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+ SUBROUTINE DSYTRS( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, 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, LDB, N, NRHS
+* ..
+* .. Array Arguments ..
+ INTEGER IPIV( * )
+ DOUBLE PRECISION A( LDA, * ), B( LDB, * )
+* ..
+*
+* Purpose
+* =======
+*
+* DSYTRS solves a system of linear equations A*X = B with a real
+* symmetric 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.
+*
+* NRHS (input) INTEGER
+* The number of right hand sides, i.e., the number of columns
+* of the matrix B. NRHS >= 0.
+*
+* A (input) DOUBLE PRECISION array, dimension (LDA,N)
+* The block diagonal matrix D and the multipliers used to
+* obtain the factor U or L as computed by DSYTRF.
+*
+* 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.
+*
+* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
+* On entry, the right hand side matrix B.
+* On exit, the solution matrix X.
+*
+* LDB (input) INTEGER
+* The leading dimension of the array B. LDB >= max(1,N).
+*
+* INFO (output) INTEGER
+* = 0: successful exit
+* < 0: if INFO = -i, the i-th argument had an illegal value
+*
+* =====================================================================
+*
+* .. Parameters ..
+ DOUBLE PRECISION ONE
+ PARAMETER ( ONE = 1.0D+0 )
+* ..
+* .. Local Scalars ..
+ LOGICAL UPPER
+ INTEGER J, K, KP
+ DOUBLE PRECISION AK, AKM1, AKM1K, BK, BKM1, DENOM
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ EXTERNAL LSAME
+* ..
+* .. External Subroutines ..
+ EXTERNAL DGEMV, DGER, DSCAL, DSWAP, XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX
+* ..
+* .. Executable Statements ..
+*
+ 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( NRHS.LT.0 ) THEN
+ INFO = -3
+ ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
+ INFO = -5
+ ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
+ INFO = -8
+ END IF
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'DSYTRS', -INFO )
+ RETURN
+ END IF
+*
+* Quick return if possible
+*
+ IF( N.EQ.0 .OR. NRHS.EQ.0 )
+ $ RETURN
+*
+ IF( UPPER ) THEN
+*
+* Solve A*X = B, where A = U*D*U'.
+*
+* First solve U*D*X = B, overwriting B with X.
+*
+* K is the main loop index, decreasing from N to 1 in steps of
+* 1 or 2, depending on the size of the diagonal blocks.
+*
+ K = N
+ 10 CONTINUE
+*
+* If K < 1, exit from loop.
+*
+ IF( K.LT.1 )
+ $ GO TO 30
+*
+ IF( IPIV( K ).GT.0 ) THEN
+*
+* 1 x 1 diagonal block
+*
+* Interchange rows K and IPIV(K).
+*
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+* Multiply by inv(U(K)), where U(K) is the transformation
+* stored in column K of A.
+*
+ CALL DGER( K-1, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
+ $ B( 1, 1 ), LDB )
+*
+* Multiply by the inverse of the diagonal block.
+*
+ CALL DSCAL( NRHS, ONE / A( K, K ), B( K, 1 ), LDB )
+ K = K - 1
+ ELSE
+*
+* 2 x 2 diagonal block
+*
+* Interchange rows K-1 and -IPIV(K).
+*
+ KP = -IPIV( K )
+ IF( KP.NE.K-1 )
+ $ CALL DSWAP( NRHS, B( K-1, 1 ), LDB, B( KP, 1 ), LDB )
+*
+* Multiply by inv(U(K)), where U(K) is the transformation
+* stored in columns K-1 and K of A.
+*
+ CALL DGER( K-2, NRHS, -ONE, A( 1, K ), 1, B( K, 1 ), LDB,
+ $ B( 1, 1 ), LDB )
+ CALL DGER( K-2, NRHS, -ONE, A( 1, K-1 ), 1, B( K-1, 1 ),
+ $ LDB, B( 1, 1 ), LDB )
+*
+* Multiply by the inverse of the diagonal block.
+*
+ AKM1K = A( K-1, K )
+ AKM1 = A( K-1, K-1 ) / AKM1K
+ AK = A( K, K ) / AKM1K
+ DENOM = AKM1*AK - ONE
+ DO 20 J = 1, NRHS
+ BKM1 = B( K-1, J ) / AKM1K
+ BK = B( K, J ) / AKM1K
+ B( K-1, J ) = ( AK*BKM1-BK ) / DENOM
+ B( K, J ) = ( AKM1*BK-BKM1 ) / DENOM
+ 20 CONTINUE
+ K = K - 2
+ END IF
+*
+ GO TO 10
+ 30 CONTINUE
+*
+* Next solve U'*X = B, overwriting B with X.
+*
+* 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
+ 40 CONTINUE
+*
+* If K > N, exit from loop.
+*
+ IF( K.GT.N )
+ $ GO TO 50
+*
+ IF( IPIV( K ).GT.0 ) THEN
+*
+* 1 x 1 diagonal block
+*
+* Multiply by inv(U'(K)), where U(K) is the transformation
+* stored in column K of A.
+*
+ CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
+ $ 1, ONE, B( K, 1 ), LDB )
+*
+* Interchange rows K and IPIV(K).
+*
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ K = K + 1
+ ELSE
+*
+* 2 x 2 diagonal block
+*
+* Multiply by inv(U'(K+1)), where U(K+1) is the transformation
+* stored in columns K and K+1 of A.
+*
+ CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, A( 1, K ),
+ $ 1, ONE, B( K, 1 ), LDB )
+ CALL DGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB,
+ $ A( 1, K+1 ), 1, ONE, B( K+1, 1 ), LDB )
+*
+* Interchange rows K and -IPIV(K).
+*
+ KP = -IPIV( K )
+ IF( KP.NE.K )
+ $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ K = K + 2
+ END IF
+*
+ GO TO 40
+ 50 CONTINUE
+*
+ ELSE
+*
+* Solve A*X = B, where A = L*D*L'.
+*
+* First solve L*D*X = B, overwriting B with X.
+*
+* 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
+ 60 CONTINUE
+*
+* If K > N, exit from loop.
+*
+ IF( K.GT.N )
+ $ GO TO 80
+*
+ IF( IPIV( K ).GT.0 ) THEN
+*
+* 1 x 1 diagonal block
+*
+* Interchange rows K and IPIV(K).
+*
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+*
+* Multiply by inv(L(K)), where L(K) is the transformation
+* stored in column K of A.
+*
+ IF( K.LT.N )
+ $ CALL DGER( N-K, NRHS, -ONE, A( K+1, K ), 1, B( K, 1 ),
+ $ LDB, B( K+1, 1 ), LDB )
+*
+* Multiply by the inverse of the diagonal block.
+*
+ CALL DSCAL( NRHS, ONE / A( K, K ), B( K, 1 ), LDB )
+ K = K + 1
+ ELSE
+*
+* 2 x 2 diagonal block
+*
+* Interchange rows K+1 and -IPIV(K).
+*
+ KP = -IPIV( K )
+ IF( KP.NE.K+1 )
+ $ CALL DSWAP( NRHS, B( K+1, 1 ), LDB, B( KP, 1 ), LDB )
+*
+* Multiply by inv(L(K)), where L(K) is the transformation
+* stored in columns K and K+1 of A.
+*
+ IF( K.LT.N-1 ) THEN
+ CALL DGER( N-K-1, NRHS, -ONE, A( K+2, K ), 1, B( K, 1 ),
+ $ LDB, B( K+2, 1 ), LDB )
+ CALL DGER( N-K-1, NRHS, -ONE, A( K+2, K+1 ), 1,
+ $ B( K+1, 1 ), LDB, B( K+2, 1 ), LDB )
+ END IF
+*
+* Multiply by the inverse of the diagonal block.
+*
+ AKM1K = A( K+1, K )
+ AKM1 = A( K, K ) / AKM1K
+ AK = A( K+1, K+1 ) / AKM1K
+ DENOM = AKM1*AK - ONE
+ DO 70 J = 1, NRHS
+ BKM1 = B( K, J ) / AKM1K
+ BK = B( K+1, J ) / AKM1K
+ B( K, J ) = ( AK*BKM1-BK ) / DENOM
+ B( K+1, J ) = ( AKM1*BK-BKM1 ) / DENOM
+ 70 CONTINUE
+ K = K + 2
+ END IF
+*
+ GO TO 60
+ 80 CONTINUE
+*
+* Next solve L'*X = B, overwriting B with X.
+*
+* K is the main loop index, decreasing from N to 1 in steps of
+* 1 or 2, depending on the size of the diagonal blocks.
+*
+ K = N
+ 90 CONTINUE
+*
+* If K < 1, exit from loop.
+*
+ IF( K.LT.1 )
+ $ GO TO 100
+*
+ IF( IPIV( K ).GT.0 ) THEN
+*
+* 1 x 1 diagonal block
+*
+* Multiply by inv(L'(K)), where L(K) is the transformation
+* stored in column K of A.
+*
+ IF( K.LT.N )
+ $ CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
+ $ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
+*
+* Interchange rows K and IPIV(K).
+*
+ KP = IPIV( K )
+ IF( KP.NE.K )
+ $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ K = K - 1
+ ELSE
+*
+* 2 x 2 diagonal block
+*
+* Multiply by inv(L'(K-1)), where L(K-1) is the transformation
+* stored in columns K-1 and K of A.
+*
+ IF( K.LT.N ) THEN
+ CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
+ $ LDB, A( K+1, K ), 1, ONE, B( K, 1 ), LDB )
+ CALL DGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
+ $ LDB, A( K+1, K-1 ), 1, ONE, B( K-1, 1 ),
+ $ LDB )
+ END IF
+*
+* Interchange rows K and -IPIV(K).
+*
+ KP = -IPIV( K )
+ IF( KP.NE.K )
+ $ CALL DSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
+ K = K - 2
+ END IF
+*
+ GO TO 90
+ 100 CONTINUE
+ END IF
+*
+ RETURN
+*
+* End of DSYTRS
+*
+ END
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