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SUBROUTINE SSPTRI( UPLO, N, AP, IPIV, WORK, INFO )
*
* -- LAPACK routine (version 3.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2006
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER INFO, N
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
REAL AP( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* SSPTRI computes the inverse of a real symmetric indefinite matrix
* A in packed storage using the factorization A = U*D*U**T or
* A = L*D*L**T computed by SSPTRF.
*
* 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.
*
* AP (input/output) REAL array, dimension (N*(N+1)/2)
* On entry, the block diagonal matrix D and the multipliers
* used to obtain the factor U or L as computed by SSPTRF,
* stored as a packed triangular matrix.
*
* On exit, if INFO = 0, the (symmetric) inverse of the original
* matrix, stored as a packed triangular matrix. The j-th column
* of inv(A) is stored in the array AP as follows:
* if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
* if UPLO = 'L',
* AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
*
* IPIV (input) INTEGER array, dimension (N)
* Details of the interchanges and the block structure of D
* as determined by SSPTRF.
*
* WORK (workspace) REAL 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 ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER J, K, KC, KCNEXT, KP, KPC, KSTEP, KX, NPP
REAL AK, AKKP1, AKP1, D, T, TEMP
* ..
* .. External Functions ..
LOGICAL LSAME
REAL SDOT
EXTERNAL LSAME, SDOT
* ..
* .. External Subroutines ..
EXTERNAL SCOPY, SSPMV, SSWAP, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS
* ..
* .. 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( 'SSPTRI', -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
*
KP = N*( N+1 ) / 2
DO 10 INFO = N, 1, -1
IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO )
$ RETURN
KP = KP - INFO
10 CONTINUE
ELSE
*
* Lower triangular storage: examine D from top to bottom.
*
KP = 1
DO 20 INFO = 1, N
IF( IPIV( INFO ).GT.0 .AND. AP( KP ).EQ.ZERO )
$ RETURN
KP = KP + N - INFO + 1
20 CONTINUE
END IF
INFO = 0
*
IF( UPPER ) THEN
*
* Compute inv(A) from the factorization A = U*D*U**T.
*
* 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
KC = 1
30 CONTINUE
*
* If K > N, exit from loop.
*
IF( K.GT.N )
$ GO TO 50
*
KCNEXT = KC + K
IF( IPIV( K ).GT.0 ) THEN
*
* 1 x 1 diagonal block
*
* Invert the diagonal block.
*
AP( KC+K-1 ) = ONE / AP( KC+K-1 )
*
* Compute column K of the inverse.
*
IF( K.GT.1 ) THEN
CALL SCOPY( K-1, AP( KC ), 1, WORK, 1 )
CALL SSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO, AP( KC ),
$ 1 )
AP( KC+K-1 ) = AP( KC+K-1 ) -
$ SDOT( K-1, WORK, 1, AP( KC ), 1 )
END IF
KSTEP = 1
ELSE
*
* 2 x 2 diagonal block
*
* Invert the diagonal block.
*
T = ABS( AP( KCNEXT+K-1 ) )
AK = AP( KC+K-1 ) / T
AKP1 = AP( KCNEXT+K ) / T
AKKP1 = AP( KCNEXT+K-1 ) / T
D = T*( AK*AKP1-ONE )
AP( KC+K-1 ) = AKP1 / D
AP( KCNEXT+K ) = AK / D
AP( KCNEXT+K-1 ) = -AKKP1 / D
*
* Compute columns K and K+1 of the inverse.
*
IF( K.GT.1 ) THEN
CALL SCOPY( K-1, AP( KC ), 1, WORK, 1 )
CALL SSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO, AP( KC ),
$ 1 )
AP( KC+K-1 ) = AP( KC+K-1 ) -
$ SDOT( K-1, WORK, 1, AP( KC ), 1 )
AP( KCNEXT+K-1 ) = AP( KCNEXT+K-1 ) -
$ SDOT( K-1, AP( KC ), 1, AP( KCNEXT ),
$ 1 )
CALL SCOPY( K-1, AP( KCNEXT ), 1, WORK, 1 )
CALL SSPMV( UPLO, K-1, -ONE, AP, WORK, 1, ZERO,
$ AP( KCNEXT ), 1 )
AP( KCNEXT+K ) = AP( KCNEXT+K ) -
$ SDOT( K-1, WORK, 1, AP( KCNEXT ), 1 )
END IF
KSTEP = 2
KCNEXT = KCNEXT + K + 1
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)
*
KPC = ( KP-1 )*KP / 2 + 1
CALL SSWAP( KP-1, AP( KC ), 1, AP( KPC ), 1 )
KX = KPC + KP - 1
DO 40 J = KP + 1, K - 1
KX = KX + J - 1
TEMP = AP( KC+J-1 )
AP( KC+J-1 ) = AP( KX )
AP( KX ) = TEMP
40 CONTINUE
TEMP = AP( KC+K-1 )
AP( KC+K-1 ) = AP( KPC+KP-1 )
AP( KPC+KP-1 ) = TEMP
IF( KSTEP.EQ.2 ) THEN
TEMP = AP( KC+K+K-1 )
AP( KC+K+K-1 ) = AP( KC+K+KP-1 )
AP( KC+K+KP-1 ) = TEMP
END IF
END IF
*
K = K + KSTEP
KC = KCNEXT
GO TO 30
50 CONTINUE
*
ELSE
*
* Compute inv(A) from the factorization A = L*D*L**T.
*
* 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.
*
NPP = N*( N+1 ) / 2
K = N
KC = NPP
60 CONTINUE
*
* If K < 1, exit from loop.
*
IF( K.LT.1 )
$ GO TO 80
*
KCNEXT = KC - ( N-K+2 )
IF( IPIV( K ).GT.0 ) THEN
*
* 1 x 1 diagonal block
*
* Invert the diagonal block.
*
AP( KC ) = ONE / AP( KC )
*
* Compute column K of the inverse.
*
IF( K.LT.N ) THEN
CALL SCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
CALL SSPMV( UPLO, N-K, -ONE, AP( KC+N-K+1 ), WORK, 1,
$ ZERO, AP( KC+1 ), 1 )
AP( KC ) = AP( KC ) - SDOT( N-K, WORK, 1, AP( KC+1 ), 1 )
END IF
KSTEP = 1
ELSE
*
* 2 x 2 diagonal block
*
* Invert the diagonal block.
*
T = ABS( AP( KCNEXT+1 ) )
AK = AP( KCNEXT ) / T
AKP1 = AP( KC ) / T
AKKP1 = AP( KCNEXT+1 ) / T
D = T*( AK*AKP1-ONE )
AP( KCNEXT ) = AKP1 / D
AP( KC ) = AK / D
AP( KCNEXT+1 ) = -AKKP1 / D
*
* Compute columns K-1 and K of the inverse.
*
IF( K.LT.N ) THEN
CALL SCOPY( N-K, AP( KC+1 ), 1, WORK, 1 )
CALL SSPMV( UPLO, N-K, -ONE, AP( KC+( N-K+1 ) ), WORK, 1,
$ ZERO, AP( KC+1 ), 1 )
AP( KC ) = AP( KC ) - SDOT( N-K, WORK, 1, AP( KC+1 ), 1 )
AP( KCNEXT+1 ) = AP( KCNEXT+1 ) -
$ SDOT( N-K, AP( KC+1 ), 1,
$ AP( KCNEXT+2 ), 1 )
CALL SCOPY( N-K, AP( KCNEXT+2 ), 1, WORK, 1 )
CALL SSPMV( UPLO, N-K, -ONE, AP( KC+( N-K+1 ) ), WORK, 1,
$ ZERO, AP( KCNEXT+2 ), 1 )
AP( KCNEXT ) = AP( KCNEXT ) -
$ SDOT( N-K, WORK, 1, AP( KCNEXT+2 ), 1 )
END IF
KSTEP = 2
KCNEXT = KCNEXT - ( N-K+3 )
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)
*
KPC = NPP - ( N-KP+1 )*( N-KP+2 ) / 2 + 1
IF( KP.LT.N )
$ CALL SSWAP( N-KP, AP( KC+KP-K+1 ), 1, AP( KPC+1 ), 1 )
KX = KC + KP - K
DO 70 J = K + 1, KP - 1
KX = KX + N - J + 1
TEMP = AP( KC+J-K )
AP( KC+J-K ) = AP( KX )
AP( KX ) = TEMP
70 CONTINUE
TEMP = AP( KC )
AP( KC ) = AP( KPC )
AP( KPC ) = TEMP
IF( KSTEP.EQ.2 ) THEN
TEMP = AP( KC-N+K-1 )
AP( KC-N+K-1 ) = AP( KC-N+KP-1 )
AP( KC-N+KP-1 ) = TEMP
END IF
END IF
*
K = K - KSTEP
KC = KCNEXT
GO TO 60
80 CONTINUE
END IF
*
RETURN
*
* End of SSPTRI
*
END
|
