cspr.f

          SUBROUTINE CSPR( UPLO, N, ALPHA, X, INCX, AP )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          UPLO
          INTEGER            INCX, N
          COMPLEX            ALPHA
    *     ..
    *     .. Array Arguments ..
          COMPLEX            AP( * ), X( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CSPR    performs the symmetric rank 1 operation
    *
    *     A := alpha*x*conjg( x' ) + A,
    *
    *  where alpha is a complex scalar, x is an n element vector and A is an
    *  n by n symmetric matrix, supplied in packed form.
    *
    *  Arguments
    *  ==========
    *
    *  UPLO     (input) 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        (input) INTEGER
    *           On entry, N specifies the order of the matrix A.
    *           N must be at least zero.
    *           Unchanged on exit.
    *
    *  ALPHA    (input) COMPLEX
    *           On entry, ALPHA specifies the scalar alpha.
    *           Unchanged on exit.
    *
    *  X        (input) COMPLEX array, 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     (input) INTEGER
    *           On entry, INCX specifies the increment for the elements of
    *           X. INCX must not be zero.
    *           Unchanged on exit.
    *
    *  AP       (input/output) COMPLEX array, 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.
    *           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.
    *
    * =====================================================================
    *
    *     .. Parameters ..
          COMPLEX            ZERO
          PARAMETER          ( ZERO = ( 0.0E+0, 0.0E+0 ) )
    *     ..
    *     .. Local Scalars ..
          INTEGER            I, INFO, IX, J, JX, K, KK, KX
          COMPLEX            TEMP
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           XERBLA
    *     ..
    *     .. Executable Statements ..
    *
    *     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( 'CSPR  ', INFO )
             RETURN
          END IF
    *
    *     Quick return if possible.
    *
          IF( ( N.EQ.0 ) .OR. ( ALPHA.EQ.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*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 ) = AP( KK+J-1 ) + X( J )*TEMP
                   ELSE
                      AP( KK+J-1 ) = 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*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 ) = AP( KK+J-1 ) + X( JX )*TEMP
                   ELSE
                      AP( KK+J-1 ) = 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*X( J )
                      AP( KK ) = AP( KK ) + 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 ) = 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*X( JX )
                      AP( KK ) = AP( KK ) + 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 ) = AP( KK )
                   END IF
                   JX = JX + INCX
                   KK = KK + N - J + 1
       80       CONTINUE
             END IF
          END IF
    *
          RETURN
    *
    *     End of CSPR
    *
          END