620 lines
19 KiB
Fortran
620 lines
19 KiB
Fortran
*> \brief \b CSPTRF
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
*> \htmlonly
|
|
*> Download CSPTRF + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/csptrf.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/csptrf.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/csptrf.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE CSPTRF( UPLO, N, AP, IPIV, INFO )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER UPLO
|
|
* INTEGER INFO, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* INTEGER IPIV( * )
|
|
* COMPLEX AP( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> CSPTRF computes the factorization of a complex symmetric matrix A
|
|
*> stored in packed format using the Bunch-Kaufman diagonal pivoting
|
|
*> method:
|
|
*>
|
|
*> A = U*D*U**T or A = L*D*L**T
|
|
*>
|
|
*> where U (or L) is a product of permutation and unit upper (lower)
|
|
*> triangular matrices, and D is symmetric and block diagonal with
|
|
*> 1-by-1 and 2-by-2 diagonal blocks.
|
|
*> \endverbatim
|
|
*
|
|
* Arguments:
|
|
* ==========
|
|
*
|
|
*> \param[in] UPLO
|
|
*> \verbatim
|
|
*> UPLO is CHARACTER*1
|
|
*> = 'U': Upper triangle of A is stored;
|
|
*> = 'L': Lower triangle of A is stored.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in] N
|
|
*> \verbatim
|
|
*> N is INTEGER
|
|
*> The order of the matrix A. N >= 0.
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[in,out] AP
|
|
*> \verbatim
|
|
*> AP is COMPLEX array, dimension (N*(N+1)/2)
|
|
*> On entry, the upper or lower triangle of the symmetric matrix
|
|
*> A, packed columnwise in a linear array. The j-th column of A
|
|
*> is stored in the array AP as follows:
|
|
*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
|
|
*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
|
|
*>
|
|
*> On exit, the block diagonal matrix D and the multipliers used
|
|
*> to obtain the factor U or L, stored as a packed triangular
|
|
*> matrix overwriting A (see below for further details).
|
|
*> \endverbatim
|
|
*>
|
|
*> \param[out] IPIV
|
|
*> \verbatim
|
|
*> IPIV is INTEGER array, dimension (N)
|
|
*> Details of the interchanges and the block structure of D.
|
|
*> 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 UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and
|
|
*> columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)
|
|
*> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) =
|
|
*> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were
|
|
*> interchanged and 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 = -i, the i-th argument had an illegal value
|
|
*> > 0: if INFO = i, D(i,i) 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 December 2016
|
|
*
|
|
*> \ingroup complexOTHERcomputational
|
|
*
|
|
*> \par Further Details:
|
|
* =====================
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> 5-96 - Based on modifications by J. Lewis, Boeing Computer Services
|
|
*> Company
|
|
*>
|
|
*> If UPLO = 'U', then A = U*D*U**T, 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**T, 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
|
|
*>
|
|
* =====================================================================
|
|
SUBROUTINE CSPTRF( UPLO, N, AP, IPIV, INFO )
|
|
*
|
|
* -- LAPACK computational routine (version 3.7.0) --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
* December 2016
|
|
*
|
|
* .. Scalar Arguments ..
|
|
CHARACTER UPLO
|
|
INTEGER INFO, N
|
|
* ..
|
|
* .. Array Arguments ..
|
|
INTEGER IPIV( * )
|
|
COMPLEX AP( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. 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 )
|
|
COMPLEX CONE
|
|
PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
LOGICAL UPPER
|
|
INTEGER I, IMAX, J, JMAX, K, KC, KK, KNC, KP, KPC,
|
|
$ KSTEP, KX, NPP
|
|
REAL ABSAKK, ALPHA, COLMAX, ROWMAX
|
|
COMPLEX D11, D12, D21, D22, R1, T, WK, WKM1, WKP1, ZDUM
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
INTEGER ICAMAX
|
|
EXTERNAL LSAME, ICAMAX
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL CSCAL, CSPR, CSWAP, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, AIMAG, MAX, REAL, SQRT
|
|
* ..
|
|
* .. Statement Functions ..
|
|
REAL CABS1
|
|
* ..
|
|
* .. Statement Function definitions ..
|
|
CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
|
|
* ..
|
|
* .. 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
|
|
END IF
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'CSPTRF', -INFO )
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Initialize ALPHA for use in choosing pivot block size.
|
|
*
|
|
ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT
|
|
*
|
|
IF( UPPER ) THEN
|
|
*
|
|
* Factorize A as U*D*U**T 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
|
|
KC = ( N-1 )*N / 2 + 1
|
|
10 CONTINUE
|
|
KNC = KC
|
|
*
|
|
* If K < 1, exit from loop
|
|
*
|
|
IF( K.LT.1 )
|
|
$ GO TO 110
|
|
KSTEP = 1
|
|
*
|
|
* Determine rows and columns to be interchanged and whether
|
|
* a 1-by-1 or 2-by-2 pivot block will be used
|
|
*
|
|
ABSAKK = CABS1( AP( KC+K-1 ) )
|
|
*
|
|
* IMAX is the row-index of the largest off-diagonal element in
|
|
* column K, and COLMAX is its absolute value
|
|
*
|
|
IF( K.GT.1 ) THEN
|
|
IMAX = ICAMAX( K-1, AP( KC ), 1 )
|
|
COLMAX = CABS1( AP( KC+IMAX-1 ) )
|
|
ELSE
|
|
COLMAX = ZERO
|
|
END IF
|
|
*
|
|
IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
|
|
*
|
|
* Column K is zero: set INFO and continue
|
|
*
|
|
IF( INFO.EQ.0 )
|
|
$ INFO = K
|
|
KP = K
|
|
ELSE
|
|
IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
|
|
*
|
|
* no interchange, use 1-by-1 pivot block
|
|
*
|
|
KP = K
|
|
ELSE
|
|
*
|
|
ROWMAX = ZERO
|
|
JMAX = IMAX
|
|
KX = IMAX*( IMAX+1 ) / 2 + IMAX
|
|
DO 20 J = IMAX + 1, K
|
|
IF( CABS1( AP( KX ) ).GT.ROWMAX ) THEN
|
|
ROWMAX = CABS1( AP( KX ) )
|
|
JMAX = J
|
|
END IF
|
|
KX = KX + J
|
|
20 CONTINUE
|
|
KPC = ( IMAX-1 )*IMAX / 2 + 1
|
|
IF( IMAX.GT.1 ) THEN
|
|
JMAX = ICAMAX( IMAX-1, AP( KPC ), 1 )
|
|
ROWMAX = MAX( ROWMAX, CABS1( AP( KPC+JMAX-1 ) ) )
|
|
END IF
|
|
*
|
|
IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
|
|
*
|
|
* no interchange, use 1-by-1 pivot block
|
|
*
|
|
KP = K
|
|
ELSE IF( CABS1( AP( KPC+IMAX-1 ) ).GE.ALPHA*ROWMAX ) THEN
|
|
*
|
|
* interchange rows and columns K and IMAX, use 1-by-1
|
|
* pivot block
|
|
*
|
|
KP = IMAX
|
|
ELSE
|
|
*
|
|
* interchange rows and columns K-1 and IMAX, use 2-by-2
|
|
* pivot block
|
|
*
|
|
KP = IMAX
|
|
KSTEP = 2
|
|
END IF
|
|
END IF
|
|
*
|
|
KK = K - KSTEP + 1
|
|
IF( KSTEP.EQ.2 )
|
|
$ KNC = KNC - K + 1
|
|
IF( KP.NE.KK ) THEN
|
|
*
|
|
* Interchange rows and columns KK and KP in the leading
|
|
* submatrix A(1:k,1:k)
|
|
*
|
|
CALL CSWAP( KP-1, AP( KNC ), 1, AP( KPC ), 1 )
|
|
KX = KPC + KP - 1
|
|
DO 30 J = KP + 1, KK - 1
|
|
KX = KX + J - 1
|
|
T = AP( KNC+J-1 )
|
|
AP( KNC+J-1 ) = AP( KX )
|
|
AP( KX ) = T
|
|
30 CONTINUE
|
|
T = AP( KNC+KK-1 )
|
|
AP( KNC+KK-1 ) = AP( KPC+KP-1 )
|
|
AP( KPC+KP-1 ) = T
|
|
IF( KSTEP.EQ.2 ) THEN
|
|
T = AP( KC+K-2 )
|
|
AP( KC+K-2 ) = AP( KC+KP-1 )
|
|
AP( KC+KP-1 ) = T
|
|
END IF
|
|
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
|
|
*
|
|
* 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
|
|
*
|
|
R1 = CONE / AP( KC+K-1 )
|
|
CALL CSPR( UPLO, K-1, -R1, AP( KC ), 1, AP )
|
|
*
|
|
* Store U(k) in column k
|
|
*
|
|
CALL CSCAL( K-1, R1, AP( KC ), 1 )
|
|
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 - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )**T
|
|
*
|
|
IF( K.GT.2 ) THEN
|
|
*
|
|
D12 = AP( K-1+( K-1 )*K / 2 )
|
|
D22 = AP( K-1+( K-2 )*( K-1 ) / 2 ) / D12
|
|
D11 = AP( K+( K-1 )*K / 2 ) / D12
|
|
T = CONE / ( D11*D22-CONE )
|
|
D12 = T / D12
|
|
*
|
|
DO 50 J = K - 2, 1, -1
|
|
WKM1 = D12*( D11*AP( J+( K-2 )*( K-1 ) / 2 )-
|
|
$ AP( J+( K-1 )*K / 2 ) )
|
|
WK = D12*( D22*AP( J+( K-1 )*K / 2 )-
|
|
$ AP( J+( K-2 )*( K-1 ) / 2 ) )
|
|
DO 40 I = J, 1, -1
|
|
AP( I+( J-1 )*J / 2 ) = AP( I+( J-1 )*J / 2 ) -
|
|
$ AP( I+( K-1 )*K / 2 )*WK -
|
|
$ AP( I+( K-2 )*( K-1 ) / 2 )*WKM1
|
|
40 CONTINUE
|
|
AP( J+( K-1 )*K / 2 ) = WK
|
|
AP( J+( K-2 )*( K-1 ) / 2 ) = WKM1
|
|
50 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 ) = -KP
|
|
IPIV( K-1 ) = -KP
|
|
END IF
|
|
*
|
|
* Decrease K and return to the start of the main loop
|
|
*
|
|
K = K - KSTEP
|
|
KC = KNC - K
|
|
GO TO 10
|
|
*
|
|
ELSE
|
|
*
|
|
* Factorize A as L*D*L**T 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
|
|
KC = 1
|
|
NPP = N*( N+1 ) / 2
|
|
60 CONTINUE
|
|
KNC = KC
|
|
*
|
|
* If K > N, exit from loop
|
|
*
|
|
IF( K.GT.N )
|
|
$ GO TO 110
|
|
KSTEP = 1
|
|
*
|
|
* Determine rows and columns to be interchanged and whether
|
|
* a 1-by-1 or 2-by-2 pivot block will be used
|
|
*
|
|
ABSAKK = CABS1( AP( KC ) )
|
|
*
|
|
* IMAX is the row-index of the largest off-diagonal element in
|
|
* column K, and COLMAX is its absolute value
|
|
*
|
|
IF( K.LT.N ) THEN
|
|
IMAX = K + ICAMAX( N-K, AP( KC+1 ), 1 )
|
|
COLMAX = CABS1( AP( KC+IMAX-K ) )
|
|
ELSE
|
|
COLMAX = ZERO
|
|
END IF
|
|
*
|
|
IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
|
|
*
|
|
* Column K is zero: set INFO and continue
|
|
*
|
|
IF( INFO.EQ.0 )
|
|
$ INFO = K
|
|
KP = K
|
|
ELSE
|
|
IF( ABSAKK.GE.ALPHA*COLMAX ) THEN
|
|
*
|
|
* no interchange, use 1-by-1 pivot block
|
|
*
|
|
KP = K
|
|
ELSE
|
|
*
|
|
* JMAX is the column-index of the largest off-diagonal
|
|
* element in row IMAX, and ROWMAX is its absolute value
|
|
*
|
|
ROWMAX = ZERO
|
|
KX = KC + IMAX - K
|
|
DO 70 J = K, IMAX - 1
|
|
IF( CABS1( AP( KX ) ).GT.ROWMAX ) THEN
|
|
ROWMAX = CABS1( AP( KX ) )
|
|
JMAX = J
|
|
END IF
|
|
KX = KX + N - J
|
|
70 CONTINUE
|
|
KPC = NPP - ( N-IMAX+1 )*( N-IMAX+2 ) / 2 + 1
|
|
IF( IMAX.LT.N ) THEN
|
|
JMAX = IMAX + ICAMAX( N-IMAX, AP( KPC+1 ), 1 )
|
|
ROWMAX = MAX( ROWMAX, CABS1( AP( KPC+JMAX-IMAX ) ) )
|
|
END IF
|
|
*
|
|
IF( ABSAKK.GE.ALPHA*COLMAX*( COLMAX / ROWMAX ) ) THEN
|
|
*
|
|
* no interchange, use 1-by-1 pivot block
|
|
*
|
|
KP = K
|
|
ELSE IF( CABS1( AP( KPC ) ).GE.ALPHA*ROWMAX ) THEN
|
|
*
|
|
* interchange rows and columns K and IMAX, use 1-by-1
|
|
* pivot block
|
|
*
|
|
KP = IMAX
|
|
ELSE
|
|
*
|
|
* interchange rows and columns K+1 and IMAX, use 2-by-2
|
|
* pivot block
|
|
*
|
|
KP = IMAX
|
|
KSTEP = 2
|
|
END IF
|
|
END IF
|
|
*
|
|
KK = K + KSTEP - 1
|
|
IF( KSTEP.EQ.2 )
|
|
$ KNC = KNC + N - K + 1
|
|
IF( KP.NE.KK ) THEN
|
|
*
|
|
* Interchange rows and columns KK and KP in the trailing
|
|
* submatrix A(k:n,k:n)
|
|
*
|
|
IF( KP.LT.N )
|
|
$ CALL CSWAP( N-KP, AP( KNC+KP-KK+1 ), 1, AP( KPC+1 ),
|
|
$ 1 )
|
|
KX = KNC + KP - KK
|
|
DO 80 J = KK + 1, KP - 1
|
|
KX = KX + N - J + 1
|
|
T = AP( KNC+J-KK )
|
|
AP( KNC+J-KK ) = AP( KX )
|
|
AP( KX ) = T
|
|
80 CONTINUE
|
|
T = AP( KNC )
|
|
AP( KNC ) = AP( KPC )
|
|
AP( KPC ) = T
|
|
IF( KSTEP.EQ.2 ) THEN
|
|
T = AP( KC+1 )
|
|
AP( KC+1 ) = AP( KC+KP-K )
|
|
AP( KC+KP-K ) = T
|
|
END IF
|
|
END IF
|
|
*
|
|
* Update the trailing submatrix
|
|
*
|
|
IF( KSTEP.EQ.1 ) THEN
|
|
*
|
|
* 1-by-1 pivot block D(k): column k 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) as
|
|
*
|
|
* A := A - L(k)*D(k)*L(k)**T = A - W(k)*(1/D(k))*W(k)**T
|
|
*
|
|
R1 = CONE / AP( KC )
|
|
CALL CSPR( UPLO, N-K, -R1, AP( KC+1 ), 1,
|
|
$ AP( KC+N-K+1 ) )
|
|
*
|
|
* Store L(k) in column K
|
|
*
|
|
CALL CSCAL( N-K, R1, AP( KC+1 ), 1 )
|
|
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
|
|
*
|
|
IF( K.LT.N-1 ) THEN
|
|
*
|
|
* 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 - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )**T
|
|
*
|
|
* where L(k) and L(k+1) are the k-th and (k+1)-th
|
|
* columns of L
|
|
*
|
|
D21 = AP( K+1+( K-1 )*( 2*N-K ) / 2 )
|
|
D11 = AP( K+1+K*( 2*N-K-1 ) / 2 ) / D21
|
|
D22 = AP( K+( K-1 )*( 2*N-K ) / 2 ) / D21
|
|
T = CONE / ( D11*D22-CONE )
|
|
D21 = T / D21
|
|
*
|
|
DO 100 J = K + 2, N
|
|
WK = D21*( D11*AP( J+( K-1 )*( 2*N-K ) / 2 )-
|
|
$ AP( J+K*( 2*N-K-1 ) / 2 ) )
|
|
WKP1 = D21*( D22*AP( J+K*( 2*N-K-1 ) / 2 )-
|
|
$ AP( J+( K-1 )*( 2*N-K ) / 2 ) )
|
|
DO 90 I = J, N
|
|
AP( I+( J-1 )*( 2*N-J ) / 2 ) = AP( I+( J-1 )*
|
|
$ ( 2*N-J ) / 2 ) - AP( I+( K-1 )*( 2*N-K ) /
|
|
$ 2 )*WK - AP( I+K*( 2*N-K-1 ) / 2 )*WKP1
|
|
90 CONTINUE
|
|
AP( J+( K-1 )*( 2*N-K ) / 2 ) = WK
|
|
AP( J+K*( 2*N-K-1 ) / 2 ) = WKP1
|
|
100 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 ) = -KP
|
|
IPIV( K+1 ) = -KP
|
|
END IF
|
|
*
|
|
* Increase K and return to the start of the main loop
|
|
*
|
|
K = K + KSTEP
|
|
KC = KNC + N - K + 2
|
|
GO TO 60
|
|
*
|
|
END IF
|
|
*
|
|
110 CONTINUE
|
|
RETURN
|
|
*
|
|
* End of CSPTRF
|
|
*
|
|
END
|