chpr.f

贝尔实验室多年开发的矩阵计算程序库的说明文件

      SUBROUTINE CHPR(UPLO,N,ALPHA,X,INCX,AP)
*     .. Scalar Arguments ..
      REAL ALPHA
      INTEGER INCX,N
      CHARACTER UPLO
*     ..
*     .. Array Arguments ..
      COMPLEX AP(*),X(*)
*     ..
*
*  Purpose
*  =======
*
*  CHPR    performs the hermitian rank 1 operation
*
*     A := alpha*x*conjg( x' ) + A,
*
*  where alpha is a real scalar, x is an n element vector and A is an
*  n by n hermitian matrix, supplied in packed form.
*
*  Arguments
*  ==========
*
*  UPLO   - CHARACTER*1.
*           On entry, UPLO specifies whether the upper or lower
*           triangular part of the matrix A is supplied in the packed
*           array AP as follows:
*
*              UPLO = 'U' or 'u'   The upper triangular part of A is
*                                  supplied in AP.
*
*              UPLO = 'L' or 'l'   The lower triangular part of A is
*                                  supplied in AP.
*
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the order of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - REAL            .
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  X      - COMPLEX          array of dimension at least
*           ( 1 + ( n - 1 )*abs( INCX ) ).
*           Before entry, the incremented array X must contain the n
*           element vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  AP     - COMPLEX          array of DIMENSION at least
*           ( ( n*( n + 1 ) )/2 ).
*           Before entry with  UPLO = 'U' or 'u', the array AP must
*           contain the upper triangular part of the hermitian matrix
*           packed sequentially, column by column, so that AP( 1 )
*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
*           and a( 2, 2 ) respectively, and so on. On exit, the array
*           AP is overwritten by the upper triangular part of the
*           updated matrix.
*           Before entry with UPLO = 'L' or 'l', the array AP must
*           contain the lower triangular part of the hermitian matrix
*           packed sequentially, column by column, so that AP( 1 )
*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
*           and a( 3, 1 ) respectively, and so on. On exit, the array
*           AP is overwritten by the lower triangular part of the
*           updated matrix.
*           Note that the imaginary parts of the diagonal elements need
*           not be set, they are assumed to be zero, and on exit they
*           are set to zero.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      COMPLEX ZERO
      PARAMETER (ZERO= (0.0E+0,0.0E+0))
*     ..
*     .. Local Scalars ..
      COMPLEX TEMP
      INTEGER I,INFO,IX,J,JX,K,KK,KX
*     ..
*     .. External Functions ..
      LOGICAL LSAME
      EXTERNAL LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC CONJG,REAL
*     ..
*
*     Test the input parameters.
*
      INFO = 0
      IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
          INFO = 1
      ELSE IF (N.LT.0) THEN
          INFO = 2
      ELSE IF (INCX.EQ.0) THEN
          INFO = 5
      END IF
      IF (INFO.NE.0) THEN
          CALL XERBLA('CHPR  ',INFO)
          RETURN
      END IF
*
*     Quick return if possible.
*
      IF ((N.EQ.0) .OR. (ALPHA.EQ.REAL(ZERO))) RETURN
*
*     Set the start point in X if the increment is not unity.
*
      IF (INCX.LE.0) THEN
          KX = 1 - (N-1)*INCX
      ELSE IF (INCX.NE.1) THEN
          KX = 1
      END IF
*
*     Start the operations. In this version the elements of the array AP
*     are accessed sequentially with one pass through AP.
*
      KK = 1
      IF (LSAME(UPLO,'U')) THEN
*
*        Form  A  when upper triangle is stored in AP.
*
          IF (INCX.EQ.1) THEN
              DO 20 J = 1,N
                  IF (X(J).NE.ZERO) THEN
                      TEMP = ALPHA*CONJG(X(J))
                      K = KK
                      DO 10 I = 1,J - 1
                          AP(K) = AP(K) + X(I)*TEMP
                          K = K + 1
   10                 CONTINUE
                      AP(KK+J-1) = REAL(AP(KK+J-1)) + REAL(X(J)*TEMP)
                  ELSE
                      AP(KK+J-1) = REAL(AP(KK+J-1))
                  END IF
                  KK = KK + J
   20         CONTINUE
          ELSE
              JX = KX
              DO 40 J = 1,N
                  IF (X(JX).NE.ZERO) THEN
                      TEMP = ALPHA*CONJG(X(JX))
                      IX = KX
                      DO 30 K = KK,KK + J - 2
                          AP(K) = AP(K) + X(IX)*TEMP
                          IX = IX + INCX
   30                 CONTINUE
                      AP(KK+J-1) = REAL(AP(KK+J-1)) + REAL(X(JX)*TEMP)
                  ELSE
                      AP(KK+J-1) = REAL(AP(KK+J-1))
                  END IF
                  JX = JX + INCX
                  KK = KK + J
   40         CONTINUE
          END IF
      ELSE
*
*        Form  A  when lower triangle is stored in AP.
*
          IF (INCX.EQ.1) THEN
              DO 60 J = 1,N
                  IF (X(J).NE.ZERO) THEN
                      TEMP = ALPHA*CONJG(X(J))
                      AP(KK) = REAL(AP(KK)) + REAL(TEMP*X(J))
                      K = KK + 1
                      DO 50 I = J + 1,N
                          AP(K) = AP(K) + X(I)*TEMP
                          K = K + 1
   50                 CONTINUE
                  ELSE
                      AP(KK) = REAL(AP(KK))
                  END IF
                  KK = KK + N - J + 1
   60         CONTINUE
          ELSE
              JX = KX
              DO 80 J = 1,N
                  IF (X(JX).NE.ZERO) THEN
                      TEMP = ALPHA*CONJG(X(JX))
                      AP(KK) = REAL(AP(KK)) + REAL(TEMP*X(JX))
                      IX = JX
                      DO 70 K = KK + 1,KK + N - J
                          IX = IX + INCX
                          AP(K) = AP(K) + X(IX)*TEMP
   70                 CONTINUE
                  ELSE
                      AP(KK) = REAL(AP(KK))
                  END IF
                  JX = JX + INCX
                  KK = KK + N - J + 1
   80         CONTINUE
          END IF
      END IF
*
      RETURN
*
*     End of CHPR  .
*
      END