zsytf2.f man page

zsytf2.f —

Synopsis

Functions/Subroutines

subroutine zsytf2 (UPLO, N, A, LDA, IPIV, INFO)
ZSYTF2 computes the factorization of a real symmetric indefinite matrix, using the diagonal pivoting method (unblocked algorithm).

Function/Subroutine Documentation

subroutine zsytf2 (characterUPLO, integerN, complex*16, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, integerINFO)

ZSYTF2 computes the factorization of a real symmetric indefinite matrix, using the diagonal pivoting method (unblocked algorithm).  

Purpose:

 ZSYTF2 computes the factorization of a complex symmetric matrix A
 using the Bunch-Kaufman diagonal pivoting method:

    A = U*D*U**T  or  A = L*D*L**T

 where U (or L) is a product of permutation and unit upper (lower)
 triangular matrices, U**T is the transpose of U, and D is symmetric and
 block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

 This is the unblocked version of the algorithm, calling Level 2 BLAS.
Parameters:

UPLO

          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is stored:
          = 'U':  Upper triangular
          = 'L':  Lower triangular

N

          N is INTEGER
          The order of the matrix A.  N >= 0.

A

          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the symmetric matrix A.  If UPLO = 'U', the leading
          n-by-n upper triangular part of A contains the upper
          triangular part of the matrix A, and the strictly lower
          triangular part of A is not referenced.  If UPLO = 'L', the
          leading n-by-n lower triangular part of A contains the lower
          triangular part of the matrix A, and the strictly upper
          triangular part of A is not referenced.

          On exit, the block diagonal matrix D and the multipliers used
          to obtain the factor U or L (see below for further details).

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

IPIV

          IPIV is INTEGER array, dimension (N)
          Details of the interchanges and the block structure of D.

          If UPLO = 'U':
             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 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':
             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 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.

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value
          > 0: if INFO = k, D(k,k) is exactly zero.  The factorization
               has been completed, but the block diagonal matrix D is
               exactly singular, and division by zero will occur if it
               is used to solve a system of equations.
Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2013

Further Details:

  If UPLO = 'U', then A = U*D*U**T, where
     U = P(n)*U(n)* ... *P(k)U(k)* ...,
  i.e., U is a product of terms P(k)*U(k), where k decreases from n to
  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such
  that if the diagonal block D(k) is of order s (s = 1 or 2), then

             (   I    v    0   )   k-s
     U(k) =  (   0    I    0   )   s
             (   0    0    I   )   n-k
                k-s   s   n-k

  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).
  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),
  and A(k,k), and v overwrites A(1:k-2,k-1:k).

  If UPLO = 'L', then A = L*D*L**T, where
     L = P(1)*L(1)* ... *P(k)*L(k)* ...,
  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to
  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1
  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as
  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such
  that if the diagonal block D(k) is of order s (s = 1 or 2), then

             (   I    0     0   )  k-1
     L(k) =  (   0    I     0   )  s
             (   0    v     I   )  n-k-s+1
                k-1   s  n-k-s+1

  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).
  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),
  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).

Contributors:

  09-29-06 - patch from
    Bobby Cheng, MathWorks

    Replace l.209 and l.377
         IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN
    by
         IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN

  1-96 - Based on modifications by J. Lewis, Boeing Computer Services
         Company

Definition at line 192 of file zsytf2.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

zsytf2(3) is an alias of zsytf2.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK