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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