dpptrs.f.html

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      SUBROUTINE <a name="DPPTRS.1"></a><a href="dpptrs.f.html#DPPTRS.1">DPPTRS</a>( UPLO, N, NRHS, AP, B, LDB, 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, LDB, N, NRHS
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      DOUBLE PRECISION   AP( * ), B( LDB, * )
<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="DPPTRS.18"></a><a href="dpptrs.f.html#DPPTRS.1">DPPTRS</a> solves a system of linear equations A*X = B with a symmetric
</span><span class="comment">*</span><span class="comment">  positive definite matrix A in packed storage using the Cholesky
</span><span class="comment">*</span><span class="comment">  factorization A = U**T*U or A = L*L**T computed by <a name="DPPTRF.20"></a><a href="dpptrf.f.html#DPPTRF.1">DPPTRF</a>.
</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">  NRHS    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of right hand sides, i.e., the number of columns
</span><span class="comment">*</span><span class="comment">          of the matrix B.  NRHS &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  AP      (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
</span><span class="comment">*</span><span class="comment">          The triangular factor U or L from the Cholesky factorization
</span><span class="comment">*</span><span class="comment">          A = U**T*U or A = L*L**T, packed columnwise in a linear
</span><span class="comment">*</span><span class="comment">          array.  The j-th column of U or L is stored in the array AP
</span><span class="comment">*</span><span class="comment">          as follows:
</span><span class="comment">*</span><span class="comment">          if UPLO = 'U', AP(i + (j-1)*j/2) = U(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) = L(i,j) for j&lt;=i&lt;=n.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
</span><span class="comment">*</span><span class="comment">          On entry, the right hand side matrix B.
</span><span class="comment">*</span><span class="comment">          On exit, the solution matrix X.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDB     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array B.  LDB &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 = -i, the i-th argument had an illegal value
</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">     .. Local Scalars ..
</span>      LOGICAL            UPPER
      INTEGER            I
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.62"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.63"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           DTPSV, <a name="XERBLA.66"></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
<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.76"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
      IF( .NOT.UPPER .AND. .NOT.<a name="LSAME.77"></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( NRHS.LT.0 ) THEN
         INFO = -3
      ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
         INFO = -6
      END IF
      IF( INFO.NE.0 ) THEN
         CALL <a name="XERBLA.87"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="DPPTRS.87"></a><a href="dpptrs.f.html#DPPTRS.1">DPPTRS</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 .OR. NRHS.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">        Solve A*X = B where A = U'*U.
</span><span class="comment">*</span><span class="comment">
</span>         DO 10 I = 1, NRHS
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve U'*X = B, overwriting B with X.
</span><span class="comment">*</span><span class="comment">
</span>            CALL DTPSV( <span class="string">'Upper'</span>, <span class="string">'Transpose'</span>, <span class="string">'Non-unit'</span>, N, AP,
     $                  B( 1, I ), 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve U*X = B, overwriting B with X.
</span><span class="comment">*</span><span class="comment">
</span>            CALL DTPSV( <span class="string">'Upper'</span>, <span class="string">'No transpose'</span>, <span class="string">'Non-unit'</span>, N, AP,
     $                  B( 1, I ), 1 )
   10    CONTINUE
      ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Solve A*X = B where A = L*L'.
</span><span class="comment">*</span><span class="comment">
</span>         DO 20 I = 1, NRHS
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve L*Y = B, overwriting B with X.
</span><span class="comment">*</span><span class="comment">
</span>            CALL DTPSV( <span class="string">'Lower'</span>, <span class="string">'No transpose'</span>, <span class="string">'Non-unit'</span>, N, AP,
     $                  B( 1, I ), 1 )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">           Solve L'*X = Y, overwriting B with X.
</span><span class="comment">*</span><span class="comment">
</span>            CALL DTPSV( <span class="string">'Lower'</span>, <span class="string">'Transpose'</span>, <span class="string">'Non-unit'</span>, N, AP,
     $                  B( 1, I ), 1 )
   20    CONTINUE
      END IF
<span class="comment">*</span><span class="comment">
</span>      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="DPPTRS.132"></a><a href="dpptrs.f.html#DPPTRS.1">DPPTRS</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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