IRIX 6.2 Development Libraries/SGI IRIX 6.2 Development Libraries.iso/dist/complib.idb/usr/share/catman/p_man/cat3/complib/csytf2.z/csytf2

Text File | 1996-03-14 | 6KB | 199 lines

CCCCSSSSYYYYTTTTFFFF2222((((3333FFFF))))                                                          CCCCSSSSYYYYTTTTFFFF2222((((3333FFFF))))



NNNNAAAAMMMMEEEE
     CSYTF2 - compute the factorization of a complex symmetric matrix A using
     the Bunch-Kaufman diagonal pivoting method

SSSSYYYYNNNNOOOOPPPPSSSSIIIISSSS
     SUBROUTINE CSYTF2( UPLO, N, A, LDA, IPIV, INFO )

         CHARACTER      UPLO

         INTEGER        INFO, LDA, N

         INTEGER        IPIV( * )

         COMPLEX        A( LDA, * )

PPPPUUUURRRRPPPPOOOOSSSSEEEE
     CSYTF2 computes the factorization of a complex symmetric matrix A using
     the Bunch-Kaufman diagonal pivoting method:

        A = U*D*U'  or  A = L*D*L'

     where U (or L) is a product of permutation and unit upper (lower)
     triangular matrices, U' 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.


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

     N       (input) INTEGER
             The order of the matrix A.  N >= 0.

     A       (input/output) COMPLEX 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).






                                                                        PPPPaaaaggggeeee 1111






CCCCSSSSYYYYTTTTFFFF2222((((3333FFFF))))                                                          CCCCSSSSYYYYTTTTFFFF2222((((3333FFFF))))



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

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

     INFO    (output) 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.

FFFFUUUURRRRTTTTHHHHEEEERRRR DDDDEEEETTTTAAAAIIIILLLLSSSS
     If UPLO = 'U', then A = U*D*U', 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', 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




                                                                        PPPPaaaaggggeeee 2222






CCCCSSSSYYYYTTTTFFFF2222((((3333FFFF))))                                                          CCCCSSSSYYYYTTTTFFFF2222((((3333FFFF))))



     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).




















































                                                                        PPPPaaaaggggeeee 3333