*DECK DSYR
SUBROUTINE DSYR (UPLO, N, ALPHA, X, INCX, A, LDA)
C***BEGIN PROLOGUE DSYR
C***PURPOSE Perform the symmetric rank 1 operation.
C***LIBRARY SLATEC (BLAS)
C***CATEGORY D1B4
C***TYPE DOUBLE PRECISION (DSYR-D)
C***KEYWORDS LEVEL 2 BLAS, LINEAR ALGEBRA
C***AUTHOR Dongarra, J. J., (ANL)
C Du Croz, J., (NAG)
C Hammarling, S., (NAG)
C Hanson, R. J., (SNLA)
C***DESCRIPTION
C
C DSYR performs the symmetric rank 1 operation
C
C A := alpha*x*x' + A,
C
C where alpha is a real scalar, x is an n element vector and A is an
C n by n symmetric matrix.
C
C Parameters
C ==========
C
C UPLO - CHARACTER*1.
C On entry, UPLO specifies whether the upper or lower
C triangular part of the array A is to be referenced as
C follows:
C
C UPLO = 'U' or 'u' Only the upper triangular part of A
C is to be referenced.
C
C UPLO = 'L' or 'l' Only the lower triangular part of A
C is to be referenced.
C
C Unchanged on exit.
C
C N - INTEGER.
C On entry, N specifies the order of the matrix A.
C N must be at least zero.
C Unchanged on exit.
C
C ALPHA - DOUBLE PRECISION.
C On entry, ALPHA specifies the scalar alpha.
C Unchanged on exit.
C
C X - DOUBLE PRECISION array of dimension at least
C ( 1 + ( n - 1)*abs( INCX)).
C Before entry, the incremented array X must contain the n
C element vector x.
C Unchanged on exit.
C
C INCX - INTEGER.
C On entry, INCX specifies the increment for the elements of
C X. INCX must not be zero.
C Unchanged on exit.
C
C A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
C Before entry with UPLO = 'U' or 'u', the leading n by n
C upper triangular part of the array A must contain the upper
C triangular part of the symmetric matrix and the strictly
C lower triangular part of A is not referenced. On exit, the
C upper triangular part of the array A is overwritten by the
C upper triangular part of the updated matrix.
C Before entry with UPLO = 'L' or 'l', the leading n by n
C lower triangular part of the array A must contain the lower
C triangular part of the symmetric matrix and the strictly
C upper triangular part of A is not referenced. On exit, the
C lower triangular part of the array A is overwritten by the
C lower triangular part of the updated matrix.
C
C LDA - INTEGER.
C On entry, LDA specifies the first dimension of A as declared
C in the calling (sub) program. LDA must be at least
C max( 1, n ).
C Unchanged on exit.
C
C***REFERENCES Dongarra, J. J., Du Croz, J., Hammarling, S., and
C Hanson, R. J. An extended set of Fortran basic linear
C algebra subprograms. ACM TOMS, Vol. 14, No. 1,
C pp. 1-17, March 1988.
C***ROUTINES CALLED LSAME, XERBLA
C***REVISION HISTORY (YYMMDD)
C 861022 DATE WRITTEN
C 910605 Modified to meet SLATEC prologue standards. Only comment
C lines were modified. (BKS)
C***END PROLOGUE DSYR
C .. Scalar Arguments ..
DOUBLE PRECISION ALPHA
INTEGER INCX, LDA, N
CHARACTER*1 UPLO
C .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), X( * )
C .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
C .. Local Scalars ..
DOUBLE PRECISION TEMP
INTEGER I, INFO, IX, J, JX, KX
C .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
C .. External Subroutines ..
EXTERNAL XERBLA
C .. Intrinsic Functions ..
INTRINSIC MAX
C***FIRST EXECUTABLE STATEMENT DSYR
C
C Test the input parameters.
C
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( LDA.LT.MAX( 1, N ) )THEN
INFO = 7
END IF
IF( INFO.NE.0 )THEN
CALL XERBLA( 'DSYR ', INFO )
RETURN
END IF
C
C Quick return if possible.
C
IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) )
$ RETURN
C
C Set the start point in X if the increment is not unity.
C
IF( INCX.LE.0 )THEN
KX = 1 - ( N - 1 )*INCX
ELSE IF( INCX.NE.1 )THEN
KX = 1
END IF
C
C Start the operations. In this version the elements of A are
C accessed sequentially with one pass through the triangular part
C of A.
C
IF( LSAME( UPLO, 'U' ) )THEN
C
C Form A when A is stored in upper triangle.
C
IF( INCX.EQ.1 )THEN
DO 20, J = 1, N
IF( X( J ).NE.ZERO )THEN
TEMP = ALPHA*X( J )
DO 10, I = 1, J
A( I, J ) = A( I, J ) + X( I )*TEMP
10 CONTINUE
END IF
20 CONTINUE
ELSE
JX = KX
DO 40, J = 1, N
IF( X( JX ).NE.ZERO )THEN
TEMP = ALPHA*X( JX )
IX = KX
DO 30, I = 1, J
A( I, J ) = A( I, J ) + X( IX )*TEMP
IX = IX + INCX
30 CONTINUE
END IF
JX = JX + INCX
40 CONTINUE
END IF
ELSE
C
C Form A when A is stored in lower triangle.
C
IF( INCX.EQ.1 )THEN
DO 60, J = 1, N
IF( X( J ).NE.ZERO )THEN
TEMP = ALPHA*X( J )
DO 50, I = J, N
A( I, J ) = A( I, J ) + X( I )*TEMP
50 CONTINUE
END IF
60 CONTINUE
ELSE
JX = KX
DO 80, J = 1, N
IF( X( JX ).NE.ZERO )THEN
TEMP = ALPHA*X( JX )
IX = JX
DO 70, I = J, N
A( I, J ) = A( I, J ) + X( IX )*TEMP
IX = IX + INCX
70 CONTINUE
END IF
JX = JX + INCX
80 CONTINUE
END IF
END IF
C
RETURN
C
C End of DSYR .
C
END