lagtm(3)

Library Functions Manual

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

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

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

          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 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.

Definition at line 143 of file clagtm.f.

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

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

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

          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 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.

Definition at line 143 of file dlagtm.f.

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

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

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

          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 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.

Definition at line 143 of file slagtm.f.

subroutine zlagtm (character trans, integer n, integer nrhs, double precision alpha, complex16, dimension( ) dl, complex16, dimension( ) d, complex16, dimension( ) du, complex16, dimension( ldx, ) x, integer ldx, double precision beta, complex16, 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 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 is COMPLEX*16 array, dimension (N-1)
          The (n-1) sub-diagonal elements of T.

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

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

          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 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.

Definition at line 143 of file zlagtm.f.

Author

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