1 SUBROUTINE ZHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY) 2 * .. Scalar Arguments .. 3 DOUBLE COMPLEX ALPHA,BETA 4 INTEGER INCX,INCY,K,LDA,N 5 CHARACTER UPLO 6 * .. 7 * .. Array Arguments .. 8 DOUBLE COMPLEX A(LDA,*),X(*),Y(*) 9 * .. 10 * 11 * Purpose 12 * ======= 13 * 14 * ZHBMV 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*16 . 48 * On entry, ALPHA specifies the scalar alpha. 49 * Unchanged on exit. 50 * 51 * A - COMPLEX*16 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*16 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*16 . 110 * On entry, BETA specifies the scalar beta. 111 * Unchanged on exit. 112 * 113 * Y - COMPLEX*16 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 DOUBLE COMPLEX ONE 138 PARAMETER (ONE= (1.0D+0,0.0D+0)) 139 DOUBLE COMPLEX ZERO 140 PARAMETER (ZERO= (0.0D+0,0.0D+0)) 141 * .. 142 * .. Local Scalars .. 143 DOUBLE 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 DBLE,DCONJG,MAX,MIN 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('ZHBMV ',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 + DCONJG(A(L+I,J))*X(I) 240 50 CONTINUE 241 Y(J) = Y(J) + TEMP1*DBLE(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 + DCONJG(A(L+I,J))*X(IX) 255 IX = IX + INCX 256 IY = IY + INCY 257 70 CONTINUE 258 Y(JY) = Y(JY) + TEMP1*DBLE(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*DBLE(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 + DCONJG(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*DBLE(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 + DCONJG(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 ZHBMV . 309 * 310 END 311
