cptsvx

NAME

cptsvx - use the factorization A = L*D*L**H to compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix and X and B are N-by-NRHS matrices

SYNOPSIS

  SUBROUTINE CPTSVX( FACT, N, NRHS, DIAG, SUB, DIAGF, SUBF, B, LDB, X, 
 *      LDX, RCOND, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 FACT
  COMPLEX SUB(*), SUBF(*), B(LDB,*), X(LDX,*), WORK(*)
  INTEGER N, NRHS, LDB, LDX, INFO
  REAL RCOND
  REAL DIAG(*), DIAGF(*), FERR(*), BERR(*), WORK2(*)
 
  SUBROUTINE CPTSVX_64( FACT, N, NRHS, DIAG, SUB, DIAGF, SUBF, B, LDB, 
 *      X, LDX, RCOND, FERR, BERR, WORK, WORK2, INFO)
  CHARACTER * 1 FACT
  COMPLEX SUB(*), SUBF(*), B(LDB,*), X(LDX,*), WORK(*)
  INTEGER*8 N, NRHS, LDB, LDX, INFO
  REAL RCOND
  REAL DIAG(*), DIAGF(*), FERR(*), BERR(*), WORK2(*)

F95 INTERFACE

  SUBROUTINE PTSVX( FACT, [N], [NRHS], DIAG, SUB, DIAGF, SUBF, B, [LDB], 
 *       X, [LDX], RCOND, FERR, BERR, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: FACT
  COMPLEX, DIMENSION(:) :: SUB, SUBF, WORK
  COMPLEX, DIMENSION(:,:) :: B, X
  INTEGER :: N, NRHS, LDB, LDX, INFO
  REAL :: RCOND
  REAL, DIMENSION(:) :: DIAG, DIAGF, FERR, BERR, WORK2
 
  SUBROUTINE PTSVX_64( FACT, [N], [NRHS], DIAG, SUB, DIAGF, SUBF, B, 
 *       [LDB], X, [LDX], RCOND, FERR, BERR, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: FACT
  COMPLEX, DIMENSION(:) :: SUB, SUBF, WORK
  COMPLEX, DIMENSION(:,:) :: B, X
  INTEGER(8) :: N, NRHS, LDB, LDX, INFO
  REAL :: RCOND
  REAL, DIMENSION(:) :: DIAG, DIAGF, FERR, BERR, WORK2

C INTERFACE

#include <sunperf.h>

void cptsvx(char fact, int n, int nrhs, float *diag, complex *sub, float *diagf, complex *subf, complex *b, int ldb, complex *x, int ldx, float *rcond, float *ferr, float *berr, int *info);

void cptsvx_64(char fact, long n, long nrhs, float *diag, complex *sub, float *diagf, complex *subf, complex *b, long ldb, complex *x, long ldx, float *rcond, float *ferr, float *berr, long *info);

PURPOSE

cptsvx uses the factorization A = L*D*L**H to compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian 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.

The following steps are performed:

1. If FACT = 'N', the matrix A is factored as A = L*D*L**H, where L is a unit lower bidiagonal matrix and D is diagonal. The factorization can also be regarded as having the form

   A = U**H*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.

ARGUMENTS

* FACT (input): Specifies whether or not the factored form of the matrix A is supplied on entry.
* N (input): The order of the matrix A. N >= 0.
* NRHS (input): The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
* DIAG (input): The n diagonal elements of the tridiagonal matrix A.
* SUB (input): The (n-1) subdiagonal elements of the tridiagonal matrix A.
* DIAGF (input/output): If FACT = 'F', then DIAGF is an input argument and on entry contains the n diagonal elements of the diagonal matrix DIAG from the L*DIAG*L**H factorization of A. If FACT = 'N', then DIAGF is an output argument and on exit contains the n diagonal elements of the diagonal matrix DIAG from the L*DIAG*L**H factorization of A.
* SUBF (input/output): If FACT = 'F', then SUBF is an input argument and on entry contains the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*DIAG*L**H factorization of A. If FACT = 'N', then SUBF is an output argument and on exit contains the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*DIAG*L**H factorization of A.
* B (input): The N-by-NRHS right hand side matrix B.
* LDB (input): The leading dimension of the array B. LDB >= max(1,N).
* X (output): If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.
* LDX (input): The leading dimension of the array X. LDX >= max(1,N).
* RCOND (output): 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.
* FERR (output): 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).
* BERR (output): 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).
* WORK (workspace): dimension(N)
* WORK2 (workspace): dimension(N)
* INFO (output)