LAPACK: BLAS/SRC/sspmv.f Source File

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00001       SUBROUTINE SSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
00002 *     .. Scalar Arguments ..
00003       REAL ALPHA,BETA
00004       INTEGER INCX,INCY,N
00005       CHARACTER UPLO
00006 *     ..
00007 *     .. Array Arguments ..
00008       REAL AP(*),X(*),Y(*)
00009 *     ..
00010 *
00011 *  Purpose
00012 *  =======
00013 *
00014 *  SSPMV  performs the matrix-vector operation
00015 *
00016 *     y := alpha*A*x + beta*y,
00017 *
00018 *  where alpha and beta are scalars, x and y are n element vectors and
00019 *  A is an n by n symmetric matrix, supplied in packed form.
00020 *
00021 *  Arguments
00022 *  ==========
00023 *
00024 *  UPLO   - CHARACTER*1.
00025 *           On entry, UPLO specifies whether the upper or lower
00026 *           triangular part of the matrix A is supplied in the packed
00027 *           array AP as follows:
00028 *
00029 *              UPLO = 'U' or 'u'   The upper triangular part of A is
00030 *                                  supplied in AP.
00031 *
00032 *              UPLO = 'L' or 'l'   The lower triangular part of A is
00033 *                                  supplied in AP.
00034 *
00035 *           Unchanged on exit.
00036 *
00037 *  N      - INTEGER.
00038 *           On entry, N specifies the order of the matrix A.
00039 *           N must be at least zero.
00040 *           Unchanged on exit.
00041 *
00042 *  ALPHA  - REAL            .
00043 *           On entry, ALPHA specifies the scalar alpha.
00044 *           Unchanged on exit.
00045 *
00046 *  AP     - REAL             array of DIMENSION at least
00047 *           ( ( n*( n + 1 ) )/2 ).
00048 *           Before entry with UPLO = 'U' or 'u', the array AP must
00049 *           contain the upper triangular part of the symmetric matrix
00050 *           packed sequentially, column by column, so that AP( 1 )
00051 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
00052 *           and a( 2, 2 ) respectively, and so on.
00053 *           Before entry with UPLO = 'L' or 'l', the array AP must
00054 *           contain the lower triangular part of the symmetric matrix
00055 *           packed sequentially, column by column, so that AP( 1 )
00056 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
00057 *           and a( 3, 1 ) respectively, and so on.
00058 *           Unchanged on exit.
00059 *
00060 *  X      - REAL             array of dimension at least
00061 *           ( 1 + ( n - 1 )*abs( INCX ) ).
00062 *           Before entry, the incremented array X must contain the n
00063 *           element vector x.
00064 *           Unchanged on exit.
00065 *
00066 *  INCX   - INTEGER.
00067 *           On entry, INCX specifies the increment for the elements of
00068 *           X. INCX must not be zero.
00069 *           Unchanged on exit.
00070 *
00071 *  BETA   - REAL            .
00072 *           On entry, BETA specifies the scalar beta. When BETA is
00073 *           supplied as zero then Y need not be set on input.
00074 *           Unchanged on exit.
00075 *
00076 *  Y      - REAL             array of dimension at least
00077 *           ( 1 + ( n - 1 )*abs( INCY ) ).
00078 *           Before entry, the incremented array Y must contain the n
00079 *           element vector y. On exit, Y is overwritten by the updated
00080 *           vector y.
00081 *
00082 *  INCY   - INTEGER.
00083 *           On entry, INCY specifies the increment for the elements of
00084 *           Y. INCY must not be zero.
00085 *           Unchanged on exit.
00086 *
00087 *  Further Details
00088 *  ===============
00089 *
00090 *  Level 2 Blas routine.
00091 *
00092 *  -- Written on 22-October-1986.
00093 *     Jack Dongarra, Argonne National Lab.
00094 *     Jeremy Du Croz, Nag Central Office.
00095 *     Sven Hammarling, Nag Central Office.
00096 *     Richard Hanson, Sandia National Labs.
00097 *
00098 *  =====================================================================
00099 *
00100 *     .. Parameters ..
00101       REAL ONE,ZERO
00102       PARAMETER (ONE=1.0E+0,ZERO=0.0E+0)
00103 *     ..
00104 *     .. Local Scalars ..
00105       REAL TEMP1,TEMP2
00106       INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
00107 *     ..
00108 *     .. External Functions ..
00109       LOGICAL LSAME
00110       EXTERNAL LSAME
00111 *     ..
00112 *     .. External Subroutines ..
00113       EXTERNAL XERBLA
00114 *     ..
00115 *
00116 *     Test the input parameters.
00117 *
00118       INFO = 0
00119       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
00120           INFO = 1
00121       ELSE IF (N.LT.0) THEN
00122           INFO = 2
00123       ELSE IF (INCX.EQ.0) THEN
00124           INFO = 6
00125       ELSE IF (INCY.EQ.0) THEN
00126           INFO = 9
00127       END IF
00128       IF (INFO.NE.0) THEN
00129           CALL XERBLA('SSPMV ',INFO)
00130           RETURN
00131       END IF
00132 *
00133 *     Quick return if possible.
00134 *
00135       IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
00136 *
00137 *     Set up the start points in  X  and  Y.
00138 *
00139       IF (INCX.GT.0) THEN
00140           KX = 1
00141       ELSE
00142           KX = 1 - (N-1)*INCX
00143       END IF
00144       IF (INCY.GT.0) THEN
00145           KY = 1
00146       ELSE
00147           KY = 1 - (N-1)*INCY
00148       END IF
00149 *
00150 *     Start the operations. In this version the elements of the array AP
00151 *     are accessed sequentially with one pass through AP.
00152 *
00153 *     First form  y := beta*y.
00154 *
00155       IF (BETA.NE.ONE) THEN
00156           IF (INCY.EQ.1) THEN
00157               IF (BETA.EQ.ZERO) THEN
00158                   DO 10 I = 1,N
00159                       Y(I) = ZERO
00160    10             CONTINUE
00161               ELSE
00162                   DO 20 I = 1,N
00163                       Y(I) = BETA*Y(I)
00164    20             CONTINUE
00165               END IF
00166           ELSE
00167               IY = KY
00168               IF (BETA.EQ.ZERO) THEN
00169                   DO 30 I = 1,N
00170                       Y(IY) = ZERO
00171                       IY = IY + INCY
00172    30             CONTINUE
00173               ELSE
00174                   DO 40 I = 1,N
00175                       Y(IY) = BETA*Y(IY)
00176                       IY = IY + INCY
00177    40             CONTINUE
00178               END IF
00179           END IF
00180       END IF
00181       IF (ALPHA.EQ.ZERO) RETURN
00182       KK = 1
00183       IF (LSAME(UPLO,'U')) THEN
00184 *
00185 *        Form  y  when AP contains the upper triangle.
00186 *
00187           IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
00188               DO 60 J = 1,N
00189                   TEMP1 = ALPHA*X(J)
00190                   TEMP2 = ZERO
00191                   K = KK
00192                   DO 50 I = 1,J - 1
00193                       Y(I) = Y(I) + TEMP1*AP(K)
00194                       TEMP2 = TEMP2 + AP(K)*X(I)
00195                       K = K + 1
00196    50             CONTINUE
00197                   Y(J) = Y(J) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2
00198                   KK = KK + J
00199    60         CONTINUE
00200           ELSE
00201               JX = KX
00202               JY = KY
00203               DO 80 J = 1,N
00204                   TEMP1 = ALPHA*X(JX)
00205                   TEMP2 = ZERO
00206                   IX = KX
00207                   IY = KY
00208                   DO 70 K = KK,KK + J - 2
00209                       Y(IY) = Y(IY) + TEMP1*AP(K)
00210                       TEMP2 = TEMP2 + AP(K)*X(IX)
00211                       IX = IX + INCX
00212                       IY = IY + INCY
00213    70             CONTINUE
00214                   Y(JY) = Y(JY) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2
00215                   JX = JX + INCX
00216                   JY = JY + INCY
00217                   KK = KK + J
00218    80         CONTINUE
00219           END IF
00220       ELSE
00221 *
00222 *        Form  y  when AP contains the lower triangle.
00223 *
00224           IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
00225               DO 100 J = 1,N
00226                   TEMP1 = ALPHA*X(J)
00227                   TEMP2 = ZERO
00228                   Y(J) = Y(J) + TEMP1*AP(KK)
00229                   K = KK + 1
00230                   DO 90 I = J + 1,N
00231                       Y(I) = Y(I) + TEMP1*AP(K)
00232                       TEMP2 = TEMP2 + AP(K)*X(I)
00233                       K = K + 1
00234    90             CONTINUE
00235                   Y(J) = Y(J) + ALPHA*TEMP2
00236                   KK = KK + (N-J+1)
00237   100         CONTINUE
00238           ELSE
00239               JX = KX
00240               JY = KY
00241               DO 120 J = 1,N
00242                   TEMP1 = ALPHA*X(JX)
00243                   TEMP2 = ZERO
00244                   Y(JY) = Y(JY) + TEMP1*AP(KK)
00245                   IX = JX
00246                   IY = JY
00247                   DO 110 K = KK + 1,KK + N - J
00248                       IX = IX + INCX
00249                       IY = IY + INCY
00250                       Y(IY) = Y(IY) + TEMP1*AP(K)
00251                       TEMP2 = TEMP2 + AP(K)*X(IX)
00252   110             CONTINUE
00253                   Y(JY) = Y(JY) + ALPHA*TEMP2
00254                   JX = JX + INCX
00255                   JY = JY + INCY
00256                   KK = KK + (N-J+1)
00257   120         CONTINUE
00258           END IF
00259       END IF
00260 *
00261       RETURN
00262 *
00263 *     End of SSPMV .
00264 *
00265       END