1 SUBROUTINE SSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) 2 * .. Scalar Arguments .. 3 REAL ALPHA,BETA 4 INTEGER INCX,INCY,K,LDA,N 5 CHARACTER UPLO 6 * .. 7 * .. Array Arguments .. 8 REAL A(LDA,*),X(*),Y(*) 9 * .. 10 * 11 * Purpose 12 * ======= 13 * 14 * SSBMV 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 - REAL . 48 * On entry, ALPHA specifies the scalar alpha. 49 * Unchanged on exit. 50 * 51 * A - REAL 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 - REAL 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 - REAL . 108 * On entry, BETA specifies the scalar beta. 109 * Unchanged on exit. 110 * 111 * Y - REAL 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 * Further Details 122 * =============== 123 * 124 * Level 2 Blas routine. 125 * 126 * -- Written on 22-October-1986. 127 * Jack Dongarra, Argonne National Lab. 128 * Jeremy Du Croz, Nag Central Office. 129 * Sven Hammarling, Nag Central Office. 130 * Richard Hanson, Sandia National Labs. 131 * 132 * ===================================================================== 133 * 134 * .. Parameters .. 135 REAL ONE,ZERO 136 PARAMETER (ONE=1.0E+0,ZERO=0.0E+0) 137 * .. 138 * .. Local Scalars .. 139 REAL TEMP1,TEMP2 140 INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L 141 * .. 142 * .. External Functions .. 143 LOGICAL LSAME 144 EXTERNAL LSAME 145 * .. 146 * .. External Subroutines .. 147 EXTERNAL XERBLA 148 * .. 149 * .. Intrinsic Functions .. 150 INTRINSIC MAX,MIN 151 * .. 152 * 153 * Test the input parameters. 154 * 155 INFO = 0 156 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 157 INFO = 1 158 ELSE IF (N.LT.0) THEN 159 INFO = 2 160 ELSE IF (K.LT.0) THEN 161 INFO = 3 162 ELSE IF (LDA.LT. (K+1)) THEN 163 INFO = 6 164 ELSE IF (INCX.EQ.0) THEN 165 INFO = 8 166 ELSE IF (INCY.EQ.0) THEN 167 INFO = 11 168 END IF 169 IF (INFO.NE.0) THEN 170 CALL XERBLA('SSBMV ',INFO) 171 RETURN 172 END IF 173 * 174 * Quick return if possible. 175 * 176 IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN 177 * 178 * Set up the start points in X and Y. 179 * 180 IF (INCX.GT.0) THEN 181 KX = 1 182 ELSE 183 KX = 1 - (N-1)*INCX 184 END IF 185 IF (INCY.GT.0) THEN 186 KY = 1 187 ELSE 188 KY = 1 - (N-1)*INCY 189 END IF 190 * 191 * Start the operations. In this version the elements of the array A 192 * are accessed sequentially with one pass through A. 193 * 194 * First form y := beta*y. 195 * 196 IF (BETA.NE.ONE) THEN 197 IF (INCY.EQ.1) THEN 198 IF (BETA.EQ.ZERO) THEN 199 DO 10 I = 1,N 200 Y(I) = ZERO 201 10 CONTINUE 202 ELSE 203 DO 20 I = 1,N 204 Y(I) = BETA*Y(I) 205 20 CONTINUE 206 END IF 207 ELSE 208 IY = KY 209 IF (BETA.EQ.ZERO) THEN 210 DO 30 I = 1,N 211 Y(IY) = ZERO 212 IY = IY + INCY 213 30 CONTINUE 214 ELSE 215 DO 40 I = 1,N 216 Y(IY) = BETA*Y(IY) 217 IY = IY + INCY 218 40 CONTINUE 219 END IF 220 END IF 221 END IF 222 IF (ALPHA.EQ.ZERO) RETURN 223 IF (LSAME(UPLO,'U')) THEN 224 * 225 * Form y when upper triangle of A is stored. 226 * 227 KPLUS1 = K + 1 228 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 229 DO 60 J = 1,N 230 TEMP1 = ALPHA*X(J) 231 TEMP2 = ZERO 232 L = KPLUS1 - J 233 DO 50 I = MAX(1,J-K),J - 1 234 Y(I) = Y(I) + TEMP1*A(L+I,J) 235 TEMP2 = TEMP2 + A(L+I,J)*X(I) 236 50 CONTINUE 237 Y(J) = Y(J) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2 238 60 CONTINUE 239 ELSE 240 JX = KX 241 JY = KY 242 DO 80 J = 1,N 243 TEMP1 = ALPHA*X(JX) 244 TEMP2 = ZERO 245 IX = KX 246 IY = KY 247 L = KPLUS1 - J 248 DO 70 I = MAX(1,J-K),J - 1 249 Y(IY) = Y(IY) + TEMP1*A(L+I,J) 250 TEMP2 = TEMP2 + A(L+I,J)*X(IX) 251 IX = IX + INCX 252 IY = IY + INCY 253 70 CONTINUE 254 Y(JY) = Y(JY) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2 255 JX = JX + INCX 256 JY = JY + INCY 257 IF (J.GT.K) THEN 258 KX = KX + INCX 259 KY = KY + INCY 260 END IF 261 80 CONTINUE 262 END IF 263 ELSE 264 * 265 * Form y when lower triangle of A is stored. 266 * 267 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 268 DO 100 J = 1,N 269 TEMP1 = ALPHA*X(J) 270 TEMP2 = ZERO 271 Y(J) = Y(J) + TEMP1*A(1,J) 272 L = 1 - J 273 DO 90 I = J + 1,MIN(N,J+K) 274 Y(I) = Y(I) + TEMP1*A(L+I,J) 275 TEMP2 = TEMP2 + A(L+I,J)*X(I) 276 90 CONTINUE 277 Y(J) = Y(J) + ALPHA*TEMP2 278 100 CONTINUE 279 ELSE 280 JX = KX 281 JY = KY 282 DO 120 J = 1,N 283 TEMP1 = ALPHA*X(JX) 284 TEMP2 = ZERO 285 Y(JY) = Y(JY) + TEMP1*A(1,J) 286 L = 1 - J 287 IX = JX 288 IY = JY 289 DO 110 I = J + 1,MIN(N,J+K) 290 IX = IX + INCX 291 IY = IY + INCY 292 Y(IY) = Y(IY) + TEMP1*A(L+I,J) 293 TEMP2 = TEMP2 + A(L+I,J)*X(IX) 294 110 CONTINUE 295 Y(JY) = Y(JY) + ALPHA*TEMP2 296 JX = JX + INCX 297 JY = JY + INCY 298 120 CONTINUE 299 END IF 300 END IF 301 * 302 RETURN 303 * 304 * End of SSBMV . 305 * 306 END 307
