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SUBROUTINE <a name="CHETF2.1"></a><a href="chetf2.f.html#CHETF2.1">CHETF2</a>( UPLO, N, A, LDA, IPIV, 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, * )
<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="CHETF2.19"></a><a href="chetf2.f.html#CHETF2.1">CHETF2</a> computes the factorization of a complex Hermitian matrix A
</span><span class="comment">*</span><span class="comment"> using the Bunch-Kaufman diagonal pivoting method:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A = U*D*U' or A = L*D*L'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> where U (or L) is a product of permutation and unit upper (lower)
</span><span class="comment">*</span><span class="comment"> triangular matrices, U' is the conjugate transpose of U, and D is
</span><span class="comment">*</span><span class="comment"> Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
</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"> Hermitian 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 >= 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 Hermitian 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, the block diagonal matrix D and the multipliers used
</span><span class="comment">*</span><span class="comment"> to obtain the factor U or L (see below for further details).
</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 (output) 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"> If IPIV(k) > 0, then rows and columns k and IPIV(k) were
</span><span class="comment">*</span><span class="comment"> interchanged and D(k,k) is a 1-by-1 diagonal block.
</span><span class="comment">*</span><span class="comment"> If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
</span><span class="comment">*</span><span class="comment"> columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
</span><span class="comment">*</span><span class="comment"> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) =
</span><span class="comment">*</span><span class="comment"> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
</span><span class="comment">*</span><span class="comment"> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
</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 = -k, the k-th argument had an illegal value
</span><span class="comment">*</span><span class="comment"> > 0: if INFO = k, D(k,k) is exactly zero. The factorization
</span><span class="comment">*</span><span class="comment"> has been completed, but the block diagonal matrix D is
</span><span class="comment">*</span><span class="comment"> exactly singular, and division by zero will occur if it
</span><span class="comment">*</span><span class="comment"> is used to solve a system of equations.
</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"> 09-29-06 - patch from
</span><span class="comment">*</span><span class="comment"> Bobby Cheng, MathWorks
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Replace l.210 and l.392
</span><span class="comment">*</span><span class="comment"> IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
</span><span class="comment">*</span><span class="comment"> by
</span><span class="comment">*</span><span class="comment"> IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. <a name="SISNAN.84"></a><a href="sisnan.f.html#SISNAN.1">SISNAN</a>(ABSAKK) ) THEN
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> 01-01-96 - Based on modifications by
</span><span class="comment">*</span><span class="comment"> J. Lewis, Boeing Computer Services Company
</span><span class="comment">*</span><span class="comment"> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If UPLO = 'U', then A = U*D*U', where
</span><span class="comment">*</span><span class="comment"> U = P(n)*U(n)* ... *P(k)U(k)* ...,
</span><span class="comment">*</span><span class="comment"> i.e., U is a product of terms P(k)*U(k), where k decreases from n to
</span><span class="comment">*</span><span class="comment"> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
</span><span class="comment">*</span><span class="comment"> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
</span><span class="comment">*</span><span class="comment"> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
</span><span class="comment">*</span><span class="comment"> that if the diagonal block D(k) is of order s (s = 1 or 2), then
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ( I v 0 ) k-s
</span><span class="comment">*</span><span class="comment"> U(k) = ( 0 I 0 ) s
</span><span class="comment">*</span><span class="comment"> ( 0 0 I ) n-k
</span><span class="comment">*</span><span class="comment"> k-s s n-k
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
</span><span class="comment">*</span><span class="comment"> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
</span><span class="comment">*</span><span class="comment"> and A(k,k), and v overwrites A(1:k-2,k-1:k).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If UPLO = 'L', then A = L*D*L', where
</span><span class="comment">*</span><span class="comment"> L = P(1)*L(1)* ... *P(k)*L(k)* ...,
</span><span class="comment">*</span><span class="comment"> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
</span><span class="comment">*</span><span class="comment"> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
</span><span class="comment">*</span><span class="comment"> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
</span><span class="comment">*</span><span class="comment"> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
</span><span class="comment">*</span><span class="comment"> that if the diagonal block D(k) is of order s (s = 1 or 2), then
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ( I 0 0 ) k-1
</span><span class="comment">*</span><span class="comment"> L(k) = ( 0 I 0 ) s
</span><span class="comment">*</span><span class="comment"> ( 0 v I ) n-k-s+1
</span><span class="comment">*</span><span class="comment"> k-1 s n-k-s+1
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
</span><span class="comment">*</span><span class="comment"> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
</span><span class="comment">*</span><span class="comment"> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
</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 ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
REAL EIGHT, SEVTEN
PARAMETER ( EIGHT = 8.0E+0, SEVTEN = 17.0E+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL UPPER
INTEGER I, IMAX, J, JMAX, K, KK, KP, KSTEP
REAL ABSAKK, ALPHA, COLMAX, D, D11, D22, R1, ROWMAX,
$ TT
COMPLEX D12, D21, T, WK, WKM1, WKP1, ZDUM
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.140"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="SISNAN.140"></a><a href="sisnan.f.html#SISNAN.1">SISNAN</a>
INTEGER ICAMAX
REAL <a name="SLAPY2.142"></a><a href="slapy2.f.html#SLAPY2.1">SLAPY2</a>
EXTERNAL <a name="LSAME.143"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, ICAMAX, <a name="SLAPY2.143"></a><a href="slapy2.f.html#SLAPY2.1">SLAPY2</a>, <a name="SISNAN.143"></a><a href="sisnan.f.html#SISNAN.1">SISNAN</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL CHER, CSSCAL, CSWAP, <a name="XERBLA.146"></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, AIMAG, CMPLX, CONJG, MAX, REAL, SQRT
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Statement Functions ..
</span> REAL CABS1
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Statement Function definitions ..
</span> CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
<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.162"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> )
IF( .NOT.UPPER .AND. .NOT.<a name="LSAME.163"></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.171"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="CHETF2.171"></a><a href="chetf2.f.html#CHETF2.1">CHETF2</a>'</span>, -INFO )
RETURN
END IF
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