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Diffstat (limited to 'src/fortran/lapack/dsytri.f')
| -rw-r--r-- | src/fortran/lapack/dsytri.f | 312 |
1 files changed, 312 insertions, 0 deletions
diff --git a/src/fortran/lapack/dsytri.f b/src/fortran/lapack/dsytri.f new file mode 100644 index 0000000..361de9a --- /dev/null +++ b/src/fortran/lapack/dsytri.f @@ -0,0 +1,312 @@ + 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 |