dpptrf.f.html

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      SUBROUTINE <a name="DPPTRF.1"></a><a href="dpptrf.f.html#DPPTRF.1">DPPTRF</a>( UPLO, N, AP, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          UPLO
      INTEGER            INFO, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION   AP( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="DPPTRF.18"></a><a href="dpptrf.f.html#DPPTRF.1">DPPTRF</a> computes the Cholesky factorization of a real symmetric
</span><span class="comment">*</span><span class="comment">  positive definite matrix A stored in packed format.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The factorization has the form
</span><span class="comment">*</span><span class="comment">     A = U**T * U,  if UPLO = 'U', or
</span><span class="comment">*</span><span class="comment">     A = L  * L**T,  if UPLO = 'L',
</span><span class="comment">*</span><span class="comment">  where U is an upper triangular matrix and L is lower triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  UPLO    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'U':  Upper triangle of A is stored;
</span><span class="comment">*</span><span class="comment">          = 'L':  Lower triangle of A is stored.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix A.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
</span><span class="comment">*</span><span class="comment">          On entry, the upper or lower triangle of the symmetric matrix
</span><span class="comment">*</span><span class="comment">          A, packed columnwise in a linear array.  The j-th column of A
</span><span class="comment">*</span><span class="comment">          is stored in the array AP as follows:
</span><span class="comment">*</span><span class="comment">          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1&lt;=i&lt;=j;
</span><span class="comment">*</span><span class="comment">          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j&lt;=i&lt;=n.
</span><span class="comment">*</span><span class="comment">          See below for further details.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, the triangular factor U or L from the
</span><span class="comment">*</span><span class="comment">          Cholesky factorization A = U**T*U or A = L*L**T, in the same
</span><span class="comment">*</span><span class="comment">          storage format as A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">          &gt; 0:  if INFO = i, the leading minor of order i is not
</span><span class="comment">*</span><span class="comment">                positive definite, and the factorization could not be
</span><span class="comment">*</span><span class="comment">                completed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further Details
</span><span class="comment">*</span><span class="comment">  ======= =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The packed storage scheme is illustrated by the following example
</span><span class="comment">*</span><span class="comment">  when N = 4, UPLO = 'U':
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Two-dimensional storage of the symmetric matrix A:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     a11 a12 a13 a14
</span><span class="comment">*</span><span class="comment">         a22 a23 a24
</span><span class="comment">*</span><span class="comment">             a33 a34     (aij = aji)
</span><span class="comment">*</span><span class="comment">                 a44
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Packed storage of the upper triangle of A:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      LOGICAL            UPPER
      INTEGER            J, JC, JJ
      DOUBLE PRECISION   AJJ
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.84"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      DOUBLE PRECISION   DDOT
      EXTERNAL           <a name="LSAME.86"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, DDOT
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           DSCAL, DSPR, DTPSV, <a name="XERBLA.89"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          SQRT
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      UPPER = <a name="LSAME.99"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
      IF( .NOT.UPPER .AND. .NOT.<a name="LSAME.100"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</span> ) ) THEN
         INFO = -1
      ELSE IF( N.LT.0 ) THEN
         INFO = -2
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.106"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DPPTRF.106"></a><a href="dpptrf.f.html#DPPTRF.1">DPPTRF</a>'</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span>      IF( N.EQ.0 )
     $   RETURN
<span class="comment">*</span><span class="comment">
</span>      IF( UPPER ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Compute the Cholesky factorization A = U'*U.
</span><span class="comment">*</span><span class="comment">
</span>         JJ = 0
         DO 10 J = 1, N
            JC = JJ + 1
            JJ = JJ + J
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute elements 1:J-1 of column J.
</span><span class="comment">*</span><span class="comment">
</span>            IF( J.GT.1 )
     $         CALL DTPSV( <span class="string">'Upper'</span>, <span class="string">'Transpose'</span>, <span class="string">'Non-unit'</span>, J-1, AP,
     $                     AP( JC ), 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute U(J,J) and test for non-positive-definiteness.
</span><span class="comment">*</span><span class="comment">
</span>            AJJ = AP( JJ ) - DDOT( J-1, AP( JC ), 1, AP( JC ), 1 )
            IF( AJJ.LE.ZERO ) THEN
               AP( JJ ) = AJJ
               GO TO 30
            END IF
            AP( JJ ) = SQRT( AJJ )
   10    CONTINUE
      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Compute the Cholesky factorization A = L*L'.
</span><span class="comment">*</span><span class="comment">
</span>         JJ = 1
         DO 20 J = 1, N
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute L(J,J) and test for non-positive-definiteness.
</span><span class="comment">*</span><span class="comment">
</span>            AJJ = AP( JJ )
            IF( AJJ.LE.ZERO ) THEN
               AP( JJ ) = AJJ
               GO TO 30
            END IF
            AJJ = SQRT( AJJ )
            AP( JJ ) = AJJ
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute elements J+1:N of column J and update the trailing
</span><span class="comment">*</span><span class="comment">           submatrix.
</span><span class="comment">*</span><span class="comment">
</span>            IF( J.LT.N ) THEN
               CALL DSCAL( N-J, ONE / AJJ, AP( JJ+1 ), 1 )
               CALL DSPR( <span class="string">'Lower'</span>, N-J, -ONE, AP( JJ+1 ), 1,
     $                    AP( JJ+N-J+1 ) )
               JJ = JJ + N - J + 1
            END IF
   20    CONTINUE
      END IF
      GO TO 40
<span class="comment">*</span><span class="comment">
</span>   30 CONTINUE
      INFO = J
<span class="comment">*</span><span class="comment">
</span>   40 CONTINUE
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="DPPTRF.175"></a><a href="dpptrf.f.html#DPPTRF.1">DPPTRF</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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