dsytrs()

subroutine dsytrs	(	character	uplo,
		integer	n,
		integer	nrhs,
		double precision, dimension( lda, * )	a,
		integer	lda,
		integer, dimension( * )	ipiv,
		double precision, dimension( ldb, * )	b,
		integer	ldb,
		integer	info
	)

DSYTRS

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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.

Parameters

[in]	UPLO	UPLO is 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.
[in]	N	N is INTEGER The order of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in]	A	A is 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.
[in]	LDA	LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).
[in]	IPIV	IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by DSYTRF.
[in,out]	B	B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	INFO	INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 119 of file dsytrs.f.

*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDA, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      DOUBLE PRECISION   A( LDA, * ), B( LDB, * )
*     ..
*
*  =====================================================================
*
*     .. 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**T.
*
*        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**T *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**T(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**T(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**T.
*
*        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**T *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**T(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**T(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
*

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