IRIX Base Documentation 2002 November/SGI IRIX Base Documentation 2002 November.iso/usr/share/catman/p_man/cat3/SCSL/zsptrf.z/zsptrf

Text File | 2002-10-03 | 6.4 KB | 199 lines

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     ZSPTRF - compute the factorization of a complex symmetric matrix A stored
     in packed format using the Bunch-Kaufman diagonal pivoting method

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     SUBROUTINE ZSPTRF( UPLO, N, AP, IPIV, INFO )

         CHARACTER      UPLO

         INTEGER        INFO, N

         INTEGER        IPIV( * )

         COMPLEX*16     AP( * )

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     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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     ZSPTRF computes the factorization of a complex symmetric matrix A stored
     in packed format 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, and D is symmetric and block diagonal with 1-by-1
     and 2-by-2 diagonal blocks.


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     UPLO    (input) CHARACTER*1
             = 'U':  Upper triangle of A is stored;
             = 'L':  Lower triangle of A is stored.

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

     AP      (input/output) COMPLEX*16 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.



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             On exit, the block diagonal matrix D and the multipliers used to
             obtain the factor U or L, stored as a packed triangular matrix
             overwriting A (see below for further details).

     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 = -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, and division by zero will occur if it is used to solve
             a system of equations.

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     5-96 - Based on modifications by J. Lewis, Boeing Computer Services
            Company

     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



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        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).


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     INTRO_LAPACK(3S), INTRO_SCSL(3S)

     This man page is available only online.










































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