dpotf2.f.html

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      SUBROUTINE <a name="DPOTF2.1"></a><a href="dpotf2.f.html#DPOTF2.1">DPOTF2</a>( UPLO, N, A, LDA, 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, LDA, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION   A( LDA, * )
<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="DPOTF2.18"></a><a href="dpotf2.f.html#DPOTF2.1">DPOTF2</a> computes the Cholesky factorization of a real symmetric
</span><span class="comment">*</span><span class="comment">  positive definite matrix A.
</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' * U ,  if UPLO = 'U', or
</span><span class="comment">*</span><span class="comment">     A = L  * L',  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">  This is the unblocked version of the algorithm, calling Level 2 BLAS.
</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">          Specifies whether the upper or lower triangular part of the
</span><span class="comment">*</span><span class="comment">          symmetric matrix A is stored.
</span><span class="comment">*</span><span class="comment">          = 'U':  Upper triangular
</span><span class="comment">*</span><span class="comment">          = 'L':  Lower triangular
</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">  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment">          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
</span><span class="comment">*</span><span class="comment">          n by n upper triangular part of A contains the upper
</span><span class="comment">*</span><span class="comment">          triangular part of the matrix A, and the strictly lower
</span><span class="comment">*</span><span class="comment">          triangular part of A is not referenced.  If UPLO = 'L', the
</span><span class="comment">*</span><span class="comment">          leading n by n lower triangular part of A contains the lower
</span><span class="comment">*</span><span class="comment">          triangular part of the matrix A, and the strictly upper
</span><span class="comment">*</span><span class="comment">          triangular part of A is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, the factor U or L from the Cholesky
</span><span class="comment">*</span><span class="comment">          factorization A = U'*U  or A = L*L'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array A.  LDA &gt;= max(1,N).
</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 = -k, the k-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">          &gt; 0: if INFO = k, the leading minor of order k 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">  =====================================================================
</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
      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.74"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      DOUBLE PRECISION   DDOT
      EXTERNAL           <a name="LSAME.76"></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           DGEMV, DSCAL, <a name="XERBLA.79"></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          MAX, 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.89"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
      IF( .NOT.UPPER .AND. .NOT.<a name="LSAME.90"></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
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -4
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.98"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DPOTF2.98"></a><a href="dpotf2.f.html#DPOTF2.1">DPOTF2</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>         DO 10 J = 1, N
<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 = A( J, J ) - DDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 )
            IF( AJJ.LE.ZERO ) THEN
               A( J, J ) = AJJ
               GO TO 30
            END IF
            AJJ = SQRT( AJJ )
            A( J, J ) = AJJ
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute elements J+1:N of row J.
</span><span class="comment">*</span><span class="comment">
</span>            IF( J.LT.N ) THEN
               CALL DGEMV( <span class="string">'Transpose'</span>, J-1, N-J, -ONE, A( 1, J+1 ),
     $                     LDA, A( 1, J ), 1, ONE, A( J, J+1 ), LDA )
               CALL DSCAL( N-J, ONE / AJJ, A( J, J+1 ), LDA )
            END IF
   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>         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 = A( J, J ) - DDOT( J-1, A( J, 1 ), LDA, A( J, 1 ),
     $            LDA )
            IF( AJJ.LE.ZERO ) THEN
               A( J, J ) = AJJ
               GO TO 30
            END IF
            AJJ = SQRT( AJJ )
            A( J, J ) = AJJ
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Compute elements J+1:N of column J.
</span><span class="comment">*</span><span class="comment">
</span>            IF( J.LT.N ) THEN
               CALL DGEMV( <span class="string">'No transpose'</span>, N-J, J-1, -ONE, A( J+1, 1 ),
     $                     LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 )
               CALL DSCAL( N-J, ONE / AJJ, A( J+1, 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="DPOTF2.165"></a><a href="dpotf2.f.html#DPOTF2.1">DPOTF2</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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