[136] | 1 | SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
|
---|
| 2 | * .. Scalar Arguments ..
|
---|
| 3 | DOUBLE COMPLEX ALPHA,BETA
|
---|
| 4 | INTEGER INCX,INCY,N
|
---|
| 5 | CHARACTER UPLO
|
---|
| 6 | * ..
|
---|
| 7 | * .. Array Arguments ..
|
---|
| 8 | DOUBLE COMPLEX AP(*),X(*),Y(*)
|
---|
| 9 | * ..
|
---|
| 10 | *
|
---|
| 11 | * Purpose
|
---|
| 12 | * =======
|
---|
| 13 | *
|
---|
| 14 | * ZHPMV 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 matrix, supplied in packed form.
|
---|
| 20 | *
|
---|
| 21 | * Arguments
|
---|
| 22 | * ==========
|
---|
| 23 | *
|
---|
| 24 | * UPLO - CHARACTER*1.
|
---|
| 25 | * On entry, UPLO specifies whether the upper or lower
|
---|
| 26 | * triangular part of the matrix A is supplied in the packed
|
---|
| 27 | * array AP as follows:
|
---|
| 28 | *
|
---|
| 29 | * UPLO = 'U' or 'u' The upper triangular part of A is
|
---|
| 30 | * supplied in AP.
|
---|
| 31 | *
|
---|
| 32 | * UPLO = 'L' or 'l' The lower triangular part of A is
|
---|
| 33 | * supplied in AP.
|
---|
| 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 | * ALPHA - COMPLEX*16 .
|
---|
| 43 | * On entry, ALPHA specifies the scalar alpha.
|
---|
| 44 | * Unchanged on exit.
|
---|
| 45 | *
|
---|
| 46 | * AP - COMPLEX*16 array of DIMENSION at least
|
---|
| 47 | * ( ( n*( n + 1 ) )/2 ).
|
---|
| 48 | * Before entry with UPLO = 'U' or 'u', the array AP must
|
---|
| 49 | * contain the upper triangular part of the hermitian matrix
|
---|
| 50 | * packed sequentially, column by column, so that AP( 1 )
|
---|
| 51 | * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
|
---|
| 52 | * and a( 2, 2 ) respectively, and so on.
|
---|
| 53 | * Before entry with UPLO = 'L' or 'l', the array AP must
|
---|
| 54 | * contain the lower triangular part of the hermitian matrix
|
---|
| 55 | * packed sequentially, column by column, so that AP( 1 )
|
---|
| 56 | * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
|
---|
| 57 | * and a( 3, 1 ) respectively, and so on.
|
---|
| 58 | * Note that the imaginary parts of the diagonal elements need
|
---|
| 59 | * not be set and are assumed to be zero.
|
---|
| 60 | * Unchanged on exit.
|
---|
| 61 | *
|
---|
| 62 | * X - COMPLEX*16 array of dimension at least
|
---|
| 63 | * ( 1 + ( n - 1 )*abs( INCX ) ).
|
---|
| 64 | * Before entry, the incremented array X must contain the n
|
---|
| 65 | * element vector x.
|
---|
| 66 | * Unchanged on exit.
|
---|
| 67 | *
|
---|
| 68 | * INCX - INTEGER.
|
---|
| 69 | * On entry, INCX specifies the increment for the elements of
|
---|
| 70 | * X. INCX must not be zero.
|
---|
| 71 | * Unchanged on exit.
|
---|
| 72 | *
|
---|
| 73 | * BETA - COMPLEX*16 .
|
---|
| 74 | * On entry, BETA specifies the scalar beta. When BETA is
|
---|
| 75 | * supplied as zero then Y need not be set on input.
|
---|
| 76 | * Unchanged on exit.
|
---|
| 77 | *
|
---|
| 78 | * Y - COMPLEX*16 array of dimension at least
|
---|
| 79 | * ( 1 + ( n - 1 )*abs( INCY ) ).
|
---|
| 80 | * Before entry, the incremented array Y must contain the n
|
---|
| 81 | * element vector y. On exit, Y is overwritten by the updated
|
---|
| 82 | * vector y.
|
---|
| 83 | *
|
---|
| 84 | * INCY - INTEGER.
|
---|
| 85 | * On entry, INCY specifies the increment for the elements of
|
---|
| 86 | * Y. INCY must not be zero.
|
---|
| 87 | * Unchanged on exit.
|
---|
| 88 | *
|
---|
| 89 | * Further Details
|
---|
| 90 | * ===============
|
---|
| 91 | *
|
---|
| 92 | * Level 2 Blas routine.
|
---|
| 93 | *
|
---|
| 94 | * -- Written on 22-October-1986.
|
---|
| 95 | * Jack Dongarra, Argonne National Lab.
|
---|
| 96 | * Jeremy Du Croz, Nag Central Office.
|
---|
| 97 | * Sven Hammarling, Nag Central Office.
|
---|
| 98 | * Richard Hanson, Sandia National Labs.
|
---|
| 99 | *
|
---|
| 100 | * =====================================================================
|
---|
| 101 | *
|
---|
| 102 | * .. Parameters ..
|
---|
| 103 | DOUBLE COMPLEX ONE
|
---|
| 104 | PARAMETER (ONE= (1.0D+0,0.0D+0))
|
---|
| 105 | DOUBLE COMPLEX ZERO
|
---|
| 106 | PARAMETER (ZERO= (0.0D+0,0.0D+0))
|
---|
| 107 | * ..
|
---|
| 108 | * .. Local Scalars ..
|
---|
| 109 | DOUBLE COMPLEX TEMP1,TEMP2
|
---|
| 110 | INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
|
---|
| 111 | * ..
|
---|
| 112 | * .. External Functions ..
|
---|
| 113 | LOGICAL LSAME
|
---|
| 114 | EXTERNAL LSAME
|
---|
| 115 | * ..
|
---|
| 116 | * .. External Subroutines ..
|
---|
| 117 | EXTERNAL XERBLA
|
---|
| 118 | * ..
|
---|
| 119 | * .. Intrinsic Functions ..
|
---|
| 120 | INTRINSIC DBLE,DCONJG
|
---|
| 121 | * ..
|
---|
| 122 | *
|
---|
| 123 | * Test the input parameters.
|
---|
| 124 | *
|
---|
| 125 | INFO = 0
|
---|
| 126 | IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
|
---|
| 127 | INFO = 1
|
---|
| 128 | ELSE IF (N.LT.0) THEN
|
---|
| 129 | INFO = 2
|
---|
| 130 | ELSE IF (INCX.EQ.0) THEN
|
---|
| 131 | INFO = 6
|
---|
| 132 | ELSE IF (INCY.EQ.0) THEN
|
---|
| 133 | INFO = 9
|
---|
| 134 | END IF
|
---|
| 135 | IF (INFO.NE.0) THEN
|
---|
| 136 | CALL XERBLA('ZHPMV ',INFO)
|
---|
| 137 | RETURN
|
---|
| 138 | END IF
|
---|
| 139 | *
|
---|
| 140 | * Quick return if possible.
|
---|
| 141 | *
|
---|
| 142 | IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
|
---|
| 143 | *
|
---|
| 144 | * Set up the start points in X and Y.
|
---|
| 145 | *
|
---|
| 146 | IF (INCX.GT.0) THEN
|
---|
| 147 | KX = 1
|
---|
| 148 | ELSE
|
---|
| 149 | KX = 1 - (N-1)*INCX
|
---|
| 150 | END IF
|
---|
| 151 | IF (INCY.GT.0) THEN
|
---|
| 152 | KY = 1
|
---|
| 153 | ELSE
|
---|
| 154 | KY = 1 - (N-1)*INCY
|
---|
| 155 | END IF
|
---|
| 156 | *
|
---|
| 157 | * Start the operations. In this version the elements of the array AP
|
---|
| 158 | * are accessed sequentially with one pass through AP.
|
---|
| 159 | *
|
---|
| 160 | * First form y := beta*y.
|
---|
| 161 | *
|
---|
| 162 | IF (BETA.NE.ONE) THEN
|
---|
| 163 | IF (INCY.EQ.1) THEN
|
---|
| 164 | IF (BETA.EQ.ZERO) THEN
|
---|
| 165 | DO 10 I = 1,N
|
---|
| 166 | Y(I) = ZERO
|
---|
| 167 | 10 CONTINUE
|
---|
| 168 | ELSE
|
---|
| 169 | DO 20 I = 1,N
|
---|
| 170 | Y(I) = BETA*Y(I)
|
---|
| 171 | 20 CONTINUE
|
---|
| 172 | END IF
|
---|
| 173 | ELSE
|
---|
| 174 | IY = KY
|
---|
| 175 | IF (BETA.EQ.ZERO) THEN
|
---|
| 176 | DO 30 I = 1,N
|
---|
| 177 | Y(IY) = ZERO
|
---|
| 178 | IY = IY + INCY
|
---|
| 179 | 30 CONTINUE
|
---|
| 180 | ELSE
|
---|
| 181 | DO 40 I = 1,N
|
---|
| 182 | Y(IY) = BETA*Y(IY)
|
---|
| 183 | IY = IY + INCY
|
---|
| 184 | 40 CONTINUE
|
---|
| 185 | END IF
|
---|
| 186 | END IF
|
---|
| 187 | END IF
|
---|
| 188 | IF (ALPHA.EQ.ZERO) RETURN
|
---|
| 189 | KK = 1
|
---|
| 190 | IF (LSAME(UPLO,'U')) THEN
|
---|
| 191 | *
|
---|
| 192 | * Form y when AP contains the upper triangle.
|
---|
| 193 | *
|
---|
| 194 | IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
|
---|
| 195 | DO 60 J = 1,N
|
---|
| 196 | TEMP1 = ALPHA*X(J)
|
---|
| 197 | TEMP2 = ZERO
|
---|
| 198 | K = KK
|
---|
| 199 | DO 50 I = 1,J - 1
|
---|
| 200 | Y(I) = Y(I) + TEMP1*AP(K)
|
---|
| 201 | TEMP2 = TEMP2 + DCONJG(AP(K))*X(I)
|
---|
| 202 | K = K + 1
|
---|
| 203 | 50 CONTINUE
|
---|
| 204 | Y(J) = Y(J) + TEMP1*DBLE(AP(KK+J-1)) + ALPHA*TEMP2
|
---|
| 205 | KK = KK + J
|
---|
| 206 | 60 CONTINUE
|
---|
| 207 | ELSE
|
---|
| 208 | JX = KX
|
---|
| 209 | JY = KY
|
---|
| 210 | DO 80 J = 1,N
|
---|
| 211 | TEMP1 = ALPHA*X(JX)
|
---|
| 212 | TEMP2 = ZERO
|
---|
| 213 | IX = KX
|
---|
| 214 | IY = KY
|
---|
| 215 | DO 70 K = KK,KK + J - 2
|
---|
| 216 | Y(IY) = Y(IY) + TEMP1*AP(K)
|
---|
| 217 | TEMP2 = TEMP2 + DCONJG(AP(K))*X(IX)
|
---|
| 218 | IX = IX + INCX
|
---|
| 219 | IY = IY + INCY
|
---|
| 220 | 70 CONTINUE
|
---|
| 221 | Y(JY) = Y(JY) + TEMP1*DBLE(AP(KK+J-1)) + ALPHA*TEMP2
|
---|
| 222 | JX = JX + INCX
|
---|
| 223 | JY = JY + INCY
|
---|
| 224 | KK = KK + J
|
---|
| 225 | 80 CONTINUE
|
---|
| 226 | END IF
|
---|
| 227 | ELSE
|
---|
| 228 | *
|
---|
| 229 | * Form y when AP contains the lower triangle.
|
---|
| 230 | *
|
---|
| 231 | IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
|
---|
| 232 | DO 100 J = 1,N
|
---|
| 233 | TEMP1 = ALPHA*X(J)
|
---|
| 234 | TEMP2 = ZERO
|
---|
| 235 | Y(J) = Y(J) + TEMP1*DBLE(AP(KK))
|
---|
| 236 | K = KK + 1
|
---|
| 237 | DO 90 I = J + 1,N
|
---|
| 238 | Y(I) = Y(I) + TEMP1*AP(K)
|
---|
| 239 | TEMP2 = TEMP2 + DCONJG(AP(K))*X(I)
|
---|
| 240 | K = K + 1
|
---|
| 241 | 90 CONTINUE
|
---|
| 242 | Y(J) = Y(J) + ALPHA*TEMP2
|
---|
| 243 | KK = KK + (N-J+1)
|
---|
| 244 | 100 CONTINUE
|
---|
| 245 | ELSE
|
---|
| 246 | JX = KX
|
---|
| 247 | JY = KY
|
---|
| 248 | DO 120 J = 1,N
|
---|
| 249 | TEMP1 = ALPHA*X(JX)
|
---|
| 250 | TEMP2 = ZERO
|
---|
| 251 | Y(JY) = Y(JY) + TEMP1*DBLE(AP(KK))
|
---|
| 252 | IX = JX
|
---|
| 253 | IY = JY
|
---|
| 254 | DO 110 K = KK + 1,KK + N - J
|
---|
| 255 | IX = IX + INCX
|
---|
| 256 | IY = IY + INCY
|
---|
| 257 | Y(IY) = Y(IY) + TEMP1*AP(K)
|
---|
| 258 | TEMP2 = TEMP2 + DCONJG(AP(K))*X(IX)
|
---|
| 259 | 110 CONTINUE
|
---|
| 260 | Y(JY) = Y(JY) + ALPHA*TEMP2
|
---|
| 261 | JX = JX + INCX
|
---|
| 262 | JY = JY + INCY
|
---|
| 263 | KK = KK + (N-J+1)
|
---|
| 264 | 120 CONTINUE
|
---|
| 265 | END IF
|
---|
| 266 | END IF
|
---|
| 267 | *
|
---|
| 268 | RETURN
|
---|
| 269 | *
|
---|
| 270 | * End of ZHPMV .
|
---|
| 271 | *
|
---|
| 272 | END
|
---|