SUBROUTINE DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP) * .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER INCX,INCY,N CHARACTER UPLO * .. * .. Array Arguments .. DOUBLE PRECISION AP(*),X(*),Y(*) * .. * * Purpose * ======= * * DSPR2 performs the symmetric rank 2 operation * * A := alpha*x*y**T + alpha*y*x**T + A, * * where alpha is a scalar, x and y are n element vectors and A is an * n by n symmetric 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 - DOUBLE PRECISION. * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - DOUBLE PRECISION 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION 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 symmetric 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 symmetric 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. * * 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 .. DOUBLE PRECISION ZERO PARAMETER (ZERO=0.0D+0) * .. * .. Local Scalars .. DOUBLE PRECISION TEMP1,TEMP2 INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA * .. * * 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('DSPR2 ',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*Y(J) TEMP2 = ALPHA*X(J) K = KK DO 10 I = 1,J AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 K = K + 1 10 CONTINUE 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*Y(JY) TEMP2 = ALPHA*X(JX) IX = KX IY = KY DO 30 K = KK,KK + J - 1 AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 IX = IX + INCX IY = IY + INCY 30 CONTINUE 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*Y(J) TEMP2 = ALPHA*X(J) K = KK DO 50 I = J,N AP(K) = AP(K) + X(I)*TEMP1 + Y(I)*TEMP2 K = K + 1 50 CONTINUE 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*Y(JY) TEMP2 = ALPHA*X(JX) IX = JX IY = JY DO 70 K = KK,KK + N - J AP(K) = AP(K) + X(IX)*TEMP1 + Y(IY)*TEMP2 IX = IX + INCX IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX JY = JY + INCY KK = KK + N - J + 1 80 CONTINUE END IF END IF * RETURN * * End of DSPR2 . * END