| SUBROUTINE CHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) |
| * .. Scalar Arguments .. |
| COMPLEX ALPHA |
| INTEGER INCX,INCY,N |
| CHARACTER UPLO |
| * .. |
| * .. Array Arguments .. |
| COMPLEX AP(*),X(*),Y(*) |
| * .. |
| * |
| * Purpose |
| * ======= |
| * |
| * CHPR2 performs the hermitian rank 2 operation |
| * |
| * A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A, |
| * |
| * where alpha is a scalar, x and y are n element vectors 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 - COMPLEX . |
| * 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. |
| * |
| * Y - COMPLEX array of dimension at least |
| * ( 1 + ( n - 1 )*abs( INCY ) ). |
| * Before entry, the incremented array Y must contain the n |
| * element vector y. |
| * Unchanged on exit. |
| * |
| * INCY - INTEGER. |
| * On entry, INCY specifies the increment for the elements of |
| * Y. INCY 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. |
| * |
| * Further Details |
| * =============== |
| * |
| * 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 TEMP1,TEMP2 |
| INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY |
| * .. |
| * .. 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 |
| ELSE IF (INCY.EQ.0) THEN |
| INFO = 7 |
| END IF |
| IF (INFO.NE.0) THEN |
| CALL XERBLA('CHPR2 ',INFO) |
| RETURN |
| END IF |
| * |
| * Quick return if possible. |
| * |
| IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN |
| * |
| * Set up the start points in X and Y if the increments are not both |
| * unity. |
| * |
| IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN |
| IF (INCX.GT.0) THEN |
| KX = 1 |
| ELSE |
| KX = 1 - (N-1)*INCX |
| END IF |
| IF (INCY.GT.0) THEN |
| KY = 1 |
| ELSE |
| KY = 1 - (N-1)*INCY |
| END IF |
| JX = KX |
| JY = KY |
| 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) .AND. (INCY.EQ.1)) THEN |
| DO 20 J = 1,N |
| IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN |
| TEMP1 = ALPHA*CONJG(Y(J)) |
| TEMP2 = CONJG(ALPHA*X(J)) |
| K = KK |
| DO 10 I = 1,J - 1 |
| AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 |
| K = K + 1 |
| 10 CONTINUE |
| AP(KK+J-1) = REAL(AP(KK+J-1)) + |
| + REAL(X(J)*TEMP1+Y(J)*TEMP2) |
| ELSE |
| AP(KK+J-1) = REAL(AP(KK+J-1)) |
| END IF |
| KK = KK + J |
| 20 CONTINUE |
| ELSE |
| DO 40 J = 1,N |
| IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN |
| TEMP1 = ALPHA*CONJG(Y(JY)) |
| TEMP2 = CONJG(ALPHA*X(JX)) |
| IX = KX |
| IY = KY |
| DO 30 K = KK,KK + J - 2 |
| AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 |
| IX = IX + INCX |
| IY = IY + INCY |
| 30 CONTINUE |
| AP(KK+J-1) = REAL(AP(KK+J-1)) + |
| + REAL(X(JX)*TEMP1+Y(JY)*TEMP2) |
| ELSE |
| AP(KK+J-1) = REAL(AP(KK+J-1)) |
| END IF |
| JX = JX + INCX |
| JY = JY + INCY |
| KK = KK + J |
| 40 CONTINUE |
| END IF |
| ELSE |
| * |
| * Form A when lower triangle is stored in AP. |
| * |
| IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN |
| DO 60 J = 1,N |
| IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN |
| TEMP1 = ALPHA*CONJG(Y(J)) |
| TEMP2 = CONJG(ALPHA*X(J)) |
| AP(KK) = REAL(AP(KK)) + |
| + REAL(X(J)*TEMP1+Y(J)*TEMP2) |
| K = KK + 1 |
| DO 50 I = J + 1,N |
| AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 |
| K = K + 1 |
| 50 CONTINUE |
| ELSE |
| AP(KK) = REAL(AP(KK)) |
| END IF |
| KK = KK + N - J + 1 |
| 60 CONTINUE |
| ELSE |
| DO 80 J = 1,N |
| IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN |
| TEMP1 = ALPHA*CONJG(Y(JY)) |
| TEMP2 = CONJG(ALPHA*X(JX)) |
| AP(KK) = REAL(AP(KK)) + |
| + REAL(X(JX)*TEMP1+Y(JY)*TEMP2) |
| IX = JX |
| IY = JY |
| DO 70 K = KK + 1,KK + N - J |
| IX = IX + INCX |
| IY = IY + INCY |
| AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 |
| 70 CONTINUE |
| ELSE |
| AP(KK) = REAL(AP(KK)) |
| END IF |
| JX = JX + INCX |
| JY = JY + INCY |
| KK = KK + N - J + 1 |
| 80 CONTINUE |
| END IF |
| END IF |
| * |
| RETURN |
| * |
| * End of CHPR2 . |
| * |
| END |
