LAPACK 3.3.0

zsysv.f

Go to the documentation of this file.
00001       SUBROUTINE ZSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
00002      $                  LWORK, INFO )
00003 *
00004 *  -- LAPACK driver routine (version 3.2.2) --
00005 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00006 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00007 *     June 2010
00008 *
00009 *     .. Scalar Arguments ..
00010       CHARACTER          UPLO
00011       INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
00012 *     ..
00013 *     .. Array Arguments ..
00014       INTEGER            IPIV( * )
00015       COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  ZSYSV computes the solution to a complex system of linear equations
00022 *     A * X = B,
00023 *  where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
00024 *  matrices.
00025 *
00026 *  The diagonal pivoting method is used to factor A as
00027 *     A = U * D * U**T,  if UPLO = 'U', or
00028 *     A = L * D * L**T,  if UPLO = 'L',
00029 *  where U (or L) is a product of permutation and unit upper (lower)
00030 *  triangular matrices, and D is symmetric and block diagonal with
00031 *  1-by-1 and 2-by-2 diagonal blocks.  The factored form of A is then
00032 *  used to solve the system of equations A * X = B.
00033 *
00034 *  Arguments
00035 *  =========
00036 *
00037 *  UPLO    (input) CHARACTER*1
00038 *          = 'U':  Upper triangle of A is stored;
00039 *          = 'L':  Lower triangle of A is stored.
00040 *
00041 *  N       (input) INTEGER
00042 *          The number of linear equations, i.e., the order of the
00043 *          matrix A.  N >= 0.
00044 *
00045 *  NRHS    (input) INTEGER
00046 *          The number of right hand sides, i.e., the number of columns
00047 *          of the matrix B.  NRHS >= 0.
00048 *
00049 *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
00050 *          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
00051 *          N-by-N upper triangular part of A contains the upper
00052 *          triangular part of the matrix A, and the strictly lower
00053 *          triangular part of A is not referenced.  If UPLO = 'L', the
00054 *          leading N-by-N lower triangular part of A contains the lower
00055 *          triangular part of the matrix A, and the strictly upper
00056 *          triangular part of A is not referenced.
00057 *
00058 *          On exit, if INFO = 0, the block diagonal matrix D and the
00059 *          multipliers used to obtain the factor U or L from the
00060 *          factorization A = U*D*U**T or A = L*D*L**T as computed by
00061 *          ZSYTRF.
00062 *
00063 *  LDA     (input) INTEGER
00064 *          The leading dimension of the array A.  LDA >= max(1,N).
00065 *
00066 *  IPIV    (output) INTEGER array, dimension (N)
00067 *          Details of the interchanges and the block structure of D, as
00068 *          determined by ZSYTRF.  If IPIV(k) > 0, then rows and columns
00069 *          k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
00070 *          diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
00071 *          then rows and columns k-1 and -IPIV(k) were interchanged and
00072 *          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
00073 *          IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
00074 *          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
00075 *          diagonal block.
00076 *
00077 *  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
00078 *          On entry, the N-by-NRHS right hand side matrix B.
00079 *          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
00080 *
00081 *  LDB     (input) INTEGER
00082 *          The leading dimension of the array B.  LDB >= max(1,N).
00083 *
00084 *  WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
00085 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
00086 *
00087 *  LWORK   (input) INTEGER
00088 *          The length of WORK.  LWORK >= 1, and for best performance
00089 *          LWORK >= max(1,N*NB), where NB is the optimal blocksize for
00090 *          ZSYTRF.
00091 *
00092 *          If LWORK = -1, then a workspace query is assumed; the routine
00093 *          only calculates the optimal size of the WORK array, returns
00094 *          this value as the first entry of the WORK array, and no error
00095 *          message related to LWORK is issued by XERBLA.
00096 *
00097 *  INFO    (output) INTEGER
00098 *          = 0: successful exit
00099 *          < 0: if INFO = -i, the i-th argument had an illegal value
00100 *          > 0: if INFO = i, D(i,i) is exactly zero.  The factorization
00101 *               has been completed, but the block diagonal matrix D is
00102 *               exactly singular, so the solution could not be computed.
00103 *
00104 *  =====================================================================
00105 *
00106 *     .. Local Scalars ..
00107       LOGICAL            LQUERY
00108       INTEGER            LWKOPT, NB
00109 *     ..
00110 *     .. External Functions ..
00111       LOGICAL            LSAME
00112       INTEGER            ILAENV
00113       EXTERNAL           LSAME, ILAENV
00114 *     ..
00115 *     .. External Subroutines ..
00116       EXTERNAL           XERBLA, ZSYTRF, ZSYTRS2
00117 *     ..
00118 *     .. Intrinsic Functions ..
00119       INTRINSIC          MAX
00120 *     ..
00121 *     .. Executable Statements ..
00122 *
00123 *     Test the input parameters.
00124 *
00125       INFO = 0
00126       LQUERY = ( LWORK.EQ.-1 )
00127       IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00128          INFO = -1
00129       ELSE IF( N.LT.0 ) THEN
00130          INFO = -2
00131       ELSE IF( NRHS.LT.0 ) THEN
00132          INFO = -3
00133       ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
00134          INFO = -5
00135       ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
00136          INFO = -8
00137       ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
00138          INFO = -10
00139       END IF
00140 *
00141       IF( INFO.EQ.0 ) THEN
00142          IF( N.EQ.0 ) THEN
00143             LWKOPT = 1
00144          ELSE
00145             NB = ILAENV( 1, 'ZSYTRF', UPLO, N, -1, -1, -1 )
00146             LWKOPT = N*NB
00147          END IF
00148          WORK( 1 ) = LWKOPT
00149       END IF
00150 *
00151       IF( INFO.NE.0 ) THEN
00152          CALL XERBLA( 'ZSYSV ', -INFO )
00153          RETURN
00154       ELSE IF( LQUERY ) THEN
00155          RETURN
00156       END IF
00157 *
00158 *     Compute the factorization A = U*D*U' or A = L*D*L'.
00159 *
00160       CALL ZSYTRF( UPLO, N, A, LDA, IPIV, WORK, LWORK, INFO )
00161       IF( INFO.EQ.0 ) THEN
00162 *
00163 *        Solve the system A*X = B, overwriting B with X.
00164 *
00165          CALL ZSYTRS2( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, INFO )
00166 *
00167       END IF
00168 *
00169       WORK( 1 ) = LWKOPT
00170 *
00171       RETURN
00172 *
00173 *     End of ZSYSV
00174 *
00175       END
 All Files Functions