * accessed sequentially with one pass through the triangular part |
---|
| 157 | * of A. |
---|
| 158 | * |
---|
| 159 | * First form y := beta*y. |
---|
| 160 | * |
---|
| 161 | IF (BETA.NE.ONE) THEN |
---|
| 162 | IF (INCY.EQ.1) THEN |
---|
| 163 | IF (BETA.EQ.ZERO) THEN |
---|
| 164 | DO 10 I = 1,N |
---|
| 165 | Y(I) = ZERO |
---|
| 166 | 10 CONTINUE |
---|
| 167 | ELSE |
---|
| 168 | DO 20 I = 1,N |
---|
| 169 | Y(I) = BETA*Y(I) |
---|
| 170 | 20 CONTINUE |
---|
| 171 | END IF |
---|
| 172 | ELSE |
---|
| 173 | IY = KY |
---|
| 174 | IF (BETA.EQ.ZERO) THEN |
---|
| 175 | DO 30 I = 1,N |
---|
| 176 | Y(IY) = ZERO |
---|
| 177 | IY = IY + INCY |
---|
| 178 | 30 CONTINUE |
---|
| 179 | ELSE |
---|
| 180 | DO 40 I = 1,N |
---|
| 181 | Y(IY) = BETA*Y(IY) |
---|
| 182 | IY = IY + INCY |
---|
| 183 | 40 CONTINUE |
---|
| 184 | END IF |
---|
| 185 | END IF |
---|
| 186 | END IF |
---|
| 187 | IF (ALPHA.EQ.ZERO) RETURN |
---|
| 188 | IF (LSAME(UPLO,'U')) THEN |
---|
| 189 | * |
---|
| 190 | * Form y when A is stored in upper triangle. |
---|
| 191 | * |
---|
| 192 | IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN |
---|
| 193 | DO 60 J = 1,N |
---|
| 194 | TEMP1 = ALPHA*X(J) |
---|
| 195 | TEMP2 = ZERO |
---|
| 196 | DO 50 I = 1,J - 1 |
---|
| 197 | Y(I) = Y(I) + TEMP1*A(I,J) |
---|
| 198 | TEMP2 = TEMP2 + A(I,J)*X(I) |
---|
| 199 | 50 CONTINUE |
---|
| 200 | Y(J) = Y(J) + TEMP1*A(J,J) + ALPHA*TEMP2 |
---|
| 201 | 60 CONTINUE |
---|
| 202 | ELSE |
---|
| 203 | JX = KX |
---|
| 204 | JY = KY |
---|
| 205 | DO 80 J = 1,N |
---|
| 206 | TEMP1 = ALPHA*X(JX) |
---|
| 207 | TEMP2 = ZERO |
---|
| 208 | IX = KX |
---|
| 209 | IY = KY |
---|
| 210 | DO 70 I = 1,J - 1 |
---|
| 211 | Y(IY) = Y(IY) + TEMP1*A(I,J) |
---|
| 212 | TEMP2 = TEMP2 + A(I,J)*X(IX) |
---|
| 213 | IX = IX + INCX |
---|
| 214 | IY = IY + INCY |
---|
| 215 | 70 CONTINUE |
---|
| 216 | Y(JY) = Y(JY) + TEMP1*A(J,J) + ALPHA*TEMP2 |
---|
| 217 | JX = JX + INCX |
---|
| 218 | JY = JY + INCY |
---|
| 219 | 80 CONTINUE |
---|
| 220 | END IF |
---|
| 221 | ELSE |
---|
| 222 | * |
---|
| 223 | * Form y when A is stored in lower triangle. |
---|
| 224 | * |
---|
| 225 | IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN |
---|
| 226 | DO 100 J = 1,N |
---|
| 227 | TEMP1 = ALPHA*X(J) |
---|
| 228 | TEMP2 = ZERO |
---|
| 229 | Y(J) = Y(J) + TEMP1*A(J,J) |
---|
| 230 | DO 90 I = J + 1,N |
---|
| 231 | Y(I) = Y(I) + TEMP1*A(I,J) |
---|
| 232 | TEMP2 = TEMP2 + A(I,J)*X(I) |
---|
| 233 | 90 CONTINUE |
---|
| 234 | Y(J) = Y(J) + ALPHA*TEMP2 |
---|
| 235 | 100 CONTINUE |
---|
| 236 | ELSE |
---|
| 237 | JX = KX |
---|
| 238 | JY = KY |
---|
| 239 | DO 120 J = 1,N |
---|
| 240 | TEMP1 = ALPHA*X(JX) |
---|
| 241 | TEMP2 = ZERO |
---|
| 242 | Y(JY) = Y(JY) + TEMP1*A(J,J) |
---|
| 243 | IX = JX |
---|
| 244 | IY = JY |
---|
| 245 | DO 110 I = J + 1,N |
---|
| 246 | IX = IX + INCX |
---|
| 247 | IY = IY + INCY |
---|
| 248 | Y(IY) = Y(IY) + TEMP1*A(I,J) |
---|
| 249 | TEMP2 = TEMP2 + A(I,J)*X(IX) |
---|
| 250 | 110 CONTINUE |
---|
| 251 | Y(JY) = Y(JY) + ALPHA*TEMP2 |
---|
| 252 | JX = JX + INCX |
---|
| 253 | JY = JY + INCY |
---|
| 254 | 120 CONTINUE |
---|
| 255 | END IF |
---|
| 256 | END IF |
---|
| 257 | * |
---|
| 258 | RETURN |
---|
| 259 | * |
---|
| 260 | * End of DSYMV . |
---|
| 261 | * |
---|
| 262 | END |
---|