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SUBROUTINE <a name="CHETRI.1"></a><a href="chetri.f.html#CHETRI.1">CHETRI</a>( UPLO, N, A, LDA, IPIV, WORK, 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> INTEGER IPIV( * )
COMPLEX A( LDA, * ), WORK( * )
<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="CHETRI.19"></a><a href="chetri.f.html#CHETRI.1">CHETRI</a> computes the inverse of a complex Hermitian indefinite matrix
</span><span class="comment">*</span><span class="comment"> A using the factorization A = U*D*U**H or A = L*D*L**H computed by
</span><span class="comment">*</span><span class="comment"> <a name="CHETRF.21"></a><a href="chetrf.f.html#CHETRF.1">CHETRF</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"> Specifies whether the details of the factorization are stored
</span><span class="comment">*</span><span class="comment"> as an upper or lower triangular matrix.
</span><span class="comment">*</span><span class="comment"> = 'U': Upper triangular, form is A = U*D*U**H;
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangular, form is A = L*D*L**H.
</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"> A (input/output) COMPLEX array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment"> On entry, the block diagonal matrix D and the multipliers
</span><span class="comment">*</span><span class="comment"> used to obtain the factor U or L as computed by <a name="CHETRF.37"></a><a href="chetrf.f.html#CHETRF.1">CHETRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, the (Hermitian) inverse of the original
</span><span class="comment">*</span><span class="comment"> matrix. If UPLO = 'U', the upper triangular part of the
</span><span class="comment">*</span><span class="comment"> inverse is formed and the part of A below the diagonal is not
</span><span class="comment">*</span><span class="comment"> referenced; if UPLO = 'L' the lower triangular part of the
</span><span class="comment">*</span><span class="comment"> inverse is formed and the part of A above the diagonal is
</span><span class="comment">*</span><span class="comment"> not referenced.
</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 >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IPIV (input) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment"> Details of the interchanges and the block structure of D
</span><span class="comment">*</span><span class="comment"> as determined by <a name="CHETRF.51"></a><a href="chetrf.f.html#CHETRF.1">CHETRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace) COMPLEX array, dimension (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"> < 0: if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment"> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
</span><span class="comment">*</span><span class="comment"> 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
COMPLEX CONE, ZERO
PARAMETER ( ONE = 1.0E+0, CONE = ( 1.0E+0, 0.0E+0 ),
$ ZERO = ( 0.0E+0, 0.0E+0 ) )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL UPPER
INTEGER J, K, KP, KSTEP
REAL AK, AKP1, D, T
COMPLEX AKKP1, TEMP
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.76"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
COMPLEX CDOTC
EXTERNAL <a name="LSAME.78"></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 CCOPY, CHEMV, CSWAP, <a name="XERBLA.81"></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 ABS, CONJG, MAX, 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.91"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
IF( .NOT.UPPER .AND. .NOT.<a name="LSAME.92"></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.100"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="CHETRI.100"></a><a href="chetri.f.html#CHETRI.1">CHETRI</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"> Check that the diagonal matrix D is nonsingular.
</span><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"> Upper triangular storage: examine D from bottom to top
</span><span class="comment">*</span><span class="comment">
</span> DO 10 INFO = N, 1, -1
IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
$ RETURN
10 CONTINUE
ELSE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Lower triangular storage: examine D from top to bottom.
</span><span class="comment">*</span><span class="comment">
</span> DO 20 INFO = 1, N
IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
$ RETURN
20 CONTINUE
END IF
INFO = 0
<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 inv(A) from the factorization A = U*D*U'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> K is the main loop index, increasing from 1 to N in steps of
</span><span class="comment">*</span><span class="comment"> 1 or 2, depending on the size of the diagonal blocks.
</span><span class="comment">*</span><span class="comment">
</span> K = 1
30 CONTINUE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If K > N, exit from loop.
</span><span class="comment">*</span><span class="comment">
</span> IF( K.GT.N )
$ GO TO 50
<span class="comment">*</span><span class="comment">
</span> IF( IPIV( K ).GT.0 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> 1 x 1 diagonal block
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Invert the diagonal block.
</span><span class="comment">*</span><span class="comment">
</span> A( K, K ) = ONE / REAL( A( K, K ) )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Compute column K of the inverse.
</span><span class="comment">*</span><span class="comment">
</span> IF( K.GT.1 ) THEN
CALL CCOPY( K-1, A( 1, K ), 1, WORK, 1 )
CALL CHEMV( UPLO, K-1, -CONE, A, LDA, WORK, 1, ZERO,
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