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authorjofret2009-04-28 07:17:00 +0000
committerjofret2009-04-28 07:17:00 +0000
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Moving lapack to right place
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- SUBROUTINE DSYTRI( UPLO, N, A, LDA, IPIV, WORK, INFO )
-*
-* -- LAPACK routine (version 3.1) --
-* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
-* November 2006
-*
-* .. Scalar Arguments ..
- CHARACTER UPLO
- INTEGER INFO, LDA, N
-* ..
-* .. Array Arguments ..
- INTEGER IPIV( * )
- DOUBLE PRECISION A( LDA, * ), WORK( * )
-* ..
-*
-* Purpose
-* =======
-*
-* DSYTRI computes the inverse of a real symmetric indefinite matrix
-* A using the factorization A = U*D*U**T or A = L*D*L**T computed by
-* DSYTRF.
-*
-* Arguments
-* =========
-*
-* UPLO (input) CHARACTER*1
-* Specifies whether the details of the factorization are stored
-* as an upper or lower triangular matrix.
-* = 'U': Upper triangular, form is A = U*D*U**T;
-* = 'L': Lower triangular, form is A = L*D*L**T.
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0.
-*
-* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
-* On entry, the block diagonal matrix D and the multipliers
-* used to obtain the factor U or L as computed by DSYTRF.
-*
-* On exit, if INFO = 0, the (symmetric) inverse of the original
-* matrix. If UPLO = 'U', the upper triangular part of the
-* inverse is formed and the part of A below the diagonal is not
-* referenced; if UPLO = 'L' the lower triangular part of the
-* inverse is formed and the part of A above the diagonal is
-* not referenced.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,N).
-*
-* IPIV (input) INTEGER array, dimension (N)
-* Details of the interchanges and the block structure of D
-* as determined by DSYTRF.
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension (N)
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-* > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
-* inverse could not be computed.
-*
-* =====================================================================
-*
-* .. Parameters ..
- DOUBLE PRECISION ONE, ZERO
- PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
-* ..
-* .. Local Scalars ..
- LOGICAL UPPER
- INTEGER K, KP, KSTEP
- DOUBLE PRECISION AK, AKKP1, AKP1, D, T, TEMP
-* ..
-* .. External Functions ..
- LOGICAL LSAME
- DOUBLE PRECISION DDOT
- EXTERNAL LSAME, DDOT
-* ..
-* .. External Subroutines ..
- EXTERNAL DCOPY, DSWAP, DSYMV, XERBLA
-* ..
-* .. Intrinsic Functions ..
- INTRINSIC ABS, MAX
-* ..
-* .. 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( 'DSYTRI', -INFO )
- RETURN
- END IF
-*
-* Quick return if possible
-*
- IF( N.EQ.0 )
- $ RETURN
-*
-* Check that the diagonal matrix D is nonsingular.
-*
- IF( UPPER ) THEN
-*
-* Upper triangular storage: examine D from bottom to top
-*
- DO 10 INFO = N, 1, -1
- IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
- $ RETURN
- 10 CONTINUE
- ELSE
-*
-* Lower triangular storage: examine D from top to bottom.
-*
- DO 20 INFO = 1, N
- IF( IPIV( INFO ).GT.0 .AND. A( INFO, INFO ).EQ.ZERO )
- $ RETURN
- 20 CONTINUE
- END IF
- INFO = 0
-*
- IF( UPPER ) THEN
-*
-* Compute inv(A) from the factorization A = U*D*U'.
-*
-* K is the main loop index, increasing from 1 to N in steps of
-* 1 or 2, depending on the size of the diagonal blocks.
-*
- K = 1
- 30 CONTINUE
-*
-* If K > N, exit from loop.
-*
- IF( K.GT.N )
- $ GO TO 40
-*
- IF( IPIV( K ).GT.0 ) THEN
-*
-* 1 x 1 diagonal block
-*
-* Invert the diagonal block.
-*
- A( K, K ) = ONE / A( K, K )
-*
-* Compute column K of the inverse.
-*
- IF( K.GT.1 ) THEN
- CALL DCOPY( K-1, A( 1, K ), 1, WORK, 1 )
- CALL DSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
- $ A( 1, K ), 1 )
- A( K, K ) = A( K, K ) - DDOT( K-1, WORK, 1, A( 1, K ),
- $ 1 )
- END IF
- KSTEP = 1
- ELSE
-*
-* 2 x 2 diagonal block
-*
-* Invert the diagonal block.
-*
- T = ABS( A( K, K+1 ) )
- AK = A( K, K ) / T
- AKP1 = A( K+1, K+1 ) / T
- AKKP1 = A( K, K+1 ) / T
- D = T*( AK*AKP1-ONE )
- A( K, K ) = AKP1 / D
- A( K+1, K+1 ) = AK / D
- A( K, K+1 ) = -AKKP1 / D
-*
-* Compute columns K and K+1 of the inverse.
-*
- IF( K.GT.1 ) THEN
- CALL DCOPY( K-1, A( 1, K ), 1, WORK, 1 )
- CALL DSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
- $ A( 1, K ), 1 )
- A( K, K ) = A( K, K ) - DDOT( K-1, WORK, 1, A( 1, K ),
- $ 1 )
- A( K, K+1 ) = A( K, K+1 ) -
- $ DDOT( K-1, A( 1, K ), 1, A( 1, K+1 ), 1 )
- CALL DCOPY( K-1, A( 1, K+1 ), 1, WORK, 1 )
- CALL DSYMV( UPLO, K-1, -ONE, A, LDA, WORK, 1, ZERO,
- $ A( 1, K+1 ), 1 )
- A( K+1, K+1 ) = A( K+1, K+1 ) -
- $ DDOT( K-1, WORK, 1, A( 1, K+1 ), 1 )
- END IF
- KSTEP = 2
- END IF
-*
- KP = ABS( IPIV( K ) )
- IF( KP.NE.K ) THEN
-*
-* Interchange rows and columns K and KP in the leading
-* submatrix A(1:k+1,1:k+1)
-*
- CALL DSWAP( KP-1, A( 1, K ), 1, A( 1, KP ), 1 )
- CALL DSWAP( K-KP-1, A( KP+1, K ), 1, A( KP, KP+1 ), LDA )
- TEMP = A( K, K )
- A( K, K ) = A( KP, KP )
- A( KP, KP ) = TEMP
- IF( KSTEP.EQ.2 ) THEN
- TEMP = A( K, K+1 )
- A( K, K+1 ) = A( KP, K+1 )
- A( KP, K+1 ) = TEMP
- END IF
- END IF
-*
- K = K + KSTEP
- GO TO 30
- 40 CONTINUE
-*
- ELSE
-*
-* Compute inv(A) from the factorization A = L*D*L'.
-*
-* K is the main loop index, increasing from 1 to N in steps of
-* 1 or 2, depending on the size of the diagonal blocks.
-*
- K = N
- 50 CONTINUE
-*
-* If K < 1, exit from loop.
-*
- IF( K.LT.1 )
- $ GO TO 60
-*
- IF( IPIV( K ).GT.0 ) THEN
-*
-* 1 x 1 diagonal block
-*
-* Invert the diagonal block.
-*
- A( K, K ) = ONE / A( K, K )
-*
-* Compute column K of the inverse.
-*
- IF( K.LT.N ) THEN
- CALL DCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
- CALL DSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
- $ ZERO, A( K+1, K ), 1 )
- A( K, K ) = A( K, K ) - DDOT( N-K, WORK, 1, A( K+1, K ),
- $ 1 )
- END IF
- KSTEP = 1
- ELSE
-*
-* 2 x 2 diagonal block
-*
-* Invert the diagonal block.
-*
- T = ABS( A( K, K-1 ) )
- AK = A( K-1, K-1 ) / T
- AKP1 = A( K, K ) / T
- AKKP1 = A( K, K-1 ) / T
- D = T*( AK*AKP1-ONE )
- A( K-1, K-1 ) = AKP1 / D
- A( K, K ) = AK / D
- A( K, K-1 ) = -AKKP1 / D
-*
-* Compute columns K-1 and K of the inverse.
-*
- IF( K.LT.N ) THEN
- CALL DCOPY( N-K, A( K+1, K ), 1, WORK, 1 )
- CALL DSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
- $ ZERO, A( K+1, K ), 1 )
- A( K, K ) = A( K, K ) - DDOT( N-K, WORK, 1, A( K+1, K ),
- $ 1 )
- A( K, K-1 ) = A( K, K-1 ) -
- $ DDOT( N-K, A( K+1, K ), 1, A( K+1, K-1 ),
- $ 1 )
- CALL DCOPY( N-K, A( K+1, K-1 ), 1, WORK, 1 )
- CALL DSYMV( UPLO, N-K, -ONE, A( K+1, K+1 ), LDA, WORK, 1,
- $ ZERO, A( K+1, K-1 ), 1 )
- A( K-1, K-1 ) = A( K-1, K-1 ) -
- $ DDOT( N-K, WORK, 1, A( K+1, K-1 ), 1 )
- END IF
- KSTEP = 2
- END IF
-*
- KP = ABS( IPIV( K ) )
- IF( KP.NE.K ) THEN
-*
-* Interchange rows and columns K and KP in the trailing
-* submatrix A(k-1:n,k-1:n)
-*
- IF( KP.LT.N )
- $ CALL DSWAP( N-KP, A( KP+1, K ), 1, A( KP+1, KP ), 1 )
- CALL DSWAP( KP-K-1, A( K+1, K ), 1, A( KP, K+1 ), LDA )
- TEMP = A( K, K )
- A( K, K ) = A( KP, KP )
- A( KP, KP ) = TEMP
- IF( KSTEP.EQ.2 ) THEN
- TEMP = A( K, K-1 )
- A( K, K-1 ) = A( KP, K-1 )
- A( KP, K-1 ) = TEMP
- END IF
- END IF
-*
- K = K - KSTEP
- GO TO 50
- 60 CONTINUE
- END IF
-*
- RETURN
-*
-* End of DSYTRI
-*
- END