Collaboration diagram for real:

Functions/Subroutines
subroutine	sptsv (N, NRHS, D, E, B, LDB, INFO)
	*SPTSV computes the solution to system of linear equations A X = B for PT matrices**
subroutine	sptsvx (FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, INFO)
	*SPTSVX computes the solution to system of linear equations A X = B for PT matrices**

Detailed Description

This is the group of real solve driver functions for PT matrices

Function/Subroutine Documentation

subroutine sptsv	(	integer	N,
		integer	NRHS,
		real, dimension( * )	D,
		real, dimension( * )	E,
		real, dimension( ldb, * )	B,
		integer	LDB,
		integer	INFO
	)

SPTSV computes the solution to system of linear equations A * X = B for PT matrices

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

Purpose:

 SPTSV computes the solution to a real system of linear equations
 A*X = B, where A is an N-by-N symmetric positive definite tridiagonal
 matrix, and X and B are N-by-NRHS matrices.

 A is factored as A = L*D*L**T, and the factored form of A is then
 used to solve the system of equations.

Parameters:

[in]	N	N is INTEGER 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]	D	D is REAL array, dimension (N) On entry, the n diagonal elements of the tridiagonal matrix A. On exit, the n diagonal elements of the diagonal matrix D from the factorization A = LDL**T.
[in,out]	E	E is REAL array, dimension (N-1) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A. On exit, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the LDLT factorization of A. (E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the UTDU factorization of A.)
[in,out]	B	B is REAL 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, the leading minor of order i is not positive definite, and the solution has not been computed. The factorization has not been completed unless i = N.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: September 2012

Definition at line 115 of file sptsv.f.

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subroutine sptsvx	(	character	FACT,
		integer	N,
		integer	NRHS,
		real, dimension( * )	D,
		real, dimension( * )	E,
		real, dimension( * )	DF,
		real, dimension( * )	EF,
		real, dimension( ldb, * )	B,
		integer	LDB,
		real, dimension( ldx, * )	X,
		integer	LDX,
		real	RCOND,
		real, dimension( * )	FERR,
		real, dimension( * )	BERR,
		real, dimension( * )	WORK,
		integer	INFO
	)

SPTSVX computes the solution to system of linear equations A * X = B for PT matrices

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

Purpose:

 SPTSVX uses the factorization A = L*D*L**T to compute the solution
 to a real system of linear equations A*X = B, where A is an N-by-N
 symmetric positive definite tridiagonal matrix and X and B are
 N-by-NRHS matrices.

 Error bounds on the solution and a condition estimate are also
 provided.

Description:

 The following steps are performed:

 1. If FACT = 'N', the matrix A is factored as A = L*D*L**T, where L
    is a unit lower bidiagonal matrix and D is diagonal.  The
    factorization can also be regarded as having the form
    A = U**T*D*U.

 2. If the leading i-by-i principal minor is not positive definite,
    then the routine returns with INFO = i. Otherwise, the factored
    form of A is used to estimate the condition number of the matrix
    A.  If the reciprocal of the condition number is less than machine
    precision, INFO = N+1 is returned as a warning, but the routine
    still goes on to solve for X and compute error bounds as
    described below.

 3. The system of equations is solved for X using the factored form
    of A.

 4. Iterative refinement is applied to improve the computed solution
    matrix and calculate error bounds and backward error estimates
    for it.

Parameters:

[in]	FACT	FACT is CHARACTER*1 Specifies whether or not the factored form of A has been supplied on entry. = 'F': On entry, DF and EF contain the factored form of A. D, E, DF, and EF will not be modified. = 'N': The matrix A will be copied to DF and EF and factored.
[in]	N	N is INTEGER 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 matrices B and X. NRHS >= 0.
[in]	D	D is REAL array, dimension (N) The n diagonal elements of the tridiagonal matrix A.
[in]	E	E is REAL array, dimension (N-1) The (n-1) subdiagonal elements of the tridiagonal matrix A.
[in,out]	DF	DF is REAL array, dimension (N) If FACT = 'F', then DF is an input argument and on entry contains the n diagonal elements of the diagonal matrix D from the LDL*T factorization of A. If FACT = 'N', then DF is an output argument and on exit contains the n diagonal elements of the diagonal matrix D from the LDL*T factorization of A.
[in,out]	EF	EF is REAL array, dimension (N-1) If FACT = 'F', then EF is an input argument and on entry contains the (n-1) subdiagonal elements of the unit bidiagonal factor L from the LDL*T factorization of A. If FACT = 'N', then EF is an output argument and on exit contains the (n-1) subdiagonal elements of the unit bidiagonal factor L from the LDL*T factorization of A.
[in]	B	B is REAL array, dimension (LDB,NRHS) The N-by-NRHS right hand side matrix B.
[in]	LDB	LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).
[out]	X	X is REAL array, dimension (LDX,NRHS) If INFO = 0 of INFO = N+1, the N-by-NRHS solution matrix X.
[in]	LDX	LDX is INTEGER The leading dimension of the array X. LDX >= max(1,N).
[out]	RCOND	RCOND is REAL The reciprocal condition number of the matrix A. If RCOND is less than the machine precision (in particular, if RCOND = 0), the matrix is singular to working precision. This condition is indicated by a return code of INFO > 0.
[out]	FERR	FERR is REAL array, dimension (NRHS) The forward error bound for each solution vector X(j) (the j-th column of the solution matrix X). If XTRUE is the true solution corresponding to X(j), FERR(j) is an estimated upper bound for the magnitude of the largest element in (X(j) - XTRUE) divided by the magnitude of the largest element in X(j).
[out]	BERR	BERR is REAL array, dimension (NRHS) The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution).
[out]	WORK	WORK is REAL array, dimension (2*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, and i is <= N: the leading minor of order i of A is not positive definite, so the factorization could not be completed, and the solution has not been computed. RCOND = 0 is returned. = N+1: U is nonsingular, but RCOND is less than machine precision, meaning that the matrix is singular to working precision. Nevertheless, the solution and error bounds are computed because there are a number of situations where the computed solution can be more accurate than the value of RCOND would suggest.

Author:: Univ. of Tennessee; Univ. of California Berkeley; Univ. of Colorado Denver; NAG Ltd.

Date:: September 2012

Definition at line 228 of file sptsvx.f.

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Functions/Subroutines

Detailed Description

Function/Subroutine Documentation