cspsv.f File Reference

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Functions/Subroutines
subroutine	cspsv (UPLO, N, NRHS, AP, IPIV, B, LDB, INFO)
	CSPSV computes the solution to system of linear equations A * X = B for OTHER matrices

---

Function/Subroutine Documentation

subroutine cspsv	(	character	UPLO,
		integer	N,
		integer	NRHS,
		complex, dimension( * )	AP,
		integer, dimension( * )	IPIV,
		complex, dimension( ldb, * )	B,
		integer	LDB,
		integer	INFO
	)

CSPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Download CSPSV + dependencies [TGZ] [ZIP] [TXT]

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.

Parameters:

[in]	UPLO	UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
[in]	N	N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.
[in]	NRHS	NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
[in,out]	AP	AP is 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.
[out]	IPIV	IPIV is 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.
[in,out]	B	B is 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.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	INFO	INFO is 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.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

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 ]

Definition at line 163 of file cspsv.f.

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