1 SUBROUTINE DSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) 2 * .. Scalar Arguments .. 3 DOUBLE PRECISION ALPHA,BETA 4 INTEGER INCX,INCY,K,LDA,N 5 CHARACTER UPLO 6 * .. 7 * .. Array Arguments .. 8 DOUBLE PRECISION A(LDA,*),X(*),Y(*) 9 * .. 10 * 11 * Purpose 12 * ======= 13 * 14 * DSBMV 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 band matrix, with k super-diagonals. 20 * 21 * Arguments 22 * ========== 23 * 24 * UPLO - CHARACTER*1. 25 * On entry, UPLO specifies whether the upper or lower 26 * triangular part of the band matrix A is being supplied as 27 * follows: 28 * 29 * UPLO = 'U' or 'u' The upper triangular part of A is 30 * being supplied. 31 * 32 * UPLO = 'L' or 'l' The lower triangular part of A is 33 * being supplied. 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 * K - INTEGER. 43 * On entry, K specifies the number of super-diagonals of the 44 * matrix A. K must satisfy 0 .le. K. 45 * Unchanged on exit. 46 * 47 * ALPHA - DOUBLE PRECISION. 48 * On entry, ALPHA specifies the scalar alpha. 49 * Unchanged on exit. 50 * 51 * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). 52 * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) 53 * by n part of the array A must contain the upper triangular 54 * band part of the symmetric matrix, supplied column by 55 * column, with the leading diagonal of the matrix in row 56 * ( k + 1 ) of the array, the first super-diagonal starting at 57 * position 2 in row k, and so on. The top left k by k triangle 58 * of the array A is not referenced. 59 * The following program segment will transfer the upper 60 * triangular part of a symmetric band matrix from conventional 61 * full matrix storage to band storage: 62 * 63 * DO 20, J = 1, N 64 * M = K + 1 - J 65 * DO 10, I = MAX( 1, J - K ), J 66 * A( M + I, J ) = matrix( I, J ) 67 * 10 CONTINUE 68 * 20 CONTINUE 69 * 70 * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) 71 * by n part of the array A must contain the lower triangular 72 * band part of the symmetric matrix, supplied column by 73 * column, with the leading diagonal of the matrix in row 1 of 74 * the array, the first sub-diagonal starting at position 1 in 75 * row 2, and so on. The bottom right k by k triangle of the 76 * array A is not referenced. 77 * The following program segment will transfer the lower 78 * triangular part of a symmetric band matrix from conventional 79 * full matrix storage to band storage: 80 * 81 * DO 20, J = 1, N 82 * M = 1 - J 83 * DO 10, I = J, MIN( N, J + K ) 84 * A( M + I, J ) = matrix( I, J ) 85 * 10 CONTINUE 86 * 20 CONTINUE 87 * 88 * Unchanged on exit. 89 * 90 * LDA - INTEGER. 91 * On entry, LDA specifies the first dimension of A as declared 92 * in the calling (sub) program. LDA must be at least 93 * ( k + 1 ). 94 * Unchanged on exit. 95 * 96 * X - DOUBLE PRECISION array of DIMENSION at least 97 * ( 1 + ( n - 1 )*abs( INCX ) ). 98 * Before entry, the incremented array X must contain the 99 * vector x. 100 * Unchanged on exit. 101 * 102 * INCX - INTEGER. 103 * On entry, INCX specifies the increment for the elements of 104 * X. INCX must not be zero. 105 * Unchanged on exit. 106 * 107 * BETA - DOUBLE PRECISION. 108 * On entry, BETA specifies the scalar beta. 109 * Unchanged on exit. 110 * 111 * Y - DOUBLE PRECISION array of DIMENSION at least 112 * ( 1 + ( n - 1 )*abs( INCY ) ). 113 * Before entry, the incremented array Y must contain the 114 * vector y. On exit, Y is overwritten by the updated vector y. 115 * 116 * INCY - INTEGER. 117 * On entry, INCY specifies the increment for the elements of 118 * Y. INCY must not be zero. 119 * Unchanged on exit. 120 * 121 * 122 * Level 2 Blas routine. 123 * 124 * -- Written on 22-October-1986. 125 * Jack Dongarra, Argonne National Lab. 126 * Jeremy Du Croz, Nag Central Office. 127 * Sven Hammarling, Nag Central Office. 128 * Richard Hanson, Sandia National Labs. 129 * 130 * ===================================================================== 131 * 132 * .. Parameters .. 133 DOUBLE PRECISION ONE,ZERO 134 PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) 135 * .. 136 * .. Local Scalars .. 137 DOUBLE PRECISION TEMP1,TEMP2 138 INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L 139 * .. 140 * .. External Functions .. 141 LOGICAL LSAME 142 EXTERNAL LSAME 143 * .. 144 * .. External Subroutines .. 145 EXTERNAL XERBLA 146 * .. 147 * .. Intrinsic Functions .. 148 INTRINSIC MAX,MIN 149 * .. 150 * 151 * Test the input parameters. 152 * 153 INFO = 0 154 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 155 INFO = 1 156 ELSE IF (N.LT.0) THEN 157 INFO = 2 158 ELSE IF (K.LT.0) THEN 159 INFO = 3 160 ELSE IF (LDA.LT. (K+1)) THEN 161 INFO = 6 162 ELSE IF (INCX.EQ.0) THEN 163 INFO = 8 164 ELSE IF (INCY.EQ.0) THEN 165 INFO = 11 166 END IF 167 IF (INFO.NE.0) THEN 168 CALL XERBLA('DSBMV ',INFO) 169 RETURN 170 END IF 171 * 172 * Quick return if possible. 173 * 174 IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN 175 * 176 * Set up the start points in X and Y. 177 * 178 IF (INCX.GT.0) THEN 179 KX = 1 180 ELSE 181 KX = 1 - (N-1)*INCX 182 END IF 183 IF (INCY.GT.0) THEN 184 KY = 1 185 ELSE 186 KY = 1 - (N-1)*INCY 187 END IF 188 * 189 * Start the operations. In this version the elements of the array A 190 * are accessed sequentially with one pass through A. 191 * 192 * First form y := beta*y. 193 * 194 IF (BETA.NE.ONE) THEN 195 IF (INCY.EQ.1) THEN 196 IF (BETA.EQ.ZERO) THEN 197 DO 10 I = 1,N 198 Y(I) = ZERO 199 10 CONTINUE 200 ELSE 201 DO 20 I = 1,N 202 Y(I) = BETA*Y(I) 203 20 CONTINUE 204 END IF 205 ELSE 206 IY = KY 207 IF (BETA.EQ.ZERO) THEN 208 DO 30 I = 1,N 209 Y(IY) = ZERO 210 IY = IY + INCY 211 30 CONTINUE 212 ELSE 213 DO 40 I = 1,N 214 Y(IY) = BETA*Y(IY) 215 IY = IY + INCY 216 40 CONTINUE 217 END IF 218 END IF 219 END IF 220 IF (ALPHA.EQ.ZERO) RETURN 221 IF (LSAME(UPLO,'U')) THEN 222 * 223 * Form y when upper triangle of A is stored. 224 * 225 KPLUS1 = K + 1 226 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 227 DO 60 J = 1,N 228 TEMP1 = ALPHA*X(J) 229 TEMP2 = ZERO 230 L = KPLUS1 - J 231 DO 50 I = MAX(1,J-K),J - 1 232 Y(I) = Y(I) + TEMP1*A(L+I,J) 233 TEMP2 = TEMP2 + A(L+I,J)*X(I) 234 50 CONTINUE 235 Y(J) = Y(J) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2 236 60 CONTINUE 237 ELSE 238 JX = KX 239 JY = KY 240 DO 80 J = 1,N 241 TEMP1 = ALPHA*X(JX) 242 TEMP2 = ZERO 243 IX = KX 244 IY = KY 245 L = KPLUS1 - J 246 DO 70 I = MAX(1,J-K),J - 1 247 Y(IY) = Y(IY) + TEMP1*A(L+I,J) 248 TEMP2 = TEMP2 + A(L+I,J)*X(IX) 249 IX = IX + INCX 250 IY = IY + INCY 251 70 CONTINUE 252 Y(JY) = Y(JY) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2 253 JX = JX + INCX 254 JY = JY + INCY 255 IF (J.GT.K) THEN 256 KX = KX + INCX 257 KY = KY + INCY 258 END IF 259 80 CONTINUE 260 END IF 261 ELSE 262 * 263 * Form y when lower triangle of A is stored. 264 * 265 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 266 DO 100 J = 1,N 267 TEMP1 = ALPHA*X(J) 268 TEMP2 = ZERO 269 Y(J) = Y(J) + TEMP1*A(1,J) 270 L = 1 - J 271 DO 90 I = J + 1,MIN(N,J+K) 272 Y(I) = Y(I) + TEMP1*A(L+I,J) 273 TEMP2 = TEMP2 + A(L+I,J)*X(I) 274 90 CONTINUE 275 Y(J) = Y(J) + ALPHA*TEMP2 276 100 CONTINUE 277 ELSE 278 JX = KX 279 JY = KY 280 DO 120 J = 1,N 281 TEMP1 = ALPHA*X(JX) 282 TEMP2 = ZERO 283 Y(JY) = Y(JY) + TEMP1*A(1,J) 284 L = 1 - J 285 IX = JX 286 IY = JY 287 DO 110 I = J + 1,MIN(N,J+K) 288 IX = IX + INCX 289 IY = IY + INCY 290 Y(IY) = Y(IY) + TEMP1*A(L+I,J) 291 TEMP2 = TEMP2 + A(L+I,J)*X(IX) 292 110 CONTINUE 293 Y(JY) = Y(JY) + ALPHA*TEMP2 294 JX = JX + INCX 295 JY = JY + INCY 296 120 CONTINUE 297 END IF 298 END IF 299 * 300 RETURN 301 * 302 * End of DSBMV . 303 * 304 END 305
