gttrs(3)

Library Functions Manual

gttrs(3)

NAME

gttrs - gttrs: triangular solve using factor

SYNOPSIS

Functions

subroutine cgttrs (trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info)
CGTTRS subroutine dgttrs (trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info)
DGTTRS subroutine sgttrs (trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info)
SGTTRS subroutine zgttrs (trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info)
ZGTTRS

Detailed Description

Function Documentation

subroutine cgttrs (character trans, integer n, integer nrhs, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( * ) du2, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, integer info)

CGTTRS

Purpose:

!>
!> CGTTRS solves one of the systems of equations
!>    A * X = B,  A**T * X = B,  or  A**H * X = B,
!> with a tridiagonal matrix A using the LU factorization computed
!> by CGTTRF.
!>

Parameters

TRANS

!>          TRANS is CHARACTER*1
!>          Specifies the form of the system of equations.
!>          = 'N':  A * X = B     (No transpose)
!>          = 'T':  A**T * X = B  (Transpose)
!>          = 'C':  A**H * X = B  (Conjugate transpose)
!>

!>          N is INTEGER
!>          The order of the matrix A.
!>

NRHS

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

!>          DL is COMPLEX array, dimension (N-1)
!>          The (n-1) multipliers that define the matrix L from the
!>          LU factorization of A.
!>

!>          D is COMPLEX array, dimension (N)
!>          The n diagonal elements of the upper triangular matrix U from
!>          the LU factorization of A.
!>

!>          DU is COMPLEX array, dimension (N-1)
!>          The (n-1) elements of the first super-diagonal of U.
!>

DU2

!>          DU2 is COMPLEX array, dimension (N-2)
!>          The (n-2) elements of the second super-diagonal of U.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          The pivot indices; for 1 <= i <= n, row i of the matrix was
!>          interchanged with row IPIV(i).  IPIV(i) will always be either
!>          i or i+1; IPIV(i) = i indicates a row interchange was not
!>          required.
!>

!>          B is COMPLEX array, dimension (LDB,NRHS)
!>          On entry, the matrix of right hand side vectors B.
!>          On exit, B is overwritten by 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 136 of file cgttrs.f.

subroutine dgttrs (character trans, integer n, integer nrhs, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du, double precision, dimension( * ) du2, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DGTTRS

Purpose:

!>
!> DGTTRS solves one of the systems of equations
!>    A*X = B  or  A**T*X = B,
!> with a tridiagonal matrix A using the LU factorization computed
!> by DGTTRF.
!>

Parameters

TRANS

!>          TRANS is CHARACTER*1
!>          Specifies the form of the system of equations.
!>          = 'N':  A * X = B  (No transpose)
!>          = 'T':  A**T* X = B  (Transpose)
!>          = 'C':  A**T* X = B  (Conjugate transpose = Transpose)
!>

!>          N is INTEGER
!>          The order of the matrix A.
!>

NRHS

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

!>          DL is DOUBLE PRECISION array, dimension (N-1)
!>          The (n-1) multipliers that define the matrix L from the
!>          LU factorization of A.
!>

!>          D is DOUBLE PRECISION array, dimension (N)
!>          The n diagonal elements of the upper triangular matrix U from
!>          the LU factorization of A.
!>

!>          DU is DOUBLE PRECISION array, dimension (N-1)
!>          The (n-1) elements of the first super-diagonal of U.
!>

DU2

!>          DU2 is DOUBLE PRECISION array, dimension (N-2)
!>          The (n-2) elements of the second super-diagonal of U.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          The pivot indices; for 1 <= i <= n, row i of the matrix was
!>          interchanged with row IPIV(i).  IPIV(i) will always be either
!>          i or i+1; IPIV(i) = i indicates a row interchange was not
!>          required.
!>

!>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
!>          On entry, the matrix of right hand side vectors B.
!>          On exit, B is overwritten by 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 = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 136 of file dgttrs.f.

subroutine sgttrs (character trans, integer n, integer nrhs, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( * ) du2, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, integer info)

SGTTRS

Purpose:

!>
!> SGTTRS solves one of the systems of equations
!>    A*X = B  or  A**T*X = B,
!> with a tridiagonal matrix A using the LU factorization computed
!> by SGTTRF.
!>

Parameters

TRANS

!>          TRANS is CHARACTER*1
!>          Specifies the form of the system of equations.
!>          = 'N':  A * X = B  (No transpose)
!>          = 'T':  A**T* X = B  (Transpose)
!>          = 'C':  A**T* X = B  (Conjugate transpose = Transpose)
!>

!>          N is INTEGER
!>          The order of the matrix A.
!>

NRHS

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

!>          DL is REAL array, dimension (N-1)
!>          The (n-1) multipliers that define the matrix L from the
!>          LU factorization of A.
!>

!>          D is REAL array, dimension (N)
!>          The n diagonal elements of the upper triangular matrix U from
!>          the LU factorization of A.
!>

!>          DU is REAL array, dimension (N-1)
!>          The (n-1) elements of the first super-diagonal of U.
!>

DU2

!>          DU2 is REAL array, dimension (N-2)
!>          The (n-2) elements of the second super-diagonal of U.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          The pivot indices; for 1 <= i <= n, row i of the matrix was
!>          interchanged with row IPIV(i).  IPIV(i) will always be either
!>          i or i+1; IPIV(i) = i indicates a row interchange was not
!>          required.
!>

!>          B is REAL array, dimension (LDB,NRHS)
!>          On entry, the matrix of right hand side vectors B.
!>          On exit, B is overwritten by 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 = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 136 of file sgttrs.f.

subroutine zgttrs (character trans, integer n, integer nrhs, complex16, dimension( ) dl, complex16, dimension( ) d, complex16, dimension( ) du, complex16, dimension( ) du2, integer, dimension( * ) ipiv, complex16, dimension( ldb, ) b, integer ldb, integer info)

ZGTTRS

Purpose:

!>
!> ZGTTRS solves one of the systems of equations
!>    A * X = B,  A**T * X = B,  or  A**H * X = B,
!> with a tridiagonal matrix A using the LU factorization computed
!> by ZGTTRF.
!>

Parameters

TRANS

!>          TRANS is CHARACTER*1
!>          Specifies the form of the system of equations.
!>          = 'N':  A * X = B     (No transpose)
!>          = 'T':  A**T * X = B  (Transpose)
!>          = 'C':  A**H * X = B  (Conjugate transpose)
!>

!>          N is INTEGER
!>          The order of the matrix A.
!>

NRHS

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

!>          DL is COMPLEX*16 array, dimension (N-1)
!>          The (n-1) multipliers that define the matrix L from the
!>          LU factorization of A.
!>

!>          D is COMPLEX*16 array, dimension (N)
!>          The n diagonal elements of the upper triangular matrix U from
!>          the LU factorization of A.
!>

!>          DU is COMPLEX*16 array, dimension (N-1)
!>          The (n-1) elements of the first super-diagonal of U.
!>

DU2

!>          DU2 is COMPLEX*16 array, dimension (N-2)
!>          The (n-2) elements of the second super-diagonal of U.
!>

IPIV

!>          IPIV is INTEGER array, dimension (N)
!>          The pivot indices; for 1 <= i <= n, row i of the matrix was
!>          interchanged with row IPIV(i).  IPIV(i) will always be either
!>          i or i+1; IPIV(i) = i indicates a row interchange was not
!>          required.
!>

!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the matrix of right hand side vectors B.
!>          On exit, B is overwritten by 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 136 of file zgttrs.f.

Author

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