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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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