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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