zsysv.f.html

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      SUBROUTINE <a name="ZSYSV.1"></a><a href="zsysv.f.html#ZSYSV.1">ZSYSV</a>( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
     $                  LWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK driver routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          UPLO
      INTEGER            INFO, LDA, LDB, LWORK, N, NRHS
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            IPIV( * )
      COMPLEX*16         A( LDA, * ), B( LDB, * ), WORK( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="ZSYSV.20"></a><a href="zsysv.f.html#ZSYSV.1">ZSYSV</a> computes the solution to a complex system of linear equations
</span><span class="comment">*</span><span class="comment">     A * X = B,
</span><span class="comment">*</span><span class="comment">  where A is an N-by-N symmetric matrix and X and B are N-by-NRHS
</span><span class="comment">*</span><span class="comment">  matrices.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The diagonal pivoting method is used to factor A as
</span><span class="comment">*</span><span class="comment">     A = U * D * U**T,  if UPLO = 'U', or
</span><span class="comment">*</span><span class="comment">     A = L * D * L**T,  if UPLO = 'L',
</span><span class="comment">*</span><span class="comment">  where U (or L) is a product of permutation and unit upper (lower)
</span><span class="comment">*</span><span class="comment">  triangular matrices, and D is symmetric and block diagonal with
</span><span class="comment">*</span><span class="comment">  1-by-1 and 2-by-2 diagonal blocks.  The factored form of A is then
</span><span class="comment">*</span><span class="comment">  used to solve the system of equations A * X = B.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  UPLO    (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'U':  Upper triangle of A is stored;
</span><span class="comment">*</span><span class="comment">          = 'L':  Lower triangle of A is stored.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of linear equations, i.e., the order of the
</span><span class="comment">*</span><span class="comment">          matrix A.  N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  NRHS    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of right hand sides, i.e., the number of columns
</span><span class="comment">*</span><span class="comment">          of the matrix B.  NRHS &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment">          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
</span><span class="comment">*</span><span class="comment">          N-by-N upper triangular part of A contains the upper
</span><span class="comment">*</span><span class="comment">          triangular part of the matrix A, and the strictly lower
</span><span class="comment">*</span><span class="comment">          triangular part of A is not referenced.  If UPLO = 'L', the
</span><span class="comment">*</span><span class="comment">          leading N-by-N lower triangular part of A contains the lower
</span><span class="comment">*</span><span class="comment">          triangular part of the matrix A, and the strictly upper
</span><span class="comment">*</span><span class="comment">          triangular part of A is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, the block diagonal matrix D and the
</span><span class="comment">*</span><span class="comment">          multipliers used to obtain the factor U or L from the
</span><span class="comment">*</span><span class="comment">          factorization A = U*D*U**T or A = L*D*L**T as computed by
</span><span class="comment">*</span><span class="comment">          <a name="ZSYTRF.60"></a><a href="zsytrf.f.html#ZSYTRF.1">ZSYTRF</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array A.  LDA &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IPIV    (output) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment">          Details of the interchanges and the block structure of D, as
</span><span class="comment">*</span><span class="comment">          determined by <a name="ZSYTRF.67"></a><a href="zsytrf.f.html#ZSYTRF.1">ZSYTRF</a>.  If IPIV(k) &gt; 0, then rows and columns
</span><span class="comment">*</span><span class="comment">          k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
</span><span class="comment">*</span><span class="comment">          diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) &lt; 0,
</span><span class="comment">*</span><span class="comment">          then rows and columns k-1 and -IPIV(k) were interchanged and
</span><span class="comment">*</span><span class="comment">          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
</span><span class="comment">*</span><span class="comment">          IPIV(k) = IPIV(k+1) &lt; 0, then rows and columns k+1 and
</span><span class="comment">*</span><span class="comment">          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
</span><span class="comment">*</span><span class="comment">          diagonal block.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
</span><span class="comment">*</span><span class="comment">          On entry, the N-by-NRHS right hand side matrix B.
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, the N-by-NRHS solution matrix X.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDB     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array B.  LDB &gt;= max(1,N).
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