1 SUBROUTINE CHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) 2* .. Scalar Arguments .. 3 COMPLEX ALPHA,BETA 4 INTEGER INCX,INCY,K,LDA,N 5 CHARACTER UPLO 6* .. 7* .. Array Arguments .. 8 COMPLEX A(LDA,*),X(*),Y(*) 9* .. 10* 11* Purpose 12* ======= 13* 14* CHBMV 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 hermitian 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 - COMPLEX . 48* On entry, ALPHA specifies the scalar alpha. 49* Unchanged on exit. 50* 51* A - COMPLEX 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 hermitian 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 hermitian 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 hermitian 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 hermitian 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* Note that the imaginary parts of the diagonal elements need 89* not be set and are assumed to be zero. 90* Unchanged on exit. 91* 92* LDA - INTEGER. 93* On entry, LDA specifies the first dimension of A as declared 94* in the calling (sub) program. LDA must be at least 95* ( k + 1 ). 96* Unchanged on exit. 97* 98* X - COMPLEX array of DIMENSION at least 99* ( 1 + ( n - 1 )*abs( INCX ) ). 100* Before entry, the incremented array X must contain the 101* vector x. 102* Unchanged on exit. 103* 104* INCX - INTEGER. 105* On entry, INCX specifies the increment for the elements of 106* X. INCX must not be zero. 107* Unchanged on exit. 108* 109* BETA - COMPLEX . 110* On entry, BETA specifies the scalar beta. 111* Unchanged on exit. 112* 113* Y - COMPLEX array of DIMENSION at least 114* ( 1 + ( n - 1 )*abs( INCY ) ). 115* Before entry, the incremented array Y must contain the 116* vector y. On exit, Y is overwritten by the updated vector y. 117* 118* INCY - INTEGER. 119* On entry, INCY specifies the increment for the elements of 120* Y. INCY must not be zero. 121* Unchanged on exit. 122* 123* Further Details 124* =============== 125* 126* Level 2 Blas routine. 127* 128* -- Written on 22-October-1986. 129* Jack Dongarra, Argonne National Lab. 130* Jeremy Du Croz, Nag Central Office. 131* Sven Hammarling, Nag Central Office. 132* Richard Hanson, Sandia National Labs. 133* 134* ===================================================================== 135* 136* .. Parameters .. 137 COMPLEX ONE 138 PARAMETER (ONE= (1.0E+0,0.0E+0)) 139 COMPLEX ZERO 140 PARAMETER (ZERO= (0.0E+0,0.0E+0)) 141* .. 142* .. Local Scalars .. 143 COMPLEX TEMP1,TEMP2 144 INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L 145* .. 146* .. External Functions .. 147 LOGICAL LSAME 148 EXTERNAL LSAME 149* .. 150* .. External Subroutines .. 151 EXTERNAL XERBLA 152* .. 153* .. Intrinsic Functions .. 154 INTRINSIC CONJG,MAX,MIN,REAL 155* .. 156* 157* Test the input parameters. 158* 159 INFO = 0 160 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN 161 INFO = 1 162 ELSE IF (N.LT.0) THEN 163 INFO = 2 164 ELSE IF (K.LT.0) THEN 165 INFO = 3 166 ELSE IF (LDA.LT. (K+1)) THEN 167 INFO = 6 168 ELSE IF (INCX.EQ.0) THEN 169 INFO = 8 170 ELSE IF (INCY.EQ.0) THEN 171 INFO = 11 172 END IF 173 IF (INFO.NE.0) THEN 174 CALL XERBLA('CHBMV ',INFO) 175 RETURN 176 END IF 177* 178* Quick return if possible. 179* 180 IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN 181* 182* Set up the start points in X and Y. 183* 184 IF (INCX.GT.0) THEN 185 KX = 1 186 ELSE 187 KX = 1 - (N-1)*INCX 188 END IF 189 IF (INCY.GT.0) THEN 190 KY = 1 191 ELSE 192 KY = 1 - (N-1)*INCY 193 END IF 194* 195* Start the operations. In this version the elements of the array A 196* are accessed sequentially with one pass through A. 197* 198* First form y := beta*y. 199* 200 IF (BETA.NE.ONE) THEN 201 IF (INCY.EQ.1) THEN 202 IF (BETA.EQ.ZERO) THEN 203 DO 10 I = 1,N 204 Y(I) = ZERO 205 10 CONTINUE 206 ELSE 207 DO 20 I = 1,N 208 Y(I) = BETA*Y(I) 209 20 CONTINUE 210 END IF 211 ELSE 212 IY = KY 213 IF (BETA.EQ.ZERO) THEN 214 DO 30 I = 1,N 215 Y(IY) = ZERO 216 IY = IY + INCY 217 30 CONTINUE 218 ELSE 219 DO 40 I = 1,N 220 Y(IY) = BETA*Y(IY) 221 IY = IY + INCY 222 40 CONTINUE 223 END IF 224 END IF 225 END IF 226 IF (ALPHA.EQ.ZERO) RETURN 227 IF (LSAME(UPLO,'U')) THEN 228* 229* Form y when upper triangle of A is stored. 230* 231 KPLUS1 = K + 1 232 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 233 DO 60 J = 1,N 234 TEMP1 = ALPHA*X(J) 235 TEMP2 = ZERO 236 L = KPLUS1 - J 237 DO 50 I = MAX(1,J-K),J - 1 238 Y(I) = Y(I) + TEMP1*A(L+I,J) 239 TEMP2 = TEMP2 + CONJG(A(L+I,J))*X(I) 240 50 CONTINUE 241 Y(J) = Y(J) + TEMP1*REAL(A(KPLUS1,J)) + ALPHA*TEMP2 242 60 CONTINUE 243 ELSE 244 JX = KX 245 JY = KY 246 DO 80 J = 1,N 247 TEMP1 = ALPHA*X(JX) 248 TEMP2 = ZERO 249 IX = KX 250 IY = KY 251 L = KPLUS1 - J 252 DO 70 I = MAX(1,J-K),J - 1 253 Y(IY) = Y(IY) + TEMP1*A(L+I,J) 254 TEMP2 = TEMP2 + CONJG(A(L+I,J))*X(IX) 255 IX = IX + INCX 256 IY = IY + INCY 257 70 CONTINUE 258 Y(JY) = Y(JY) + TEMP1*REAL(A(KPLUS1,J)) + ALPHA*TEMP2 259 JX = JX + INCX 260 JY = JY + INCY 261 IF (J.GT.K) THEN 262 KX = KX + INCX 263 KY = KY + INCY 264 END IF 265 80 CONTINUE 266 END IF 267 ELSE 268* 269* Form y when lower triangle of A is stored. 270* 271 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN 272 DO 100 J = 1,N 273 TEMP1 = ALPHA*X(J) 274 TEMP2 = ZERO 275 Y(J) = Y(J) + TEMP1*REAL(A(1,J)) 276 L = 1 - J 277 DO 90 I = J + 1,MIN(N,J+K) 278 Y(I) = Y(I) + TEMP1*A(L+I,J) 279 TEMP2 = TEMP2 + CONJG(A(L+I,J))*X(I) 280 90 CONTINUE 281 Y(J) = Y(J) + ALPHA*TEMP2 282 100 CONTINUE 283 ELSE 284 JX = KX 285 JY = KY 286 DO 120 J = 1,N 287 TEMP1 = ALPHA*X(JX) 288 TEMP2 = ZERO 289 Y(JY) = Y(JY) + TEMP1*REAL(A(1,J)) 290 L = 1 - J 291 IX = JX 292 IY = JY 293 DO 110 I = J + 1,MIN(N,J+K) 294 IX = IX + INCX 295 IY = IY + INCY 296 Y(IY) = Y(IY) + TEMP1*A(L+I,J) 297 TEMP2 = TEMP2 + CONJG(A(L+I,J))*X(IX) 298 110 CONTINUE 299 Y(JY) = Y(JY) + ALPHA*TEMP2 300 JX = JX + INCX 301 JY = JY + INCY 302 120 CONTINUE 303 END IF 304 END IF 305* 306 RETURN 307* 308* End of CHBMV . 309* 310 END 311