cpptri.f.html
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SUBROUTINE <a name="CPPTRI.1"></a><a href="cpptri.f.html#CPPTRI.1">CPPTRI</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> COMPLEX 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="CPPTRI.18"></a><a href="cpptri.f.html#CPPTRI.1">CPPTRI</a> computes the inverse of a complex Hermitian positive definite
</span><span class="comment">*</span><span class="comment"> matrix A using the Cholesky factorization A = U**H*U or A = L*L**H
</span><span class="comment">*</span><span class="comment"> computed by <a name="CPPTRF.20"></a><a href="cpptrf.f.html#CPPTRF.1">CPPTRF</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 triangular factor is stored in AP;
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangular factor is stored in AP.
</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 >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AP (input/output) COMPLEX array, dimension (N*(N+1)/2)
</span><span class="comment">*</span><span class="comment"> On entry, the triangular factor U or L from the Cholesky
</span><span class="comment">*</span><span class="comment"> factorization A = U**H*U or A = L*L**H, packed columnwise as
</span><span class="comment">*</span><span class="comment"> a linear array. The j-th column of U or L is stored in the
</span><span class="comment">*</span><span class="comment"> array AP as follows:
</span><span class="comment">*</span><span class="comment"> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
</span><span class="comment">*</span><span class="comment"> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, the upper or lower triangle of the (Hermitian)
</span><span class="comment">*</span><span class="comment"> inverse of A, overwriting the input factor U or L.
</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"> < 0: if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment"> > 0: if INFO = i, the (i,i) element of the factor U or L is
</span><span class="comment">*</span><span class="comment"> zero, and the inverse could not be computed.
</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> REAL ONE
PARAMETER ( ONE = 1.0E+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, JJN
REAL AJJ
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.61"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
COMPLEX CDOTC
EXTERNAL <a name="LSAME.63"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, CDOTC
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL CHPR, CSSCAL, CTPMV, <a name="CTPTRI.66"></a><a href="ctptri.f.html#CTPTRI.1">CTPTRI</a>, <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 REAL
<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
END IF
IF( INFO.NE.0 ) THEN
CALL <a name="XERBLA.83"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="CPPTRI.83"></a><a href="cpptri.f.html#CPPTRI.1">CPPTRI</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><span class="comment">*</span><span class="comment"> Invert the triangular Cholesky factor U or L.
</span><span class="comment">*</span><span class="comment">
</span> CALL <a name="CTPTRI.94"></a><a href="ctptri.f.html#CTPTRI.1">CTPTRI</a>( UPLO, <span class="string">'Non-unit'</span>, N, AP, INFO )
IF( INFO.GT.0 )
$ RETURN
IF( UPPER ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Compute the product inv(U) * inv(U)'.
</span><span class="comment">*</span><span class="comment">
</span> JJ = 0
DO 10 J = 1, N
JC = JJ + 1
JJ = JJ + J
IF( J.GT.1 )
$ CALL CHPR( <span class="string">'Upper'</span>, J-1, ONE, AP( JC ), 1, AP )
AJJ = AP( JJ )
CALL CSSCAL( J, AJJ, AP( JC ), 1 )
10 CONTINUE
<span class="comment">*</span><span class="comment">
</span> ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Compute the product inv(L)' * inv(L).
</span><span class="comment">*</span><span class="comment">
</span> JJ = 1
DO 20 J = 1, N
JJN = JJ + N - J + 1
AP( JJ ) = REAL( CDOTC( N-J+1, AP( JJ ), 1, AP( JJ ), 1 ) )
IF( J.LT.N )
$ CALL CTPMV( <span class="string">'Lower'</span>, <span class="string">'Conjugate transpose'</span>, <span class="string">'Non-unit'</span>,
$ N-J, AP( JJN ), AP( JJ+1 ), 1 )
JJ = JJN
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="CPPTRI.128"></a><a href="cpptri.f.html#CPPTRI.1">CPPTRI</a>
</span><span class="comment">*</span><span class="comment">
</span> END
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