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