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lagtm(3) LAPACK lagtm(3)

NAME

lagtm - lagtm: tridiagonal matrix-matrix multiply

SYNOPSIS

Functions


subroutine clagtm (trans, n, nrhs, alpha, dl, d, du, x, ldx, beta, b, ldb)
CLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1. subroutine dlagtm (trans, n, nrhs, alpha, dl, d, du, x, ldx, beta, b, ldb)
DLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1. subroutine slagtm (trans, n, nrhs, alpha, dl, d, du, x, ldx, beta, b, ldb)
SLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1. subroutine zlagtm (trans, n, nrhs, alpha, dl, d, du, x, ldx, beta, b, ldb)
ZLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1.

Detailed Description

Function Documentation

subroutine clagtm (character trans, integer n, integer nrhs, real alpha, complex, dimension( * ) dl, complex, dimension( * ) d, complex, dimension( * ) du, complex, dimension( ldx, * ) x, integer ldx, real beta, complex, dimension( ldb, * ) b, integer ldb)

CLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1.

Purpose:

!>
!> CLAGTM performs a matrix-matrix product of the form
!>
!>    B := alpha * A * X + beta * B
!>
!> where A is a tridiagonal matrix of order N, B and X are N by NRHS
!> matrices, and alpha and beta are real scalars, each of which may be
!> 0., 1., or -1.
!>

Parameters

TRANS 

!>          TRANS is CHARACTER*1
!>          Specifies the operation applied to A.
!>          = 'N':  No transpose, B := alpha * A * X + beta * B
!>          = 'T':  Transpose,    B := alpha * A**T * X + beta * B
!>          = 'C':  Conjugate transpose, B := alpha * A**H * X + beta * B
!>

N

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

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrices X and B.
!>

ALPHA

!>          ALPHA is REAL
!>          The scalar alpha.  ALPHA must be 0., 1., or -1.; otherwise,
!>          it is assumed to be 0.
!>

DL

!>          DL is COMPLEX array, dimension (N-1)
!>          The (n-1) sub-diagonal elements of T.
!>

D

!>          D is COMPLEX array, dimension (N)
!>          The diagonal elements of T.
!>

DU

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

X

!>          X is COMPLEX array, dimension (LDX,NRHS)
!>          The N by NRHS matrix X.
!>

LDX

!>          LDX is INTEGER
!>          The leading dimension of the array X.  LDX >= max(N,1).
!>

BETA

!>          BETA is REAL
!>          The scalar beta.  BETA must be 0., 1., or -1.; otherwise,
!>          it is assumed to be 1.
!>

B

!>          B is COMPLEX array, dimension (LDB,NRHS)
!>          On entry, the N by NRHS matrix B.
!>          On exit, B is overwritten by the matrix expression
!>          B := alpha * A * X + beta * B.
!>

LDB

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dlagtm (character trans, integer n, integer nrhs, double precision alpha, double precision, dimension( * ) dl, double precision, dimension( * ) d, double precision, dimension( * ) du, double precision, dimension( ldx, * ) x, integer ldx, double precision beta, double precision, dimension( ldb, * ) b, integer ldb)

DLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1.

Purpose:

!>
!> DLAGTM performs a matrix-matrix product of the form
!>
!>    B := alpha * A * X + beta * B
!>
!> where A is a tridiagonal matrix of order N, B and X are N by NRHS
!> matrices, and alpha and beta are real scalars, each of which may be
!> 0., 1., or -1.
!>

Parameters

TRANS 

!>          TRANS is CHARACTER*1
!>          Specifies the operation applied to A.
!>          = 'N':  No transpose, B := alpha * A * X + beta * B
!>          = 'T':  Transpose,    B := alpha * A'* X + beta * B
!>          = 'C':  Conjugate transpose = Transpose
!>

N

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

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrices X and B.
!>

ALPHA

!>          ALPHA is DOUBLE PRECISION
!>          The scalar alpha.  ALPHA must be 0., 1., or -1.; otherwise,
!>          it is assumed to be 0.
!>

DL

!>          DL is DOUBLE PRECISION array, dimension (N-1)
!>          The (n-1) sub-diagonal elements of T.
!>

D

!>          D is DOUBLE PRECISION array, dimension (N)
!>          The diagonal elements of T.
!>

DU

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

X

!>          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
!>          The N by NRHS matrix X.
!>

LDX

!>          LDX is INTEGER
!>          The leading dimension of the array X.  LDX >= max(N,1).
!>

BETA

!>          BETA is DOUBLE PRECISION
!>          The scalar beta.  BETA must be 0., 1., or -1.; otherwise,
!>          it is assumed to be 1.
!>

B

!>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
!>          On entry, the N by NRHS matrix B.
!>          On exit, B is overwritten by the matrix expression
!>          B := alpha * A * X + beta * B.
!>

LDB

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine slagtm (character trans, integer n, integer nrhs, real alpha, real, dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du, real, dimension( ldx, * ) x, integer ldx, real beta, real, dimension( ldb, * ) b, integer ldb)

SLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1.

Purpose:

!>
!> SLAGTM performs a matrix-matrix product of the form
!>
!>    B := alpha * A * X + beta * B
!>
!> where A is a tridiagonal matrix of order N, B and X are N by NRHS
!> matrices, and alpha and beta are real scalars, each of which may be
!> 0., 1., or -1.
!>

Parameters

TRANS 

!>          TRANS is CHARACTER*1
!>          Specifies the operation applied to A.
!>          = 'N':  No transpose, B := alpha * A * X + beta * B
!>          = 'T':  Transpose,    B := alpha * A'* X + beta * B
!>          = 'C':  Conjugate transpose = Transpose
!>

N

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

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrices X and B.
!>

ALPHA

!>          ALPHA is REAL
!>          The scalar alpha.  ALPHA must be 0., 1., or -1.; otherwise,
!>          it is assumed to be 0.
!>

DL

!>          DL is REAL array, dimension (N-1)
!>          The (n-1) sub-diagonal elements of T.
!>

D

!>          D is REAL array, dimension (N)
!>          The diagonal elements of T.
!>

DU

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

X

!>          X is REAL array, dimension (LDX,NRHS)
!>          The N by NRHS matrix X.
!>

LDX

!>          LDX is INTEGER
!>          The leading dimension of the array X.  LDX >= max(N,1).
!>

BETA

!>          BETA is REAL
!>          The scalar beta.  BETA must be 0., 1., or -1.; otherwise,
!>          it is assumed to be 1.
!>

B

!>          B is REAL array, dimension (LDB,NRHS)
!>          On entry, the N by NRHS matrix B.
!>          On exit, B is overwritten by the matrix expression
!>          B := alpha * A * X + beta * B.
!>

LDB

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zlagtm (character trans, integer n, integer nrhs, double precision alpha, complex*16, dimension( * ) dl, complex*16, dimension( * ) d, complex*16, dimension( * ) du, complex*16, dimension( ldx, * ) x, integer ldx, double precision beta, complex*16, dimension( ldb, * ) b, integer ldb)

ZLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1.

Purpose:

!>
!> ZLAGTM performs a matrix-matrix product of the form
!>
!>    B := alpha * A * X + beta * B
!>
!> where A is a tridiagonal matrix of order N, B and X are N by NRHS
!> matrices, and alpha and beta are real scalars, each of which may be
!> 0., 1., or -1.
!>

Parameters

TRANS 

!>          TRANS is CHARACTER*1
!>          Specifies the operation applied to A.
!>          = 'N':  No transpose, B := alpha * A * X + beta * B
!>          = 'T':  Transpose,    B := alpha * A**T * X + beta * B
!>          = 'C':  Conjugate transpose, B := alpha * A**H * X + beta * B
!>

N

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

NRHS

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrices X and B.
!>

ALPHA

!>          ALPHA is DOUBLE PRECISION
!>          The scalar alpha.  ALPHA must be 0., 1., or -1.; otherwise,
!>          it is assumed to be 0.
!>

DL

!>          DL is COMPLEX*16 array, dimension (N-1)
!>          The (n-1) sub-diagonal elements of T.
!>

D

!>          D is COMPLEX*16 array, dimension (N)
!>          The diagonal elements of T.
!>

DU

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

X

!>          X is COMPLEX*16 array, dimension (LDX,NRHS)
!>          The N by NRHS matrix X.
!>

LDX

!>          LDX is INTEGER
!>          The leading dimension of the array X.  LDX >= max(N,1).
!>

BETA

!>          BETA is DOUBLE PRECISION
!>          The scalar beta.  BETA must be 0., 1., or -1.; otherwise,
!>          it is assumed to be 1.
!>

B

!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the N by NRHS matrix B.
!>          On exit, B is overwritten by the matrix expression
!>          B := alpha * A * X + beta * B.
!>

LDB

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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