DSPSV man page on IRIX

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DSPSV(3F)							     DSPSV(3F)

NAME
     DSPSV - compute the solution to a real system of linear equations	A * X
     = B,

SYNOPSIS
     SUBROUTINE DSPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )

	 CHARACTER     UPLO

	 INTEGER       INFO, LDB, N, NRHS

	 INTEGER       IPIV( * )

	 DOUBLE	       PRECISION AP( * ), B( LDB, * )

PURPOSE
     DSPSV computes the solution to a real 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) DOUBLE PRECISION 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 DSPTRF, stored as a packed triangular

									Page 1

DSPSV(3F)							     DSPSV(3F)

	     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 DSPTRF.  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) DOUBLE PRECISION 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 ]

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