LAPACK: BLAS/SRC/chpr.f Source File

Go to the documentation of this file.
00001       SUBROUTINE CHPR(UPLO,N,ALPHA,X,INCX,AP)
00002 *     .. Scalar Arguments ..
00003       REAL ALPHA
00004       INTEGER INCX,N
00005       CHARACTER UPLO
00006 *     ..
00007 *     .. Array Arguments ..
00008       COMPLEX AP(*),X(*)
00009 *     ..
00010 *
00011 *  Purpose
00012 *  =======
00013 *
00014 *  CHPR    performs the hermitian rank 1 operation
00015 *
00016 *     A := alpha*x*conjg( x' ) + A,
00017 *
00018 *  where alpha is a real scalar, x is an n element vector and A is an
00019 *  n by n hermitian 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 *  X      - COMPLEX          array of dimension at least
00047 *           ( 1 + ( n - 1 )*abs( INCX ) ).
00048 *           Before entry, the incremented array X must contain the n
00049 *           element vector x.
00050 *           Unchanged on exit.
00051 *
00052 *  INCX   - INTEGER.
00053 *           On entry, INCX specifies the increment for the elements of
00054 *           X. INCX must not be zero.
00055 *           Unchanged on exit.
00056 *
00057 *  AP     - COMPLEX          array of DIMENSION at least
00058 *           ( ( n*( n + 1 ) )/2 ).
00059 *           Before entry with  UPLO = 'U' or 'u', the array AP must
00060 *           contain the upper triangular part of the hermitian matrix
00061 *           packed sequentially, column by column, so that AP( 1 )
00062 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
00063 *           and a( 2, 2 ) respectively, and so on. On exit, the array
00064 *           AP is overwritten by the upper triangular part of the
00065 *           updated matrix.
00066 *           Before entry with UPLO = 'L' or 'l', the array AP must
00067 *           contain the lower triangular part of the hermitian matrix
00068 *           packed sequentially, column by column, so that AP( 1 )
00069 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
00070 *           and a( 3, 1 ) respectively, and so on. On exit, the array
00071 *           AP is overwritten by the lower triangular part of the
00072 *           updated matrix.
00073 *           Note that the imaginary parts of the diagonal elements need
00074 *           not be set, they are assumed to be zero, and on exit they
00075 *           are set to zero.
00076 *
00077 *  Further Details
00078 *  ===============
00079 *
00080 *  Level 2 Blas routine.
00081 *
00082 *  -- Written on 22-October-1986.
00083 *     Jack Dongarra, Argonne National Lab.
00084 *     Jeremy Du Croz, Nag Central Office.
00085 *     Sven Hammarling, Nag Central Office.
00086 *     Richard Hanson, Sandia National Labs.
00087 *
00088 *  =====================================================================
00089 *
00090 *     .. Parameters ..
00091       COMPLEX ZERO
00092       PARAMETER (ZERO= (0.0E+0,0.0E+0))
00093 *     ..
00094 *     .. Local Scalars ..
00095       COMPLEX TEMP
00096       INTEGER I,INFO,IX,J,JX,K,KK,KX
00097 *     ..
00098 *     .. External Functions ..
00099       LOGICAL LSAME
00100       EXTERNAL LSAME
00101 *     ..
00102 *     .. External Subroutines ..
00103       EXTERNAL XERBLA
00104 *     ..
00105 *     .. Intrinsic Functions ..
00106       INTRINSIC CONJG,REAL
00107 *     ..
00108 *
00109 *     Test the input parameters.
00110 *
00111       INFO = 0
00112       IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
00113           INFO = 1
00114       ELSE IF (N.LT.0) THEN
00115           INFO = 2
00116       ELSE IF (INCX.EQ.0) THEN
00117           INFO = 5
00118       END IF
00119       IF (INFO.NE.0) THEN
00120           CALL XERBLA('CHPR  ',INFO)
00121           RETURN
00122       END IF
00123 *
00124 *     Quick return if possible.
00125 *
00126       IF ((N.EQ.0) .OR. (ALPHA.EQ.REAL(ZERO))) RETURN
00127 *
00128 *     Set the start point in X if the increment is not unity.
00129 *
00130       IF (INCX.LE.0) THEN
00131           KX = 1 - (N-1)*INCX
00132       ELSE IF (INCX.NE.1) THEN
00133           KX = 1
00134       END IF
00135 *
00136 *     Start the operations. In this version the elements of the array AP
00137 *     are accessed sequentially with one pass through AP.
00138 *
00139       KK = 1
00140       IF (LSAME(UPLO,'U')) THEN
00141 *
00142 *        Form  A  when upper triangle is stored in AP.
00143 *
00144           IF (INCX.EQ.1) THEN
00145               DO 20 J = 1,N
00146                   IF (X(J).NE.ZERO) THEN
00147                       TEMP = ALPHA*CONJG(X(J))
00148                       K = KK
00149                       DO 10 I = 1,J - 1
00150                           AP(K) = AP(K) + X(I)*TEMP
00151                           K = K + 1
00152    10                 CONTINUE
00153                       AP(KK+J-1) = REAL(AP(KK+J-1)) + REAL(X(J)*TEMP)
00154                   ELSE
00155                       AP(KK+J-1) = REAL(AP(KK+J-1))
00156                   END IF
00157                   KK = KK + J
00158    20         CONTINUE
00159           ELSE
00160               JX = KX
00161               DO 40 J = 1,N
00162                   IF (X(JX).NE.ZERO) THEN
00163                       TEMP = ALPHA*CONJG(X(JX))
00164                       IX = KX
00165                       DO 30 K = KK,KK + J - 2
00166                           AP(K) = AP(K) + X(IX)*TEMP
00167                           IX = IX + INCX
00168    30                 CONTINUE
00169                       AP(KK+J-1) = REAL(AP(KK+J-1)) + REAL(X(JX)*TEMP)
00170                   ELSE
00171                       AP(KK+J-1) = REAL(AP(KK+J-1))
00172                   END IF
00173                   JX = JX + INCX
00174                   KK = KK + J
00175    40         CONTINUE
00176           END IF
00177       ELSE
00178 *
00179 *        Form  A  when lower triangle is stored in AP.
00180 *
00181           IF (INCX.EQ.1) THEN
00182               DO 60 J = 1,N
00183                   IF (X(J).NE.ZERO) THEN
00184                       TEMP = ALPHA*CONJG(X(J))
00185                       AP(KK) = REAL(AP(KK)) + REAL(TEMP*X(J))
00186                       K = KK + 1
00187                       DO 50 I = J + 1,N
00188                           AP(K) = AP(K) + X(I)*TEMP
00189                           K = K + 1
00190    50                 CONTINUE
00191                   ELSE
00192                       AP(KK) = REAL(AP(KK))
00193                   END IF
00194                   KK = KK + N - J + 1
00195    60         CONTINUE
00196           ELSE
00197               JX = KX
00198               DO 80 J = 1,N
00199                   IF (X(JX).NE.ZERO) THEN
00200                       TEMP = ALPHA*CONJG(X(JX))
00201                       AP(KK) = REAL(AP(KK)) + REAL(TEMP*X(JX))
00202                       IX = JX
00203                       DO 70 K = KK + 1,KK + N - J
00204                           IX = IX + INCX
00205                           AP(K) = AP(K) + X(IX)*TEMP
00206    70                 CONTINUE
00207                   ELSE
00208                       AP(KK) = REAL(AP(KK))
00209                   END IF
00210                   JX = JX + INCX
00211                   KK = KK + N - J + 1
00212    80         CONTINUE
00213           END IF
00214       END IF
00215 *
00216       RETURN
00217 *
00218 *     End of CHPR  .
00219 *
00220       END