```      SUBROUTINE ZSPTRS( UPLO, N, NRHS, AP, 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, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
INTEGER            IPIV( * )
COMPLEX*16         AP( * ), B( LDB, * )
*     ..
*
*  Purpose
*  =======
*
*  ZSPTRS solves a system of linear equations A*X = B with a complex
*  symmetric matrix A stored in packed format using the factorization
*  A = U*D*U**T or A = L*D*L**T computed by ZSPTRF.
*
*  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.
*
*  AP      (input) COMPLEX*16 array, dimension (N*(N+1)/2)
*          The block diagonal matrix D and the multipliers used to
*          obtain the factor U or L as computed by ZSPTRF, stored as a
*          packed triangular matrix.
*
*  IPIV    (input) INTEGER array, dimension (N)
*          Details of the interchanges and the block structure of D
*          as determined by ZSPTRF.
*
*  B       (input/output) COMPLEX*16 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 ..
COMPLEX*16         ONE
PARAMETER          ( ONE = ( 1.0D+0, 0.0D+0 ) )
*     ..
*     .. Local Scalars ..
LOGICAL            UPPER
INTEGER            J, K, KC, KP
COMPLEX*16         AK, AKM1, AKM1K, BK, BKM1, DENOM
*     ..
*     .. External Functions ..
LOGICAL            LSAME
EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
EXTERNAL           XERBLA, ZGEMV, ZGERU, ZSCAL, ZSWAP
*     ..
*     .. 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( LDB.LT.MAX( 1, N ) ) THEN
INFO = -7
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZSPTRS', -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
KC = N*( N+1 ) / 2 + 1
10    CONTINUE
*
*        If K < 1, exit from loop.
*
IF( K.LT.1 )
\$      GO TO 30
*
KC = KC - K
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 ZSWAP( 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 ZGERU( K-1, NRHS, -ONE, AP( KC ), 1, B( K, 1 ), LDB,
\$                  B( 1, 1 ), LDB )
*
*           Multiply by the inverse of the diagonal block.
*
CALL ZSCAL( NRHS, ONE / AP( KC+K-1 ), 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 ZSWAP( 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 ZGERU( K-2, NRHS, -ONE, AP( KC ), 1, B( K, 1 ), LDB,
\$                  B( 1, 1 ), LDB )
CALL ZGERU( K-2, NRHS, -ONE, AP( KC-( K-1 ) ), 1,
\$                  B( K-1, 1 ), LDB, B( 1, 1 ), LDB )
*
*           Multiply by the inverse of the diagonal block.
*
AKM1K = AP( KC+K-2 )
AKM1 = AP( KC-1 ) / AKM1K
AK = AP( KC+K-1 ) / 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
KC = KC - K + 1
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
KC = 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 ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, AP( KC ),
\$                  1, ONE, B( K, 1 ), LDB )
*
*           Interchange rows K and IPIV(K).
*
KP = IPIV( K )
IF( KP.NE.K )
\$         CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
KC = KC + K
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 ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB, AP( KC ),
\$                  1, ONE, B( K, 1 ), LDB )
CALL ZGEMV( 'Transpose', K-1, NRHS, -ONE, B, LDB,
\$                  AP( KC+K ), 1, ONE, B( K+1, 1 ), LDB )
*
*           Interchange rows K and -IPIV(K).
*
KP = -IPIV( K )
IF( KP.NE.K )
\$         CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
KC = KC + 2*K + 1
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
KC = 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 ZSWAP( 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 ZGERU( N-K, NRHS, -ONE, AP( KC+1 ), 1, B( K, 1 ),
\$                     LDB, B( K+1, 1 ), LDB )
*
*           Multiply by the inverse of the diagonal block.
*
CALL ZSCAL( NRHS, ONE / AP( KC ), B( K, 1 ), LDB )
KC = KC + N - K + 1
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 ZSWAP( 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 ZGERU( N-K-1, NRHS, -ONE, AP( KC+2 ), 1, B( K, 1 ),
\$                     LDB, B( K+2, 1 ), LDB )
CALL ZGERU( N-K-1, NRHS, -ONE, AP( KC+N-K+2 ), 1,
\$                     B( K+1, 1 ), LDB, B( K+2, 1 ), LDB )
END IF
*
*           Multiply by the inverse of the diagonal block.
*
AKM1K = AP( KC+1 )
AKM1 = AP( KC ) / AKM1K
AK = AP( KC+N-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
KC = KC + 2*( N-K ) + 1
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
KC = N*( N+1 ) / 2 + 1
90    CONTINUE
*
*        If K < 1, exit from loop.
*
IF( K.LT.1 )
\$      GO TO 100
*
KC = KC - ( N-K+1 )
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 ZGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
\$                     LDB, AP( KC+1 ), 1, ONE, B( K, 1 ), LDB )
*
*           Interchange rows K and IPIV(K).
*
KP = IPIV( K )
IF( KP.NE.K )
\$         CALL ZSWAP( 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 ZGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
\$                     LDB, AP( KC+1 ), 1, ONE, B( K, 1 ), LDB )
CALL ZGEMV( 'Transpose', N-K, NRHS, -ONE, B( K+1, 1 ),
\$                     LDB, AP( KC-( N-K ) ), 1, ONE, B( K-1, 1 ),
\$                     LDB )
END IF
*
*           Interchange rows K and -IPIV(K).
*
KP = -IPIV( K )
IF( KP.NE.K )
\$         CALL ZSWAP( NRHS, B( K, 1 ), LDB, B( KP, 1 ), LDB )
KC = KC - ( N-K+2 )
K = K - 2
END IF
*
GO TO 90
100    CONTINUE
END IF
*
RETURN
*
*     End of ZSPTRS
*
END

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