zspsv.f.html

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      SUBROUTINE <a name="ZSPSV.1"></a><a href="zspsv.f.html#ZSPSV.1">ZSPSV</a>( UPLO, N, NRHS, AP, IPIV, B, LDB, 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, LDB, N, NRHS
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            IPIV( * )
      COMPLEX*16         AP( * ), B( LDB, * )
<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="ZSPSV.19"></a><a href="zspsv.f.html#ZSPSV.1">ZSPSV</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 stored in packed format and X
</span><span class="comment">*</span><span class="comment">  and B are N-by-NRHS 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, D is symmetric and block diagonal with 1-by-1
</span><span class="comment">*</span><span class="comment">  and 2-by-2 diagonal blocks.  The factored form of A is then used to
</span><span class="comment">*</span><span class="comment">  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">  AP      (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
</span><span class="comment">*</span><span class="comment">          On entry, the upper or lower triangle of the symmetric matrix
</span><span class="comment">*</span><span class="comment">          A, packed columnwise in a linear array.  The j-th column of A
</span><span class="comment">*</span><span class="comment">          is stored in the array AP as follows:
</span><span class="comment">*</span><span class="comment">          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1&lt;=i&lt;=j;
</span><span class="comment">*</span><span class="comment">          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j&lt;=i&lt;=n.
</span><span class="comment">*</span><span class="comment">          See below for further details.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          On exit, the block diagonal matrix D and the multipliers used
</span><span class="comment">*</span><span class="comment">          to obtain the factor U or L from the factorization
</span><span class="comment">*</span><span class="comment">          A = U*D*U**T or A = L*D*L**T as computed by <a name="ZSPTRF.57"></a><a href="zsptrf.f.html#ZSPTRF.1">ZSPTRF</a>, stored as
</span><span class="comment">*</span><span class="comment">          a packed triangular matrix in the same storage format as A.
</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="ZSPTRF.62"></a><a href="zsptrf.f.html#ZSPTRF.1">ZSPTRF</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).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">          &lt; 0:  if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment">          &gt; 0:  if INFO = i, D(i,i) is exactly zero.  The factorization
</span><span class="comment">*</span><span class="comment">                has been completed, but the block diagonal matrix D is
</span><span class="comment">*</span><span class="comment">                exactly singular, so the solution could not be
</span><span class="comment">*</span><span class="comment">                computed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further Details
</span><span class="comment">*</span><span class="comment">  ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  The packed storage scheme is illustrated by the following example
</span><span class="comment">*</span><span class="comment">  when N = 4, UPLO = 'U':
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Two-dimensional storage of the symmetric matrix A:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     a11 a12 a13 a14
</span><span class="comment">*</span><span class="comment">         a22 a23 a24
</span><span class="comment">*</span><span class="comment">             a33 a34     (aij = aji)
</span><span class="comment">*</span><span class="comment">                 a44
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Packed storage of the upper triangle of A:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. External Functions ..
</span>      LOGICAL            <a name="LSAME.106"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
      EXTERNAL           <a name="LSAME.107"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. External Subroutines ..
</span>      EXTERNAL           <a name="XERBLA.110"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>, <a name="ZSPTRF.110"></a><a href="zsptrf.f.html#ZSPTRF.1">ZSPTRF</a>, <a name="ZSPTRS.110"></a><a href="zsptrs.f.html#ZSPTRS.1">ZSPTRS</a>
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          MAX
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0
      IF( .NOT.<a name="LSAME.120"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) .AND. .NOT.<a name="LSAME.120"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</span> ) ) 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 <a name="XERBLA.130"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="ZSPSV.130"></a><a href="zspsv.f.html#ZSPSV.1">ZSPSV</a> '</span>, -INFO )
         RETURN
      END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     Compute the factorization A = U*D*U' or A = L*D*L'.
</span><span class="comment">*</span><span class="comment">
</span>      CALL <a name="ZSPTRF.136"></a><a href="zsptrf.f.html#ZSPTRF.1">ZSPTRF</a>( UPLO, N, AP, IPIV, INFO )
      IF( INFO.EQ.0 ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">        Solve the system A*X = B, overwriting B with X.
</span><span class="comment">*</span><span class="comment">
</span>         CALL <a name="ZSPTRS.141"></a><a href="zsptrs.f.html#ZSPTRS.1">ZSPTRS</a>( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
<span class="comment">*</span><span class="comment">
</span>      END IF
      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="ZSPSV.146"></a><a href="zspsv.f.html#ZSPSV.1">ZSPSV</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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