pttrs(3)

Library Functions Manual

pttrs(3)

NAME

pttrs - pttrs: triangular solve using factor

SYNOPSIS

Functions

subroutine cpttrs (uplo, n, nrhs, d, e, b, ldb, info)
CPTTRS subroutine dpttrs (n, nrhs, d, e, b, ldb, info)
DPTTRS subroutine spttrs (n, nrhs, d, e, b, ldb, info)
SPTTRS subroutine zpttrs (uplo, n, nrhs, d, e, b, ldb, info)
ZPTTRS

Detailed Description

Function Documentation

subroutine cpttrs (character uplo, integer n, integer nrhs, real, dimension( * ) d, complex, dimension( * ) e, complex, dimension( ldb, * ) b, integer ldb, integer info)

CPTTRS

Purpose:

 CPTTRS solves a tridiagonal system of the form
    A * X = B
 using the factorization A = U**H*D*U or A = L*D*L**H computed by CPTTRF.
 D is a diagonal matrix specified in the vector D, U (or L) is a unit
 bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
 the vector E, and X and B are N by NRHS matrices.

Parameters

UPLO

          UPLO is CHARACTER*1
          Specifies the form of the factorization and whether the
          vector E is the superdiagonal of the upper bidiagonal factor
          U or the subdiagonal of the lower bidiagonal factor L.
          = 'U':  A = U**H*D*U, E is the superdiagonal of U
          = 'L':  A = L*D*L**H, E is the subdiagonal of L

          N is INTEGER
          The order of the tridiagonal matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrix B.  NRHS >= 0.

          D is REAL array, dimension (N)
          The n diagonal elements of the diagonal matrix D from the
          factorization A = U**H*D*U or A = L*D*L**H.

          E is COMPLEX array, dimension (N-1)
          If UPLO = 'U', the (n-1) superdiagonal elements of the unit
          bidiagonal factor U from the factorization A = U**H*D*U.
          If UPLO = 'L', the (n-1) subdiagonal elements of the unit
          bidiagonal factor L from the factorization A = L*D*L**H.

          B is COMPLEX array, dimension (LDB,NRHS)
          On entry, the right hand side vectors B for the system of
          linear equations.
          On exit, the solution vectors, X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 120 of file cpttrs.f.

subroutine dpttrs (integer n, integer nrhs, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DPTTRS

Purpose:

 DPTTRS solves a tridiagonal system of the form
    A * X = B
 using the L*D*L**T factorization of A computed by DPTTRF.  D is a
 diagonal matrix specified in the vector D, L is a unit bidiagonal
 matrix whose subdiagonal is specified in the vector E, and X and B
 are N by NRHS matrices.

Parameters

          N is INTEGER
          The order of the tridiagonal matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrix B.  NRHS >= 0.

          D is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the diagonal matrix D from the
          L*D*L**T factorization of A.

          E is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) subdiagonal elements of the unit bidiagonal factor
          L from the L*D*L**T factorization of A.  E can also be regarded
          as the superdiagonal of the unit bidiagonal factor U from the
          factorization A = U**T*D*U.

          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
          On entry, the right hand side vectors B for the system of
          linear equations.
          On exit, the solution vectors, X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 108 of file dpttrs.f.

subroutine spttrs (integer n, integer nrhs, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldb, * ) b, integer ldb, integer info)

SPTTRS

Purpose:

 SPTTRS solves a tridiagonal system of the form
    A * X = B
 using the L*D*L**T factorization of A computed by SPTTRF.  D is a
 diagonal matrix specified in the vector D, L is a unit bidiagonal
 matrix whose subdiagonal is specified in the vector E, and X and B
 are N by NRHS matrices.

Parameters

          N is INTEGER
          The order of the tridiagonal matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrix B.  NRHS >= 0.

          D is REAL array, dimension (N)
          The n diagonal elements of the diagonal matrix D from the
          L*D*L**T factorization of A.

          E is REAL array, dimension (N-1)
          The (n-1) subdiagonal elements of the unit bidiagonal factor
          L from the L*D*L**T factorization of A.  E can also be regarded
          as the superdiagonal of the unit bidiagonal factor U from the
          factorization A = U**T*D*U.

          B is REAL array, dimension (LDB,NRHS)
          On entry, the right hand side vectors B for the system of
          linear equations.
          On exit, the solution vectors, X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 108 of file spttrs.f.

subroutine zpttrs (character uplo, integer n, integer nrhs, double precision, dimension( * ) d, complex16, dimension( ) e, complex16, dimension( ldb, ) b, integer ldb, integer info)

ZPTTRS

Purpose:

 ZPTTRS solves a tridiagonal system of the form
    A * X = B
 using the factorization A = U**H *D* U or A = L*D*L**H computed by ZPTTRF.
 D is a diagonal matrix specified in the vector D, U (or L) is a unit
 bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
 the vector E, and X and B are N by NRHS matrices.

Parameters

UPLO

          UPLO is CHARACTER*1
          Specifies the form of the factorization and whether the
          vector E is the superdiagonal of the upper bidiagonal factor
          U or the subdiagonal of the lower bidiagonal factor L.
          = 'U':  A = U**H *D*U, E is the superdiagonal of U
          = 'L':  A = L*D*L**H, E is the subdiagonal of L

          N is INTEGER
          The order of the tridiagonal matrix A.  N >= 0.

NRHS

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrix B.  NRHS >= 0.

          D is DOUBLE PRECISION array, dimension (N)
          The n diagonal elements of the diagonal matrix D from the
          factorization A = U**H *D*U or A = L*D*L**H.

          E is COMPLEX*16 array, dimension (N-1)
          If UPLO = 'U', the (n-1) superdiagonal elements of the unit
          bidiagonal factor U from the factorization A = U**H*D*U.
          If UPLO = 'L', the (n-1) subdiagonal elements of the unit
          bidiagonal factor L from the factorization A = L*D*L**H.

          B is COMPLEX*16 array, dimension (LDB,NRHS)
          On entry, the right hand side vectors B for the system of
          linear equations.
          On exit, the solution vectors, X.

LDB

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= max(1,N).

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 120 of file zpttrs.f.

Author

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