LAPACK: SRC/zspmv.f Source File

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00001       SUBROUTINE ZSPMV( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
00002 *
00003 *  -- LAPACK auxiliary routine (version 3.2) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          UPLO
00010       INTEGER            INCX, INCY, N
00011       COMPLEX*16         ALPHA, BETA
00012 *     ..
00013 *     .. Array Arguments ..
00014       COMPLEX*16         AP( * ), X( * ), Y( * )
00015 *     ..
00016 *
00017 *  Purpose
00018 *  =======
00019 *
00020 *  ZSPMV  performs the matrix-vector operation
00021 *
00022 *     y := alpha*A*x + beta*y,
00023 *
00024 *  where alpha and beta are scalars, x and y are n element vectors and
00025 *  A is an n by n symmetric matrix, supplied in packed form.
00026 *
00027 *  Arguments
00028 *  ==========
00029 *
00030 *  UPLO     (input) CHARACTER*1
00031 *           On entry, UPLO specifies whether the upper or lower
00032 *           triangular part of the matrix A is supplied in the packed
00033 *           array AP as follows:
00034 *
00035 *              UPLO = 'U' or 'u'   The upper triangular part of A is
00036 *                                  supplied in AP.
00037 *
00038 *              UPLO = 'L' or 'l'   The lower triangular part of A is
00039 *                                  supplied in AP.
00040 *
00041 *           Unchanged on exit.
00042 *
00043 *  N        (input) INTEGER
00044 *           On entry, N specifies the order of the matrix A.
00045 *           N must be at least zero.
00046 *           Unchanged on exit.
00047 *
00048 *  ALPHA    (input) COMPLEX*16
00049 *           On entry, ALPHA specifies the scalar alpha.
00050 *           Unchanged on exit.
00051 *
00052 *  AP       (input) COMPLEX*16 array, dimension at least
00053 *           ( ( N*( N + 1 ) )/2 ).
00054 *           Before entry, with UPLO = 'U' or 'u', the array AP must
00055 *           contain the upper triangular part of the symmetric matrix
00056 *           packed sequentially, column by column, so that AP( 1 )
00057 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
00058 *           and a( 2, 2 ) respectively, and so on.
00059 *           Before entry, with UPLO = 'L' or 'l', the array AP must
00060 *           contain the lower triangular part of the symmetric matrix
00061 *           packed sequentially, column by column, so that AP( 1 )
00062 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
00063 *           and a( 3, 1 ) respectively, and so on.
00064 *           Unchanged on exit.
00065 *
00066 *  X        (input) COMPLEX*16 array, dimension at least
00067 *           ( 1 + ( N - 1 )*abs( INCX ) ).
00068 *           Before entry, the incremented array X must contain the N-
00069 *           element vector x.
00070 *           Unchanged on exit.
00071 *
00072 *  INCX     (input) INTEGER
00073 *           On entry, INCX specifies the increment for the elements of
00074 *           X. INCX must not be zero.
00075 *           Unchanged on exit.
00076 *
00077 *  BETA     (input) COMPLEX*16
00078 *           On entry, BETA specifies the scalar beta. When BETA is
00079 *           supplied as zero then Y need not be set on input.
00080 *           Unchanged on exit.
00081 *
00082 *  Y        (input/output) COMPLEX*16 array, dimension at least
00083 *           ( 1 + ( N - 1 )*abs( INCY ) ).
00084 *           Before entry, the incremented array Y must contain the n
00085 *           element vector y. On exit, Y is overwritten by the updated
00086 *           vector y.
00087 *
00088 *  INCY     (input) INTEGER
00089 *           On entry, INCY specifies the increment for the elements of
00090 *           Y. INCY must not be zero.
00091 *           Unchanged on exit.
00092 *
00093 * =====================================================================
00094 *
00095 *     .. Parameters ..
00096       COMPLEX*16         ONE
00097       PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) )
00098       COMPLEX*16         ZERO
00099       PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ) )
00100 *     ..
00101 *     .. Local Scalars ..
00102       INTEGER            I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY
00103       COMPLEX*16         TEMP1, TEMP2
00104 *     ..
00105 *     .. External Functions ..
00106       LOGICAL            LSAME
00107       EXTERNAL           LSAME
00108 *     ..
00109 *     .. External Subroutines ..
00110       EXTERNAL           XERBLA
00111 *     ..
00112 *     .. Executable Statements ..
00113 *
00114 *     Test the input parameters.
00115 *
00116       INFO = 0
00117       IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00118          INFO = 1
00119       ELSE IF( N.LT.0 ) THEN
00120          INFO = 2
00121       ELSE IF( INCX.EQ.0 ) THEN
00122          INFO = 6
00123       ELSE IF( INCY.EQ.0 ) THEN
00124          INFO = 9
00125       END IF
00126       IF( INFO.NE.0 ) THEN
00127          CALL XERBLA( 'ZSPMV ', INFO )
00128          RETURN
00129       END IF
00130 *
00131 *     Quick return if possible.
00132 *
00133       IF( ( N.EQ.0 ) .OR. ( ( ALPHA.EQ.ZERO ) .AND. ( BETA.EQ.ONE ) ) )
00134      $   RETURN
00135 *
00136 *     Set up the start points in  X  and  Y.
00137 *
00138       IF( INCX.GT.0 ) THEN
00139          KX = 1
00140       ELSE
00141          KX = 1 - ( N-1 )*INCX
00142       END IF
00143       IF( INCY.GT.0 ) THEN
00144          KY = 1
00145       ELSE
00146          KY = 1 - ( N-1 )*INCY
00147       END IF
00148 *
00149 *     Start the operations. In this version the elements of the array AP
00150 *     are accessed sequentially with one pass through AP.
00151 *
00152 *     First form  y := beta*y.
00153 *
00154       IF( BETA.NE.ONE ) THEN
00155          IF( INCY.EQ.1 ) THEN
00156             IF( BETA.EQ.ZERO ) THEN
00157                DO 10 I = 1, N
00158                   Y( I ) = ZERO
00159    10          CONTINUE
00160             ELSE
00161                DO 20 I = 1, N
00162                   Y( I ) = BETA*Y( I )
00163    20          CONTINUE
00164             END IF
00165          ELSE
00166             IY = KY
00167             IF( BETA.EQ.ZERO ) THEN
00168                DO 30 I = 1, N
00169                   Y( IY ) = ZERO
00170                   IY = IY + INCY
00171    30          CONTINUE
00172             ELSE
00173                DO 40 I = 1, N
00174                   Y( IY ) = BETA*Y( IY )
00175                   IY = IY + INCY
00176    40          CONTINUE
00177             END IF
00178          END IF
00179       END IF
00180       IF( ALPHA.EQ.ZERO )
00181      $   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 ZSPMV
00264 *
00265       END