LAPACK  3.6.0
LAPACK: Linear Algebra PACKage
Collaboration diagram for complex16:

Functions

subroutine zptsv (N, NRHS, D, E, B, LDB, INFO)
  ZPTSV computes the solution to system of linear equations A * X = B for PT matrices More...
 
subroutine zptsvx (FACT, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, RCOND, FERR, BERR, WORK, RWORK, INFO)
  ZPTSVX computes the solution to system of linear equations A * X = B for PT matrices More...
 

Detailed Description

This is the group of complex16 solve driver functions for PT matrices

Function Documentation

subroutine zptsv ( integer  N,
integer  NRHS,
double precision, dimension( * )  D,
complex*16, dimension( * )  E,
complex*16, dimension( ldb, * )  B,
integer  LDB,
integer  INFO 
)

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

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

Purpose:
 ZPTSV computes 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.

 A is factored as A = L*D*L**H, 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 DOUBLE PRECISION 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 = L*D*L**H.
[in,out]E
          E is COMPLEX*16 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 L*D*L**H factorization of
          A.  E can also be regarded as the superdiagonal of the unit
          bidiagonal factor U from the U**H*D*U factorization of A.
[in,out]B
          B is COMPLEX*16 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 117 of file zptsv.f.

117 *
118 * -- LAPACK driver routine (version 3.4.2) --
119 * -- LAPACK is a software package provided by Univ. of Tennessee, --
120 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
121 * September 2012
122 *
123 * .. Scalar Arguments ..
124  INTEGER info, ldb, n, nrhs
125 * ..
126 * .. Array Arguments ..
127  DOUBLE PRECISION d( * )
128  COMPLEX*16 b( ldb, * ), e( * )
129 * ..
130 *
131 * =====================================================================
132 *
133 * .. External Subroutines ..
134  EXTERNAL xerbla, zpttrf, zpttrs
135 * ..
136 * .. Intrinsic Functions ..
137  INTRINSIC max
138 * ..
139 * .. Executable Statements ..
140 *
141 * Test the input parameters.
142 *
143  info = 0
144  IF( n.LT.0 ) THEN
145  info = -1
146  ELSE IF( nrhs.LT.0 ) THEN
147  info = -2
148  ELSE IF( ldb.LT.max( 1, n ) ) THEN
149  info = -6
150  END IF
151  IF( info.NE.0 ) THEN
152  CALL xerbla( 'ZPTSV ', -info )
153  RETURN
154  END IF
155 *
156 * Compute the L*D*L**H (or U**H*D*U) factorization of A.
157 *
158  CALL zpttrf( n, d, e, info )
159  IF( info.EQ.0 ) THEN
160 *
161 * Solve the system A*X = B, overwriting B with X.
162 *
163  CALL zpttrs( 'Lower', n, nrhs, d, e, b, ldb, info )
164  END IF
165  RETURN
166 *
167 * End of ZPTSV
168 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zpttrs(UPLO, N, NRHS, D, E, B, LDB, INFO)
ZPTTRS
Definition: zpttrs.f:123
subroutine zpttrf(N, D, E, INFO)
ZPTTRF
Definition: zpttrf.f:94

Here is the call graph for this function:

Here is the caller graph for this function:

subroutine zptsvx ( character  FACT,
integer  N,
integer  NRHS,
double precision, dimension( * )  D,
complex*16, dimension( * )  E,
double precision, dimension( * )  DF,
complex*16, dimension( * )  EF,
complex*16, dimension( ldb, * )  B,
integer  LDB,
complex*16, dimension( ldx, * )  X,
integer  LDX,
double precision  RCOND,
double precision, dimension( * )  FERR,
double precision, dimension( * )  BERR,
complex*16, dimension( * )  WORK,
double precision, dimension( * )  RWORK,
integer  INFO 
)

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

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

Purpose:
 ZPTSVX 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.
Description:
 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.
Parameters
[in]FACT
          FACT is CHARACTER*1
          Specifies whether or not the factored form of the matrix
          A is 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 DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the tridiagonal matrix A.
[in]E
          E is COMPLEX*16 array, dimension (N-1)
          The (n-1) subdiagonal elements of the tridiagonal matrix A.
[in,out]DF
          DF is DOUBLE PRECISION 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 L*D*L**H 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 L*D*L**H factorization of A.
[in,out]EF
          EF is COMPLEX*16 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 L*D*L**H 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 L*D*L**H factorization of A.
[in]B
          B is COMPLEX*16 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 COMPLEX*16 array, dimension (LDX,NRHS)
          If INFO = 0 or 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 DOUBLE PRECISION
          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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 COMPLEX*16 array, dimension (N)
[out]RWORK
          RWORK is DOUBLE PRECISION array, dimension (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 236 of file zptsvx.f.

236 *
237 * -- LAPACK driver routine (version 3.4.2) --
238 * -- LAPACK is a software package provided by Univ. of Tennessee, --
239 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
240 * September 2012
241 *
242 * .. Scalar Arguments ..
243  CHARACTER fact
244  INTEGER info, ldb, ldx, n, nrhs
245  DOUBLE PRECISION rcond
246 * ..
247 * .. Array Arguments ..
248  DOUBLE PRECISION berr( * ), d( * ), df( * ), ferr( * ),
249  $ rwork( * )
250  COMPLEX*16 b( ldb, * ), e( * ), ef( * ), work( * ),
251  $ x( ldx, * )
252 * ..
253 *
254 * =====================================================================
255 *
256 * .. Parameters ..
257  DOUBLE PRECISION zero
258  parameter( zero = 0.0d+0 )
259 * ..
260 * .. Local Scalars ..
261  LOGICAL nofact
262  DOUBLE PRECISION anorm
263 * ..
264 * .. External Functions ..
265  LOGICAL lsame
266  DOUBLE PRECISION dlamch, zlanht
267  EXTERNAL lsame, dlamch, zlanht
268 * ..
269 * .. External Subroutines ..
270  EXTERNAL dcopy, xerbla, zcopy, zlacpy, zptcon, zptrfs,
271  $ zpttrf, zpttrs
272 * ..
273 * .. Intrinsic Functions ..
274  INTRINSIC max
275 * ..
276 * .. Executable Statements ..
277 *
278 * Test the input parameters.
279 *
280  info = 0
281  nofact = lsame( fact, 'N' )
282  IF( .NOT.nofact .AND. .NOT.lsame( fact, 'F' ) ) THEN
283  info = -1
284  ELSE IF( n.LT.0 ) THEN
285  info = -2
286  ELSE IF( nrhs.LT.0 ) THEN
287  info = -3
288  ELSE IF( ldb.LT.max( 1, n ) ) THEN
289  info = -9
290  ELSE IF( ldx.LT.max( 1, n ) ) THEN
291  info = -11
292  END IF
293  IF( info.NE.0 ) THEN
294  CALL xerbla( 'ZPTSVX', -info )
295  RETURN
296  END IF
297 *
298  IF( nofact ) THEN
299 *
300 * Compute the L*D*L**H (or U**H*D*U) factorization of A.
301 *
302  CALL dcopy( n, d, 1, df, 1 )
303  IF( n.GT.1 )
304  $ CALL zcopy( n-1, e, 1, ef, 1 )
305  CALL zpttrf( n, df, ef, info )
306 *
307 * Return if INFO is non-zero.
308 *
309  IF( info.GT.0 )THEN
310  rcond = zero
311  RETURN
312  END IF
313  END IF
314 *
315 * Compute the norm of the matrix A.
316 *
317  anorm = zlanht( '1', n, d, e )
318 *
319 * Compute the reciprocal of the condition number of A.
320 *
321  CALL zptcon( n, df, ef, anorm, rcond, rwork, info )
322 *
323 * Compute the solution vectors X.
324 *
325  CALL zlacpy( 'Full', n, nrhs, b, ldb, x, ldx )
326  CALL zpttrs( 'Lower', n, nrhs, df, ef, x, ldx, info )
327 *
328 * Use iterative refinement to improve the computed solutions and
329 * compute error bounds and backward error estimates for them.
330 *
331  CALL zptrfs( 'Lower', n, nrhs, d, e, df, ef, b, ldb, x, ldx, ferr,
332  $ berr, work, rwork, info )
333 *
334 * Set INFO = N+1 if the matrix is singular to working precision.
335 *
336  IF( rcond.LT.dlamch( 'Epsilon' ) )
337  $ info = n + 1
338 *
339  RETURN
340 *
341 * End of ZPTSVX
342 *
subroutine zptrfs(UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)
ZPTRFS
Definition: zptrfs.f:185
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:105
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:52
double precision function zlanht(NORM, N, D, E)
ZLANHT returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix.
Definition: zlanht.f:103
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zpttrs(UPLO, N, NRHS, D, E, B, LDB, INFO)
ZPTTRS
Definition: zpttrs.f:123
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
subroutine zpttrf(N, D, E, INFO)
ZPTTRF
Definition: zpttrf.f:94
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:53
subroutine zptcon(N, D, E, ANORM, RCOND, RWORK, INFO)
ZPTCON
Definition: zptcon.f:121

Here is the call graph for this function:

Here is the caller graph for this function: