cspsv.f

Go to the documentation of this file.

      SUBROUTINE CSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
*
*  -- LAPACK driver routine (version 3.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2006
*
*     .. Scalar Arguments ..
      CHARACTER          UPLO
      INTEGER            INFO, LDB, N, NRHS
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      COMPLEX            AP( * ), B( LDB, * )
*     ..
*
*  Purpose
*  =======
*
*  CSPSV computes the solution to a complex system of linear equations
*     A * X = B,
*  where A is an N-by-N symmetric matrix stored in packed format and X
*  and B are N-by-NRHS matrices.
*
*  The diagonal pivoting method is used to factor A as
*     A = U * D * U**T,  if UPLO = 'U', or
*     A = L * D * L**T,  if UPLO = 'L',
*  where U (or L) is a product of permutation and unit upper (lower)
*  triangular matrices, D is symmetric and block diagonal with 1-by-1
*  and 2-by-2 diagonal blocks.  The factored form of A is then used to
*  solve the system of equations A * X = B.
*
*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          = 'U':  Upper triangle of A is stored;
*          = 'L':  Lower triangle of A is stored.
*
*  N       (input) INTEGER
*          The number of linear equations, i.e., 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/output) COMPLEX array, dimension (N*(N+1)/2)
*          On entry, the upper or lower triangle of the symmetric matrix
*          A, packed columnwise in a linear array.  The j-th column of A
*          is stored in the array AP as follows:
*          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
*          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
*          See below for further details.
*
*          On exit, the block diagonal matrix D and the multipliers used
*          to obtain the factor U or L from the factorization
*          A = U*D*U**T or A = L*D*L**T as computed by CSPTRF, stored as
*          a packed triangular matrix in the same storage format as A.
*
*  IPIV    (output) INTEGER array, dimension (N)
*          Details of the interchanges and the block structure of D, as
*          determined by CSPTRF.  If IPIV(k) > 0, then rows and columns
*          k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
*          diagonal block.  If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0,
*          then rows and columns k-1 and -IPIV(k) were interchanged and
*          D(k-1:k,k-1:k) is a 2-by-2 diagonal block.  If UPLO = 'L' and
*          IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
*          -IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
*          diagonal block.
*
*  B       (input/output) COMPLEX array, dimension (LDB,NRHS)
*          On entry, the N-by-NRHS right hand side matrix B.
*          On exit, if INFO = 0, the N-by-NRHS 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
*          > 0:  if INFO = i, D(i,i) is exactly zero.  The factorization
*                has been completed, but the block diagonal matrix D is
*                exactly singular, so the solution could not be
*                computed.
*
*  Further Details
*  ===============
*
*  The packed storage scheme is illustrated by the following example
*  when N = 4, UPLO = 'U':
*
*  Two-dimensional storage of the symmetric matrix A:
*
*     a11 a12 a13 a14
*         a22 a23 a24
*             a33 a34     (aij = aji)
*                 a44
*
*  Packed storage of the upper triangle of A:
*
*  AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
*
*  =====================================================================
*
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           CSPTRF, CSPTRS, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF( .NOT.LSAME( UPLO, 'U' ) .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( 'CSPSV ', -INFO )
         RETURN
      END IF
*
*     Compute the factorization A = U*D*U' or A = L*D*L'.
*
      CALL CSPTRF( UPLO, N, AP, IPIV, INFO )
      IF( INFO.EQ.0 ) THEN
*
*        Solve the system A*X = B, overwriting B with X.
*
         CALL CSPTRS( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
*
      END IF
      RETURN
*
*     End of CSPSV
*
      END