--- /dev/null
+*> \brief \b CHETF2_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (unblocked algorithm).
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download CHETF2_ROOK + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chetf2_rook.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chetf2_rook.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chetf2_rook.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE CHETF2_ROOK( UPLO, N, A, LDA, IPIV, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, LDA, N
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX A( LDA, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> CHETF2_ROOK computes the factorization of a complex Hermitian matrix A
+*> using the bounded Bunch-Kaufman ("rook") diagonal pivoting method:
+*>
+*> A = U*D*U**H or A = L*D*L**H
+*>
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, U**H is the conjugate transpose of U, and D is
+*> Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
+*>
+*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the upper or lower triangular part of the
+*> Hermitian matrix A is stored:
+*> = 'U': Upper triangular
+*> = 'L': Lower triangular
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX array, dimension (LDA,N)
+*> On entry, the Hermitian matrix A. If UPLO = 'U', the leading
+*> n-by-n upper triangular part of A contains the upper
+*> triangular part of the matrix A, and the strictly lower
+*> triangular part of A is not referenced. If UPLO = 'L', the
+*> leading n-by-n lower triangular part of A contains the lower
+*> triangular part of the matrix A, and the strictly upper
+*> triangular part of A is not referenced.
+*>
+*> On exit, the block diagonal matrix D and the multipliers used
+*> to obtain the factor U or L (see below for further details).
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> Details of the interchanges and the block structure of D.
+*>
+*> If UPLO = 'U':
+*> If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*> interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*> If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
+*> columns k and -IPIV(k) were interchanged and rows and
+*> columns k-1 and -IPIV(k-1) were inerchaged,
+*> D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
+*>
+*> If UPLO = 'L':
+*> If IPIV(k) > 0, then rows and columns k and IPIV(k)
+*> were interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
+*> columns k and -IPIV(k) were interchanged and rows and
+*> columns k+1 and -IPIV(k+1) were inerchaged,
+*> D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -k, the k-th argument had an illegal value
+*> > 0: if INFO = k, D(k,k) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, and division by zero will occur if it
+*> is used to solve a system of equations.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2012
+*
+*> \ingroup complexHEcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> If UPLO = 'U', then A = U*D*U**H, where
+*> U = P(n)*U(n)* ... *P(k)U(k)* ...,
+*> i.e., U is a product of terms P(k)*U(k), where k decreases from n to
+*> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
+*> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
+*> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
+*> that if the diagonal block D(k) is of order s (s = 1 or 2), then
+*>
+*> ( I v 0 ) k-s
+*> U(k) = ( 0 I 0 ) s
+*> ( 0 0 I ) n-k
+*> k-s s n-k
+*>
+*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
+*> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
+*> and A(k,k), and v overwrites A(1:k-2,k-1:k).
+*>
+*> If UPLO = 'L', then A = L*D*L**H, where
+*> L = P(1)*L(1)* ... *P(k)*L(k)* ...,
+*> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
+*> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
+*> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
+*> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
+*> that if the diagonal block D(k) is of order s (s = 1 or 2), then
+*>
+*> ( I 0 0 ) k-1
+*> L(k) = ( 0 I 0 ) s
+*> ( 0 v I ) n-k-s+1
+*> k-1 s n-k-s+1
+*>
+*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
+*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
+*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> \verbatim
+*>
+*> November 2012, Igor Kozachenko,
+*> Computer Science Division,
+*> University of California, Berkeley
+*>
+*> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*> School of Mathematics,
+*> University of Manchester
+*>
+*> 01-01-96 - Based on modifications by
+*> J. Lewis, Boeing Computer Services Company
+*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*> \endverbatim
+*
+* =====================================================================
+ SUBROUTINE CHETF2_ROOK( UPLO, N, A, LDA, IPIV, INFO )
+*
+* -- LAPACK computational routine (version 3.4.2) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2012
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER INFO, LDA, N
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX A( LDA, * )
+* ..
+*
+* ======================================================================
+*
+* .. Parameters ..
+ REAL ZERO, ONE
+ PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
+ REAL EIGHT, SEVTEN
+ PARAMETER ( EIGHT = 8.0E+0, SEVTEN = 17.0E+0 )
+* ..
+* .. Local Scalars ..
+ LOGICAL DONE, UPPER
+ INTEGER I, II, IMAX, ITEMP, J, JMAX, K, KK, KP, KSTEP,
+ $ P
+ REAL ABSAKK, ALPHA, COLMAX, D, D11, D22, R1, STEMP,
+ $ ROWMAX, TT, SFMIN
+ COMPLEX D12, D21, T, WK, WKM1, WKP1, Z
+* ..
+* .. External Functions ..
+*
+ LOGICAL LSAME
+ INTEGER ICAMAX
+ REAL SLAMCH, SLAPY2
+ EXTERNAL LSAME, ICAMAX, SLAMCH, SLAPY2
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA, CSSCAL, CHER, CSWAP
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, AIMAG, CMPLX, CONJG, MAX, REAL, SQRT
+* ..
+* .. Statement Functions ..
+ REAL CABS1
+* ..
+* .. Statement Function definitions ..
+ CABS1( Z ) = ABS( REAL( Z ) ) + ABS( AIMAG( Z ) )
+* ..
+* .. Executable Statements ..
+*
+* Test the input parameters.
+*
+ INFO = 0
+ UPPER = LSAME( UPLO, 'U' )
+ IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) 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 XERBLA( 'CHETF2_ROOK', -INFO )
+ RETURN
+ END IF
+*
+* Initialize ALPHA for use in choosing pivot block size.
+*
+ ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT
+*
+* Compute machine safe minimum
+*
+ SFMIN = SLAMCH( 'S' )
+*
+ IF( UPPER ) THEN
+*
+* Factorize A as U*D*U**H using the upper triangle of A
+*
+* K is the main loop index, decreasing from N to 1 in steps of
+* 1 or 2
+*
+ K = N
+ 10 CONTINUE
+*
+* If K < 1, exit from loop
+*
+ IF( K.LT.1 )
+ $ GO TO 70
+ KSTEP = 1
+ P = K
+*
+* Determine rows and columns to be interchanged and whether
+* a 1-by-1 or 2-by-2 pivot block will be used
+*
+ ABSAKK = ABS( REAL( A( K, K ) ) )
+*
+* IMAX is the row-index of the largest off-diagonal element in
+* column K, and COLMAX is its absolute value.
+* Determine both COLMAX and IMAX.
+*
+ IF( K.GT.1 ) THEN
+ IMAX = ICAMAX( K-1, A( 1, K ), 1 )
+ COLMAX = CABS1( A( IMAX, K ) )
+ ELSE
+ COLMAX = ZERO
+ END IF
+*
+ IF( ( MAX( ABSAKK, COLMAX ).EQ.ZERO ) ) THEN
+*
+* Column K is zero or underflow: set INFO and continue
+*
+ IF( INFO.EQ.0 )
+ $ INFO = K
+ KP = K
+ A( K, K ) = REAL( A( K, K ) )
+ ELSE
+*
+* ============================================================
+*
+* BEGIN pivot search
+*
+* Case(1)
+* Equivalent to testing for ABSAKK.GE.ALPHA*COLMAX
+* (used to handle NaN and Inf)
+*
+ IF( .NOT.( ABSAKK.LT.ALPHA*COLMAX ) ) THEN
+*
+* no interchange, use 1-by-1 pivot block
+*
+ KP = K
+*
+ ELSE
+*
+ DONE = .FALSE.
+*
+* Loop until pivot found
+*
+ 12 CONTINUE
+*
+* BEGIN pivot search loop body
+*
+*
+* JMAX is the column-index of the largest off-diagonal
+* element in row IMAX, and ROWMAX is its absolute value.
+* Determine both ROWMAX and JMAX.
+*
+ IF( IMAX.NE.K ) THEN
+ JMAX = IMAX + ICAMAX( K-IMAX, A( IMAX, IMAX+1 ),
+ $ LDA )
+ ROWMAX = CABS1( A( IMAX, JMAX ) )
+ ELSE
+ ROWMAX = ZERO
+ END IF
+*
+ IF( IMAX.GT.1 ) THEN
+ ITEMP = ICAMAX( IMAX-1, A( 1, IMAX ), 1 )
+ STEMP = CABS1( A( ITEMP, IMAX ) )
+ IF( STEMP.GT.ROWMAX ) THEN
+ ROWMAX = STEMP
+ JMAX = ITEMP
+ END IF
+ END IF
+*
+* Case(2)
+* Equivalent to testing for
+* ABS( REAL( W( IMAX,KW-1 ) ) ).GE.ALPHA*ROWMAX
+* (used to handle NaN and Inf)
+*
+ IF( .NOT.( ABS( REAL( A( IMAX, IMAX ) ) )
+ $ .LT.ALPHA*ROWMAX ) ) THEN
+*
+* interchange rows and columns K and IMAX,
+* use 1-by-1 pivot block
+*
+ KP = IMAX
+ DONE = .TRUE.
+*
+* Case(3)
+* Equivalent to testing for ROWMAX.EQ.COLMAX,
+* (used to handle NaN and Inf)
+*
+ ELSE IF( ( P.EQ.JMAX ) .OR. ( ROWMAX.LE.COLMAX ) )
+ $ THEN
+*
+* interchange rows and columns K-1 and IMAX,
+* use 2-by-2 pivot block
+*
+ KP = IMAX
+ KSTEP = 2
+ DONE = .TRUE.
+*
+* Case(4)
+ ELSE
+*
+* Pivot not found: set params and repeat
+*
+ P = IMAX
+ COLMAX = ROWMAX
+ IMAX = JMAX
+ END IF
+*
+* END pivot search loop body
+*
+ IF( .NOT.DONE ) GOTO 12
+*
+ END IF
+*
+* END pivot search
+*
+* ============================================================
+*
+* KK is the column of A where pivoting step stopped
+*
+ KK = K + KSTEP - 1
+*
+* For only a 2x2 pivot, interchange rows and columns K and P
+* in the leading submatrix A(1:k,1:k)
+*
+ IF( ( KSTEP.EQ.2 ) .AND. ( P.NE.K ) ) THEN
+* (1) Swap columnar parts
+ IF( P.GT.1 )
+ $ CALL CSWAP( P-1, A( 1, K ), 1, A( 1, P ), 1 )
+* (2) Swap and conjugate middle parts
+ DO 14 J = P + 1, K - 1
+ T = CONJG( A( J, K ) )
+ A( J, K ) = CONJG( A( P, J ) )
+ A( P, J ) = T
+ 14 CONTINUE
+* (3) Swap and conjugate corner elements at row-col interserction
+ A( P, K ) = CONJG( A( P, K ) )
+* (4) Swap diagonal elements at row-col intersection
+ R1 = REAL( A( K, K ) )
+ A( K, K ) = REAL( A( P, P ) )
+ A( P, P ) = R1
+ END IF
+*
+* For both 1x1 and 2x2 pivots, interchange rows and
+* columns KK and KP in the leading submatrix A(1:k,1:k)
+*
+ IF( KP.NE.KK ) THEN
+* (1) Swap columnar parts
+ IF( KP.GT.1 )
+ $ CALL CSWAP( KP-1, A( 1, KK ), 1, A( 1, KP ), 1 )
+* (2) Swap and conjugate middle parts
+ DO 15 J = KP + 1, KK - 1
+ T = CONJG( A( J, KK ) )
+ A( J, KK ) = CONJG( A( KP, J ) )
+ A( KP, J ) = T
+ 15 CONTINUE
+* (3) Swap and conjugate corner elements at row-col interserction
+ A( KP, KK ) = CONJG( A( KP, KK ) )
+* (4) Swap diagonal elements at row-col intersection
+ R1 = REAL( A( KK, KK ) )
+ A( KK, KK ) = REAL( A( KP, KP ) )
+ A( KP, KP ) = R1
+*
+ IF( KSTEP.EQ.2 ) THEN
+* (*) Make sure that diagonal element of pivot is real
+ A( K, K ) = REAL( A( K, K ) )
+* (5) Swap row elements
+ T = A( K-1, K )
+ A( K-1, K ) = A( KP, K )
+ A( KP, K ) = T
+ END IF
+ ELSE
+* (*) Make sure that diagonal element of pivot is real
+ A( K, K ) = REAL( A( K, K ) )
+ IF( KSTEP.EQ.2 )
+ $ A( K-1, K-1 ) = REAL( A( K-1, K-1 ) )
+ END IF
+*
+* Update the leading submatrix
+*
+ IF( KSTEP.EQ.1 ) THEN
+*
+* 1-by-1 pivot block D(k): column k now holds
+*
+* W(k) = U(k)*D(k)
+*
+* where U(k) is the k-th column of U
+*
+ IF( K.GT.1 ) THEN
+*
+* Perform a rank-1 update of A(1:k-1,1:k-1) and
+* store U(k) in column k
+*
+ IF( ABS( REAL( A( K, K ) ) ).GE.SFMIN ) THEN
+*
+* Perform a rank-1 update of A(1:k-1,1:k-1) as
+* A := A - U(k)*D(k)*U(k)**T
+* = A - W(k)*1/D(k)*W(k)**T
+*
+ D11 = ONE / REAL( A( K, K ) )
+ CALL CHER( UPLO, K-1, -D11, A( 1, K ), 1, A, LDA )
+*
+* Store U(k) in column k
+*
+ CALL ZSCAL( K-1, D11, A( 1, K ), 1 )
+ ELSE
+*
+* Store L(k) in column K
+*
+ D11 = REAL( A( K, K ) )
+ DO 16 II = 1, K - 1
+ A( II, K ) = A( II, K ) / D11
+ 16 CONTINUE
+*
+* Perform a rank-1 update of A(k+1:n,k+1:n) as
+* A := A - U(k)*D(k)*U(k)**T
+* = A - W(k)*(1/D(k))*W(k)**T
+* = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T
+*
+ CALL CHER( UPLO, K-1, -D11, A( 1, K ), 1, A, LDA )
+ END IF
+ END IF
+*
+ ELSE
+*
+* 2-by-2 pivot block D(k): columns k and k-1 now hold
+*
+* ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
+*
+* where U(k) and U(k-1) are the k-th and (k-1)-th columns
+* of U
+*
+* Perform a rank-2 update of A(1:k-2,1:k-2) as
+*
+* A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T
+* = A - ( ( A(k-1)A(k) )*inv(D(k)) ) * ( A(k-1)A(k) )**T
+*
+* and store L(k) and L(k+1) in columns k and k+1
+*
+ IF( K.GT.2 ) THEN
+* D = |A12|
+ D = SLAPY2( REAL( A( K-1, K ) ),
+ $ AIMAG( A( K-1, K ) ) )
+ D11 = A( K, K ) / D
+ D22 = A( K-1, K-1 ) / D
+ D12 = A( K-1, K ) / D
+ TT = ONE / ( D11*D22-ONE )
+*
+ DO 30 J = K - 2, 1, -1
+*
+* Compute D21 * ( W(k)W(k+1) ) * inv(D(k)) for row J
+*
+ WKM1 = TT*( D11*A( J, K-1 )-CONJG( D12 )*
+ $ A( J, K ) )
+ WK = TT*( D22*A( J, K )-D12*A( J, K-1 ) )
+*
+* Perform a rank-2 update of A(1:k-2,1:k-2)
+*
+ DO 20 I = J, 1, -1
+ A( I, J ) = A( I, J ) -
+ $ ( A( I, K ) / D )*CONJG( WK ) -
+ $ ( A( I, K-1 ) / D )*CONJG( WKM1 )
+ 20 CONTINUE
+*
+* Store U(k) and U(k-1) in cols k and k-1 for row J
+*
+ A( J, K ) = WK / D
+ A( J, K-1 ) = WKM1 / D
+* (*) Make sure that diagonal element of pivot is real
+ A( J, J ) = CMPLX( REAL( A( J, J ) ), ZERO )
+*
+ 30 CONTINUE
+*
+ END IF
+*
+ END IF
+*
+ END IF
+*
+* Store details of the interchanges in IPIV
+*
+ IF( KSTEP.EQ.1 ) THEN
+ IPIV( K ) = KP
+ ELSE
+ IPIV( K ) = -P
+ IPIV( K-1 ) = -KP
+ END IF
+*
+* Decrease K and return to the start of the main loop
+*
+ K = K - KSTEP
+ GO TO 10
+*
+ ELSE
+*
+* Factorize A as L*D*L**H using the lower triangle of A
+*
+* K is the main loop index, increasing from 1 to N in steps of
+* 1 or 2
+*
+ K = 1
+ 40 CONTINUE
+*
+* If K > N, exit from loop
+*
+ IF( K.GT.N )
+ $ GO TO 70
+ KSTEP = 1
+ P = K
+*
+* Determine rows and columns to be interchanged and whether
+* a 1-by-1 or 2-by-2 pivot block will be used
+*
+ ABSAKK = ABS( REAL( A( K, K ) ) )
+*
+* IMAX is the row-index of the largest off-diagonal element in
+* column K, and COLMAX is its absolute value.
+* Determine both COLMAX and IMAX.
+*
+ IF( K.LT.N ) THEN
+ IMAX = K + ICAMAX( N-K, A( K+1, K ), 1 )
+ COLMAX = CABS1( A( IMAX, K ) )
+ ELSE
+ COLMAX = ZERO
+ END IF
+*
+ IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
+*
+* Column K is zero or underflow: set INFO and continue
+*
+ IF( INFO.EQ.0 )
+ $ INFO = K
+ KP = K
+ A( K, K ) = REAL( A( K, K ) )
+ ELSE
+*
+* ============================================================
+*
+* BEGIN pivot search
+*
+* Case(1)
+* Equivalent to testing for ABSAKK.GE.ALPHA*COLMAX
+* (used to handle NaN and Inf)
+*
+ IF( .NOT.( ABSAKK.LT.ALPHA*COLMAX ) ) THEN
+*
+* no interchange, use 1-by-1 pivot block
+*
+ KP = K
+*
+ ELSE
+*
+ DONE = .FALSE.
+*
+* Loop until pivot found
+*
+ 42 CONTINUE
+*
+* BEGIN pivot search loop body
+*
+*
+* JMAX is the column-index of the largest off-diagonal
+* element in row IMAX, and ROWMAX is its absolute value.
+* Determine both ROWMAX and JMAX.
+*
+ IF( IMAX.NE.K ) THEN
+ JMAX = K - 1 + ICAMAX( IMAX-K, A( IMAX, K ), LDA )
+ ROWMAX = CABS1( A( IMAX, JMAX ) )
+ ELSE
+ ROWMAX = ZERO
+ END IF
+*
+ IF( IMAX.LT.N ) THEN
+ ITEMP = IMAX + ICAMAX( N-IMAX, A( IMAX+1, IMAX ),
+ $ 1 )
+ STEMP = CABS1( A( ITEMP, IMAX ) )
+ IF( STEMP.GT.ROWMAX ) THEN
+ ROWMAX = STEMP
+ JMAX = ITEMP
+ END IF
+ END IF
+*
+* Case(2)
+* Equivalent to testing for
+* ABS( REAL( W( IMAX,KW-1 ) ) ).GE.ALPHA*ROWMAX
+* (used to handle NaN and Inf)
+*
+ IF( .NOT.( ABS( REAL( A( IMAX, IMAX ) ) )
+ $ .LT.ALPHA*ROWMAX ) ) THEN
+*
+* interchange rows and columns K and IMAX,
+* use 1-by-1 pivot block
+*
+ KP = IMAX
+ DONE = .TRUE.
+*
+* Case(3)
+* Equivalent to testing for ROWMAX.EQ.COLMAX,
+* (used to handle NaN and Inf)
+*
+ ELSE IF( ( P.EQ.JMAX ) .OR. ( ROWMAX.LE.COLMAX ) )
+ $ THEN
+*
+* interchange rows and columns K+1 and IMAX,
+* use 2-by-2 pivot block
+*
+ KP = IMAX
+ KSTEP = 2
+ DONE = .TRUE.
+*
+* Case(4)
+ ELSE
+*
+* Pivot not found: set params and repeat
+*
+ P = IMAX
+ COLMAX = ROWMAX
+ IMAX = JMAX
+ END IF
+*
+*
+* END pivot search loop body
+*
+ IF( .NOT.DONE ) GOTO 42
+*
+ END IF
+*
+* END pivot search
+*
+* ============================================================
+*
+* KK is the column of A where pivoting step stopped
+*
+ KK = K + KSTEP - 1
+*
+* For only a 2x2 pivot, interchange rows and columns K and P
+* in the trailing submatrix A(k:n,k:n)
+*
+ IF( ( KSTEP.EQ.2 ) .AND. ( P.NE.K ) ) THEN
+* (1) Swap columnar parts
+ IF( P.LT.N )
+ $ CALL CSWAP( N-P, A( P+1, K ), 1, A( P+1, P ), 1 )
+* (2) Swap and conjugate middle parts
+ DO 44 J = K + 1, P - 1
+ T = CONJG( A( J, K ) )
+ A( J, K ) = CONJG( A( P, J ) )
+ A( P, J ) = T
+ 44 CONTINUE
+* (3) Swap and conjugate corner elements at row-col interserction
+ A( P, K ) = CONJG( A( P, K ) )
+* (4) Swap diagonal elements at row-col intersection
+ R1 = REAL( A( K, K ) )
+ A( K, K ) = REAL( A( P, P ) )
+ A( P, P ) = R1
+ END IF
+*
+* For both 1x1 and 2x2 pivots, interchange rows and
+* columns KK and KP in the trailing submatrix A(k:n,k:n)
+*
+ IF( KP.NE.KK ) THEN
+* (1) Swap columnar parts
+ IF( KP.LT.N )
+ $ CALL CSWAP( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ), 1 )
+* (2) Swap and conjugate middle parts
+ DO 45 J = KK + 1, KP - 1
+ T = CONJG( A( J, KK ) )
+ A( J, KK ) = CONJG( A( KP, J ) )
+ A( KP, J ) = T
+ 45 CONTINUE
+* (3) Swap and conjugate corner elements at row-col interserction
+ A( KP, KK ) = CONJG( A( KP, KK ) )
+* (4) Swap diagonal elements at row-col intersection
+ R1 = REAL( A( KK, KK ) )
+ A( KK, KK ) = REAL( A( KP, KP ) )
+ A( KP, KP ) = R1
+*
+ IF( KSTEP.EQ.2 ) THEN
+* (*) Make sure that diagonal element of pivot is real
+ A( K, K ) = REAL( A( K, K ) )
+* (5) Swap row elements
+ T = A( K+1, K )
+ A( K+1, K ) = A( KP, K )
+ A( KP, K ) = T
+ END IF
+ ELSE
+* (*) Make sure that diagonal element of pivot is real
+ A( K, K ) = REAL( A( K, K ) )
+ IF( KSTEP.EQ.2 )
+ $ A( K+1, K+1 ) = REAL( A( K+1, K+1 ) )
+ END IF
+*
+* Update the trailing submatrix
+*
+ IF( KSTEP.EQ.1 ) THEN
+*
+* 1-by-1 pivot block D(k): column k of A now holds
+*
+* W(k) = L(k)*D(k),
+*
+* where L(k) is the k-th column of L
+*
+ IF( K.LT.N ) THEN
+*
+* Perform a rank-1 update of A(k+1:n,k+1:n) and
+* store L(k) in column k
+*
+* Handle division by a small number
+*
+ IF( ABS( REAL( A( K, K ) ) ).GE.SFMIN ) THEN
+*
+* Perform a rank-1 update of A(k+1:n,k+1:n) as
+* A := A - L(k)*D(k)*L(k)**T
+* = A - W(k)*(1/D(k))*W(k)**T
+*
+ D11 = ONE / REAL( A( K, K ) )
+ CALL CHER( UPLO, N-K, -D11, A( K+1, K ), 1,
+ $ A( K+1, K+1 ), LDA )
+*
+* Store L(k) in column k
+*
+ CALL CSSCAL( N-K, D11, A( K+1, K ), 1 )
+ ELSE
+*
+* Store L(k) in column k
+*
+ D11 = REAL( A( K, K ) )
+ DO 46 II = K + 1, N
+ A( II, K ) = A( II, K ) / D11
+ 46 CONTINUE
+*
+* Perform a rank-1 update of A(k+1:n,k+1:n) as
+* A := A - L(k)*D(k)*L(k)**T
+* = A - W(k)*(1/D(k))*W(k)**T
+* = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T
+*
+ CALL CHER( UPLO, N-K, -D11, A( K+1, K ), 1,
+ $ A( K+1, K+1 ), LDA )
+ END IF
+ END IF
+*
+ ELSE
+*
+* 2-by-2 pivot block D(k): columns k and k+1 now hold
+*
+* ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k)
+*
+* where L(k) and L(k+1) are the k-th and (k+1)-th columns
+* of L
+*
+*
+* Perform a rank-2 update of A(k+2:n,k+2:n) as
+*
+* A := A - ( L(k) L(k+1) ) * D(k) * ( L(k) L(k+1) )**T
+* = A - ( ( A(k)A(k+1) )*inv(D(k) ) * ( A(k)A(k+1) )**T
+*
+* and store L(k) and L(k+1) in columns k and k+1
+*
+ IF( K.LT.N-1 ) THEN
+* D = |A21|
+ D = SLAPY2( REAL( A( K+1, K ) ),
+ $ AIMAG( A( K+1, K ) ) )
+ D11 = REAL( A( K+1, K+1 ) ) / D
+ D22 = REAL( A( K, K ) ) / D
+ D21 = A( K+1, K ) / D
+ TT = ONE / ( D11*D22-ONE )
+*
+ DO 60 J = K + 2, N
+*
+* Compute D21 * ( W(k)W(k+1) ) * inv(D(k)) for row J
+*
+ WK = TT*( D11*A( J, K )-D21*A( J, K+1 ) )
+ WKP1 = TT*( D22*A( J, K+1 )-CONJG( D21 )*
+ $ A( J, K ) )
+*
+* Perform a rank-2 update of A(k+2:n,k+2:n)
+*
+ DO 50 I = J, N
+ A( I, J ) = A( I, J ) -
+ $ ( A( I, K ) / D )*CONJG( WK ) -
+ $ ( A( I, K+1 ) / D )*CONJG( WKP1 )
+ 50 CONTINUE
+*
+* Store L(k) and L(k+1) in cols k and k+1 for row J
+*
+ A( J, K ) = WK / D
+ A( J, K+1 ) = WKP1 / D
+* (*) Make sure that diagonal element of pivot is real
+ A( J, J ) = CMPLX( REAL( A( J, J ) ), ZERO )
+*
+ 60 CONTINUE
+*
+ END IF
+*
+ END IF
+*
+ END IF
+*
+* Store details of the interchanges in IPIV
+*
+ IF( KSTEP.EQ.1 ) THEN
+ IPIV( K ) = KP
+ ELSE
+ IPIV( K ) = -P
+ IPIV( K+1 ) = -KP
+ END IF
+*
+* Increase K and return to the start of the main loop
+*
+ K = K + KSTEP
+ GO TO 40
+*
+ END IF
+*
+ 70 CONTINUE
+*
+ RETURN
+*
+* End of CHETF2_ROOK
+*
+ END
--- /dev/null
+*> \brief \b ZHETF2_ROOK computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (unblocked algorithm).
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZHETF2_ROOK + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhetf2_rook.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhetf2_rook.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhetf2_rook.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZHETF2_ROOK( UPLO, N, A, LDA, IPIV, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, LDA, N
+* ..
+* .. Array Arguments ..
+* INTEGER IPIV( * )
+* COMPLEX*16 A( LDA, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZHETF2_ROOK computes the factorization of a complex Hermitian matrix A
+*> using the bounded Bunch-Kaufman ("rook") diagonal pivoting method:
+*>
+*> A = U*D*U**H or A = L*D*L**H
+*>
+*> where U (or L) is a product of permutation and unit upper (lower)
+*> triangular matrices, U**H is the conjugate transpose of U, and D is
+*> Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
+*>
+*> This is the unblocked version of the algorithm, calling Level 2 BLAS.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the upper or lower triangular part of the
+*> Hermitian matrix A is stored:
+*> = 'U': Upper triangular
+*> = 'L': Lower triangular
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,N)
+*> On entry, the Hermitian matrix A. If UPLO = 'U', the leading
+*> n-by-n upper triangular part of A contains the upper
+*> triangular part of the matrix A, and the strictly lower
+*> triangular part of A is not referenced. If UPLO = 'L', the
+*> leading n-by-n lower triangular part of A contains the lower
+*> triangular part of the matrix A, and the strictly upper
+*> triangular part of A is not referenced.
+*>
+*> On exit, the block diagonal matrix D and the multipliers used
+*> to obtain the factor U or L (see below for further details).
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] IPIV
+*> \verbatim
+*> IPIV is INTEGER array, dimension (N)
+*> Details of the interchanges and the block structure of D.
+*>
+*> If UPLO = 'U':
+*> If IPIV(k) > 0, then rows and columns k and IPIV(k) were
+*> interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*> If IPIV(k) < 0 and IPIV(k-1) < 0, then rows and
+*> columns k and -IPIV(k) were interchanged and rows and
+*> columns k-1 and -IPIV(k-1) were inerchaged,
+*> D(k-1:k,k-1:k) is a 2-by-2 diagonal block.
+*>
+*> If UPLO = 'L':
+*> If IPIV(k) > 0, then rows and columns k and IPIV(k)
+*> were interchanged and D(k,k) is a 1-by-1 diagonal block.
+*>
+*> If IPIV(k) < 0 and IPIV(k+1) < 0, then rows and
+*> columns k and -IPIV(k) were interchanged and rows and
+*> columns k+1 and -IPIV(k+1) were inerchaged,
+*> D(k:k+1,k:k+1) is a 2-by-2 diagonal block.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -k, the k-th argument had an illegal value
+*> > 0: if INFO = k, D(k,k) is exactly zero. The factorization
+*> has been completed, but the block diagonal matrix D is
+*> exactly singular, and division by zero will occur if it
+*> is used to solve a system of equations.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2012
+*
+*> \ingroup complex16HEcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> If UPLO = 'U', then A = U*D*U**H, where
+*> U = P(n)*U(n)* ... *P(k)U(k)* ...,
+*> i.e., U is a product of terms P(k)*U(k), where k decreases from n to
+*> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
+*> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
+*> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
+*> that if the diagonal block D(k) is of order s (s = 1 or 2), then
+*>
+*> ( I v 0 ) k-s
+*> U(k) = ( 0 I 0 ) s
+*> ( 0 0 I ) n-k
+*> k-s s n-k
+*>
+*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
+*> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
+*> and A(k,k), and v overwrites A(1:k-2,k-1:k).
+*>
+*> If UPLO = 'L', then A = L*D*L**H, where
+*> L = P(1)*L(1)* ... *P(k)*L(k)* ...,
+*> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
+*> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
+*> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as
+*> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
+*> that if the diagonal block D(k) is of order s (s = 1 or 2), then
+*>
+*> ( I 0 0 ) k-1
+*> L(k) = ( 0 I 0 ) s
+*> ( 0 v I ) n-k-s+1
+*> k-1 s n-k-s+1
+*>
+*> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
+*> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
+*> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).
+*> \endverbatim
+*
+*> \par Contributors:
+* ==================
+*>
+*> \verbatim
+*>
+*> November 2012, Igor Kozachenko,
+*> Computer Science Division,
+*> University of California, Berkeley
+*>
+*> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
+*> School of Mathematics,
+*> University of Manchester
+*>
+*> 01-01-96 - Based on modifications by
+*> J. Lewis, Boeing Computer Services Company
+*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*> \endverbatim
+*
+* =====================================================================
+ SUBROUTINE ZHETF2_ROOK( UPLO, N, A, LDA, IPIV, INFO )
+*
+* -- LAPACK computational routine (version 3.4.2) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2012
+*
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER INFO, LDA, N
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ COMPLEX*16 A( LDA, * )
+* ..
+*
+* ======================================================================
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO, ONE
+ PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
+ DOUBLE PRECISION EIGHT, SEVTEN
+ PARAMETER ( EIGHT = 8.0D+0, SEVTEN = 17.0D+0 )
+* ..
+* .. Local Scalars ..
+ LOGICAL DONE, UPPER
+ INTEGER I, II, IMAX, ITEMP, J, JMAX, K, KK, KP, KSTEP,
+ $ P
+ DOUBLE PRECISION ABSAKK, ALPHA, COLMAX, D, D11, D22, R1, DTEMP,
+ $ ROWMAX, TT, SFMIN
+ COMPLEX*16 D12, D21, T, WK, WKM1, WKP1, Z
+* ..
+* .. External Functions ..
+*
+ LOGICAL LSAME
+ INTEGER IZAMAX
+ DOUBLE PRECISION DLAMCH, DLAPY2
+ EXTERNAL LSAME, IZAMAX, DLAMCH, DLAPY2
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA, ZDSCAL, ZHER, ZSWAP
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, MAX, SQRT
+* ..
+* .. Statement Functions ..
+ DOUBLE PRECISION CABS1
+* ..
+* .. Statement Function definitions ..
+ CABS1( Z ) = ABS( DBLE( Z ) ) + ABS( DIMAG( Z ) )
+* ..
+* .. Executable Statements ..
+*
+* Test the input parameters.
+*
+ INFO = 0
+ UPPER = LSAME( UPLO, 'U' )
+ IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) 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 XERBLA( 'ZHETF2_ROOK', -INFO )
+ RETURN
+ END IF
+*
+* Initialize ALPHA for use in choosing pivot block size.
+*
+ ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT
+*
+* Compute machine safe minimum
+*
+ SFMIN = DLAMCH( 'S' )
+*
+ IF( UPPER ) THEN
+*
+* Factorize A as U*D*U**H using the upper triangle of A
+*
+* K is the main loop index, decreasing from N to 1 in steps of
+* 1 or 2
+*
+ K = N
+ 10 CONTINUE
+*
+* If K < 1, exit from loop
+*
+ IF( K.LT.1 )
+ $ GO TO 70
+ KSTEP = 1
+ P = K
+*
+* Determine rows and columns to be interchanged and whether
+* a 1-by-1 or 2-by-2 pivot block will be used
+*
+ ABSAKK = ABS( DBLE( A( K, K ) ) )
+*
+* IMAX is the row-index of the largest off-diagonal element in
+* column K, and COLMAX is its absolute value.
+* Determine both COLMAX and IMAX.
+*
+ IF( K.GT.1 ) THEN
+ IMAX = IZAMAX( K-1, A( 1, K ), 1 )
+ COLMAX = CABS1( A( IMAX, K ) )
+ ELSE
+ COLMAX = ZERO
+ END IF
+*
+ IF( ( MAX( ABSAKK, COLMAX ).EQ.ZERO ) ) THEN
+*
+* Column K is zero or underflow: set INFO and continue
+*
+ IF( INFO.EQ.0 )
+ $ INFO = K
+ KP = K
+ A( K, K ) = DBLE( A( K, K ) )
+ ELSE
+*
+* ============================================================
+*
+* BEGIN pivot search
+*
+* Case(1)
+* Equivalent to testing for ABSAKK.GE.ALPHA*COLMAX
+* (used to handle NaN and Inf)
+*
+ IF( .NOT.( ABSAKK.LT.ALPHA*COLMAX ) ) THEN
+*
+* no interchange, use 1-by-1 pivot block
+*
+ KP = K
+*
+ ELSE
+*
+ DONE = .FALSE.
+*
+* Loop until pivot found
+*
+ 12 CONTINUE
+*
+* BEGIN pivot search loop body
+*
+*
+* JMAX is the column-index of the largest off-diagonal
+* element in row IMAX, and ROWMAX is its absolute value.
+* Determine both ROWMAX and JMAX.
+*
+ IF( IMAX.NE.K ) THEN
+ JMAX = IMAX + IZAMAX( K-IMAX, A( IMAX, IMAX+1 ),
+ $ LDA )
+ ROWMAX = CABS1( A( IMAX, JMAX ) )
+ ELSE
+ ROWMAX = ZERO
+ END IF
+*
+ IF( IMAX.GT.1 ) THEN
+ ITEMP = IZAMAX( IMAX-1, A( 1, IMAX ), 1 )
+ DTEMP = CABS1( A( ITEMP, IMAX ) )
+ IF( DTEMP.GT.ROWMAX ) THEN
+ ROWMAX = DTEMP
+ JMAX = ITEMP
+ END IF
+ END IF
+*
+* Case(2)
+* Equivalent to testing for
+* ABS( DBLE( W( IMAX,KW-1 ) ) ).GE.ALPHA*ROWMAX
+* (used to handle NaN and Inf)
+*
+ IF( .NOT.( ABS( DBLE( A( IMAX, IMAX ) ) )
+ $ .LT.ALPHA*ROWMAX ) ) THEN
+*
+* interchange rows and columns K and IMAX,
+* use 1-by-1 pivot block
+*
+ KP = IMAX
+ DONE = .TRUE.
+*
+* Case(3)
+* Equivalent to testing for ROWMAX.EQ.COLMAX,
+* (used to handle NaN and Inf)
+*
+ ELSE IF( ( P.EQ.JMAX ) .OR. ( ROWMAX.LE.COLMAX ) )
+ $ THEN
+*
+* interchange rows and columns K-1 and IMAX,
+* use 2-by-2 pivot block
+*
+ KP = IMAX
+ KSTEP = 2
+ DONE = .TRUE.
+*
+* Case(4)
+ ELSE
+*
+* Pivot not found: set params and repeat
+*
+ P = IMAX
+ COLMAX = ROWMAX
+ IMAX = JMAX
+ END IF
+*
+* END pivot search loop body
+*
+ IF( .NOT.DONE ) GOTO 12
+*
+ END IF
+*
+* END pivot search
+*
+* ============================================================
+*
+* KK is the column of A where pivoting step stopped
+*
+ KK = K + KSTEP - 1
+*
+* For only a 2x2 pivot, interchange rows and columns K and P
+* in the leading submatrix A(1:k,1:k)
+*
+ IF( ( KSTEP.EQ.2 ) .AND. ( P.NE.K ) ) THEN
+* (1) Swap columnar parts
+ IF( P.GT.1 )
+ $ CALL ZSWAP( P-1, A( 1, K ), 1, A( 1, P ), 1 )
+* (2) Swap and conjugate middle parts
+ DO 14 J = P + 1, K - 1
+ T = DCONJG( A( J, K ) )
+ A( J, K ) = DCONJG( A( P, J ) )
+ A( P, J ) = T
+ 14 CONTINUE
+* (3) Swap and conjugate corner elements at row-col interserction
+ A( P, K ) = DCONJG( A( P, K ) )
+* (4) Swap diagonal elements at row-col intersection
+ R1 = DBLE( A( K, K ) )
+ A( K, K ) = DBLE( A( P, P ) )
+ A( P, P ) = R1
+ END IF
+*
+* For both 1x1 and 2x2 pivots, interchange rows and
+* columns KK and KP in the leading submatrix A(1:k,1:k)
+*
+ IF( KP.NE.KK ) THEN
+* (1) Swap columnar parts
+ IF( KP.GT.1 )
+ $ CALL ZSWAP( KP-1, A( 1, KK ), 1, A( 1, KP ), 1 )
+* (2) Swap and conjugate middle parts
+ DO 15 J = KP + 1, KK - 1
+ T = DCONJG( A( J, KK ) )
+ A( J, KK ) = DCONJG( A( KP, J ) )
+ A( KP, J ) = T
+ 15 CONTINUE
+* (3) Swap and conjugate corner elements at row-col interserction
+ A( KP, KK ) = DCONJG( A( KP, KK ) )
+* (4) Swap diagonal elements at row-col intersection
+ R1 = DBLE( A( KK, KK ) )
+ A( KK, KK ) = DBLE( A( KP, KP ) )
+ A( KP, KP ) = R1
+*
+ IF( KSTEP.EQ.2 ) THEN
+* (*) Make sure that diagonal element of pivot is real
+ A( K, K ) = DBLE( A( K, K ) )
+* (5) Swap row elements
+ T = A( K-1, K )
+ A( K-1, K ) = A( KP, K )
+ A( KP, K ) = T
+ END IF
+ ELSE
+* (*) Make sure that diagonal element of pivot is real
+ A( K, K ) = DBLE( A( K, K ) )
+ IF( KSTEP.EQ.2 )
+ $ A( K-1, K-1 ) = DBLE( A( K-1, K-1 ) )
+ END IF
+*
+* Update the leading submatrix
+*
+ IF( KSTEP.EQ.1 ) THEN
+*
+* 1-by-1 pivot block D(k): column k now holds
+*
+* W(k) = U(k)*D(k)
+*
+* where U(k) is the k-th column of U
+*
+ IF( K.GT.1 ) THEN
+*
+* Perform a rank-1 update of A(1:k-1,1:k-1) and
+* store U(k) in column k
+*
+ IF( ABS( DBLE( A( K, K ) ) ).GE.SFMIN ) THEN
+*
+* Perform a rank-1 update of A(1:k-1,1:k-1) as
+* A := A - U(k)*D(k)*U(k)**T
+* = A - W(k)*1/D(k)*W(k)**T
+*
+ D11 = ONE / DBLE( A( K, K ) )
+ CALL ZHER( UPLO, K-1, -D11, A( 1, K ), 1, A, LDA )
+*
+* Store U(k) in column k
+*
+ CALL ZSCAL( K-1, D11, A( 1, K ), 1 )
+ ELSE
+*
+* Store L(k) in column K
+*
+ D11 = DBLE( A( K, K ) )
+ DO 16 II = 1, K - 1
+ A( II, K ) = A( II, K ) / D11
+ 16 CONTINUE
+*
+* Perform a rank-1 update of A(k+1:n,k+1:n) as
+* A := A - U(k)*D(k)*U(k)**T
+* = A - W(k)*(1/D(k))*W(k)**T
+* = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T
+*
+ CALL ZHER( UPLO, K-1, -D11, A( 1, K ), 1, A, LDA )
+ END IF
+ END IF
+*
+ ELSE
+*
+* 2-by-2 pivot block D(k): columns k and k-1 now hold
+*
+* ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k)
+*
+* where U(k) and U(k-1) are the k-th and (k-1)-th columns
+* of U
+*
+* Perform a rank-2 update of A(1:k-2,1:k-2) as
+*
+* A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T
+* = A - ( ( A(k-1)A(k) )*inv(D(k)) ) * ( A(k-1)A(k) )**T
+*
+* and store L(k) and L(k+1) in columns k and k+1
+*
+ IF( K.GT.2 ) THEN
+* D = |A12|
+ D = DLAPY2( DBLE( A( K-1, K ) ),
+ $ DIMAG( A( K-1, K ) ) )
+ D11 = A( K, K ) / D
+ D22 = A( K-1, K-1 ) / D
+ D12 = A( K-1, K ) / D
+ TT = ONE / ( D11*D22-ONE )
+*
+ DO 30 J = K - 2, 1, -1
+*
+* Compute D21 * ( W(k)W(k+1) ) * inv(D(k)) for row J
+*
+ WKM1 = TT*( D11*A( J, K-1 )-DCONJG( D12 )*
+ $ A( J, K ) )
+ WK = TT*( D22*A( J, K )-D12*A( J, K-1 ) )
+*
+* Perform a rank-2 update of A(1:k-2,1:k-2)
+*
+ DO 20 I = J, 1, -1
+ A( I, J ) = A( I, J ) -
+ $ ( A( I, K ) / D )*DCONJG( WK ) -
+ $ ( A( I, K-1 ) / D )*DCONJG( WKM1 )
+ 20 CONTINUE
+*
+* Store U(k) and U(k-1) in cols k and k-1 for row J
+*
+ A( J, K ) = WK / D
+ A( J, K-1 ) = WKM1 / D
+* (*) Make sure that diagonal element of pivot is real
+ A( J, J ) = DCMPLX( DBLE( A( J, J ) ), ZERO )
+*
+ 30 CONTINUE
+*
+ END IF
+*
+ END IF
+*
+ END IF
+*
+* Store details of the interchanges in IPIV
+*
+ IF( KSTEP.EQ.1 ) THEN
+ IPIV( K ) = KP
+ ELSE
+ IPIV( K ) = -P
+ IPIV( K-1 ) = -KP
+ END IF
+*
+* Decrease K and return to the start of the main loop
+*
+ K = K - KSTEP
+ GO TO 10
+*
+ ELSE
+*
+* Factorize A as L*D*L**H using the lower triangle of A
+*
+* K is the main loop index, increasing from 1 to N in steps of
+* 1 or 2
+*
+ K = 1
+ 40 CONTINUE
+*
+* If K > N, exit from loop
+*
+ IF( K.GT.N )
+ $ GO TO 70
+ KSTEP = 1
+ P = K
+*
+* Determine rows and columns to be interchanged and whether
+* a 1-by-1 or 2-by-2 pivot block will be used
+*
+ ABSAKK = ABS( DBLE( A( K, K ) ) )
+*
+* IMAX is the row-index of the largest off-diagonal element in
+* column K, and COLMAX is its absolute value.
+* Determine both COLMAX and IMAX.
+*
+ IF( K.LT.N ) THEN
+ IMAX = K + IZAMAX( N-K, A( K+1, K ), 1 )
+ COLMAX = CABS1( A( IMAX, K ) )
+ ELSE
+ COLMAX = ZERO
+ END IF
+*
+ IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
+*
+* Column K is zero or underflow: set INFO and continue
+*
+ IF( INFO.EQ.0 )
+ $ INFO = K
+ KP = K
+ A( K, K ) = DBLE( A( K, K ) )
+ ELSE
+*
+* ============================================================
+*
+* BEGIN pivot search
+*
+* Case(1)
+* Equivalent to testing for ABSAKK.GE.ALPHA*COLMAX
+* (used to handle NaN and Inf)
+*
+ IF( .NOT.( ABSAKK.LT.ALPHA*COLMAX ) ) THEN
+*
+* no interchange, use 1-by-1 pivot block
+*
+ KP = K
+*
+ ELSE
+*
+ DONE = .FALSE.
+*
+* Loop until pivot found
+*
+ 42 CONTINUE
+*
+* BEGIN pivot search loop body
+*
+*
+* JMAX is the column-index of the largest off-diagonal
+* element in row IMAX, and ROWMAX is its absolute value.
+* Determine both ROWMAX and JMAX.
+*
+ IF( IMAX.NE.K ) THEN
+ JMAX = K - 1 + IZAMAX( IMAX-K, A( IMAX, K ), LDA )
+ ROWMAX = CABS1( A( IMAX, JMAX ) )
+ ELSE
+ ROWMAX = ZERO
+ END IF
+*
+ IF( IMAX.LT.N ) THEN
+ ITEMP = IMAX + IZAMAX( N-IMAX, A( IMAX+1, IMAX ),
+ $ 1 )
+ DTEMP = CABS1( A( ITEMP, IMAX ) )
+ IF( DTEMP.GT.ROWMAX ) THEN
+ ROWMAX = DTEMP
+ JMAX = ITEMP
+ END IF
+ END IF
+*
+* Case(2)
+* Equivalent to testing for
+* ABS( DBLE( W( IMAX,KW-1 ) ) ).GE.ALPHA*ROWMAX
+* (used to handle NaN and Inf)
+*
+ IF( .NOT.( ABS( DBLE( A( IMAX, IMAX ) ) )
+ $ .LT.ALPHA*ROWMAX ) ) THEN
+*
+* interchange rows and columns K and IMAX,
+* use 1-by-1 pivot block
+*
+ KP = IMAX
+ DONE = .TRUE.
+*
+* Case(3)
+* Equivalent to testing for ROWMAX.EQ.COLMAX,
+* (used to handle NaN and Inf)
+*
+ ELSE IF( ( P.EQ.JMAX ) .OR. ( ROWMAX.LE.COLMAX ) )
+ $ THEN
+*
+* interchange rows and columns K+1 and IMAX,
+* use 2-by-2 pivot block
+*
+ KP = IMAX
+ KSTEP = 2
+ DONE = .TRUE.
+*
+* Case(4)
+ ELSE
+*
+* Pivot not found: set params and repeat
+*
+ P = IMAX
+ COLMAX = ROWMAX
+ IMAX = JMAX
+ END IF
+*
+*
+* END pivot search loop body
+*
+ IF( .NOT.DONE ) GOTO 42
+*
+ END IF
+*
+* END pivot search
+*
+* ============================================================
+*
+* KK is the column of A where pivoting step stopped
+*
+ KK = K + KSTEP - 1
+*
+* For only a 2x2 pivot, interchange rows and columns K and P
+* in the trailing submatrix A(k:n,k:n)
+*
+ IF( ( KSTEP.EQ.2 ) .AND. ( P.NE.K ) ) THEN
+* (1) Swap columnar parts
+ IF( P.LT.N )
+ $ CALL ZSWAP( N-P, A( P+1, K ), 1, A( P+1, P ), 1 )
+* (2) Swap and conjugate middle parts
+ DO 44 J = K + 1, P - 1
+ T = DCONJG( A( J, K ) )
+ A( J, K ) = DCONJG( A( P, J ) )
+ A( P, J ) = T
+ 44 CONTINUE
+* (3) Swap and conjugate corner elements at row-col interserction
+ A( P, K ) = DCONJG( A( P, K ) )
+* (4) Swap diagonal elements at row-col intersection
+ R1 = DBLE( A( K, K ) )
+ A( K, K ) = DBLE( A( P, P ) )
+ A( P, P ) = R1
+ END IF
+*
+* For both 1x1 and 2x2 pivots, interchange rows and
+* columns KK and KP in the trailing submatrix A(k:n,k:n)
+*
+ IF( KP.NE.KK ) THEN
+* (1) Swap columnar parts
+ IF( KP.LT.N )
+ $ CALL ZSWAP( N-KP, A( KP+1, KK ), 1, A( KP+1, KP ), 1 )
+* (2) Swap and conjugate middle parts
+ DO 45 J = KK + 1, KP - 1
+ T = DCONJG( A( J, KK ) )
+ A( J, KK ) = DCONJG( A( KP, J ) )
+ A( KP, J ) = T
+ 45 CONTINUE
+* (3) Swap and conjugate corner elements at row-col interserction
+ A( KP, KK ) = DCONJG( A( KP, KK ) )
+* (4) Swap diagonal elements at row-col intersection
+ R1 = DBLE( A( KK, KK ) )
+ A( KK, KK ) = DBLE( A( KP, KP ) )
+ A( KP, KP ) = R1
+*
+ IF( KSTEP.EQ.2 ) THEN
+* (*) Make sure that diagonal element of pivot is real
+ A( K, K ) = DBLE( A( K, K ) )
+* (5) Swap row elements
+ T = A( K+1, K )
+ A( K+1, K ) = A( KP, K )
+ A( KP, K ) = T
+ END IF
+ ELSE
+* (*) Make sure that diagonal element of pivot is real
+ A( K, K ) = DBLE( A( K, K ) )
+ IF( KSTEP.EQ.2 )
+ $ A( K+1, K+1 ) = DBLE( A( K+1, K+1 ) )
+ END IF
+*
+* Update the trailing submatrix
+*
+ IF( KSTEP.EQ.1 ) THEN
+*
+* 1-by-1 pivot block D(k): column k of A now holds
+*
+* W(k) = L(k)*D(k),
+*
+* where L(k) is the k-th column of L
+*
+ IF( K.LT.N ) THEN
+*
+* Perform a rank-1 update of A(k+1:n,k+1:n) and
+* store L(k) in column k
+*
+* Handle division by a small number
+*
+ IF( ABS( DBLE( A( K, K ) ) ).GE.SFMIN ) THEN
+*
+* Perform a rank-1 update of A(k+1:n,k+1:n) as
+* A := A - L(k)*D(k)*L(k)**T
+* = A - W(k)*(1/D(k))*W(k)**T
+*
+ D11 = ONE / DBLE( A( K, K ) )
+ CALL ZHER( UPLO, N-K, -D11, A( K+1, K ), 1,
+ $ A( K+1, K+1 ), LDA )
+*
+* Store L(k) in column k
+*
+ CALL ZDSCAL( N-K, D11, A( K+1, K ), 1 )
+ ELSE
+*
+* Store L(k) in column k
+*
+ D11 = DBLE( A( K, K ) )
+ DO 46 II = K + 1, N
+ A( II, K ) = A( II, K ) / D11
+ 46 CONTINUE
+*
+* Perform a rank-1 update of A(k+1:n,k+1:n) as
+* A := A - L(k)*D(k)*L(k)**T
+* = A - W(k)*(1/D(k))*W(k)**T
+* = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T
+*
+ CALL ZHER( UPLO, N-K, -D11, A( K+1, K ), 1,
+ $ A( K+1, K+1 ), LDA )
+ END IF
+ END IF
+*
+ ELSE
+*
+* 2-by-2 pivot block D(k): columns k and k+1 now hold
+*
+* ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k)
+*
+* where L(k) and L(k+1) are the k-th and (k+1)-th columns
+* of L
+*
+*
+* Perform a rank-2 update of A(k+2:n,k+2:n) as
+*
+* A := A - ( L(k) L(k+1) ) * D(k) * ( L(k) L(k+1) )**T
+* = A - ( ( A(k)A(k+1) )*inv(D(k) ) * ( A(k)A(k+1) )**T
+*
+* and store L(k) and L(k+1) in columns k and k+1
+*
+ IF( K.LT.N-1 ) THEN
+* D = |A21|
+ D = DLAPY2( DBLE( A( K+1, K ) ),
+ $ DIMAG( A( K+1, K ) ) )
+ D11 = DBLE( A( K+1, K+1 ) ) / D
+ D22 = DBLE( A( K, K ) ) / D
+ D21 = A( K+1, K ) / D
+ TT = ONE / ( D11*D22-ONE )
+*
+ DO 60 J = K + 2, N
+*
+* Compute D21 * ( W(k)W(k+1) ) * inv(D(k)) for row J
+*
+ WK = TT*( D11*A( J, K )-D21*A( J, K+1 ) )
+ WKP1 = TT*( D22*A( J, K+1 )-DCONJG( D21 )*
+ $ A( J, K ) )
+*
+* Perform a rank-2 update of A(k+2:n,k+2:n)
+*
+ DO 50 I = J, N
+ A( I, J ) = A( I, J ) -
+ $ ( A( I, K ) / D )*DCONJG( WK ) -
+ $ ( A( I, K+1 ) / D )*DCONJG( WKP1 )
+ 50 CONTINUE
+*
+* Store L(k) and L(k+1) in cols k and k+1 for row J
+*
+ A( J, K ) = WK / D
+ A( J, K+1 ) = WKP1 / D
+* (*) Make sure that diagonal element of pivot is real
+ A( J, J ) = DCMPLX( DBLE( A( J, J ) ), ZERO )
+*
+ 60 CONTINUE
+*
+ END IF
+*
+ END IF
+*
+ END IF
+*
+* Store details of the interchanges in IPIV
+*
+ IF( KSTEP.EQ.1 ) THEN
+ IPIV( K ) = KP
+ ELSE
+ IPIV( K ) = -P
+ IPIV( K+1 ) = -KP
+ END IF
+*
+* Increase K and return to the start of the main loop
+*
+ K = K + KSTEP
+ GO TO 40
+*
+ END IF
+*
+ 70 CONTINUE
+*
+ RETURN
+*
+* End of ZHETF2_ROOK
+*
+ END
projects / platform / upstream / lapack.git / commitdiff