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