Evaluates a real general matrix polynomial.

Required Arguments

A — N by N matrix for which the polynomial is to be computed.   (Input)

COEF — Vector of length NCOEF containing the coefficients of the polynomial in order of increasing power.   (Input)

B — N by N matrix containing the value of the polynomial evaluated at A.   (Output)

Optional Arguments

N — Order of the matrix A.   (Input)
Default: N = size (A,1).

LDA — Leading dimension of A exactly as specified in the dimension statement of the calling program.   (Input)
Default: LDA = size (A,1).

NCOEF — Number of coefficients.   (Input)
Default: NCOEF = size (COEF,1).

LDB — Leading dimension of B exactly as specified in the dimension statement of the calling program.   (Input)
Default: LDB = size (B,1).

FORTRAN 90 Interface

Generic:          CALL POLRG (A, COEF, B [,…])

Specific:         The specific interface names are S_POLRG and D_POLRG.

FORTRAN 77 Interface

Single:            CALL POLRG (N, A, LDA, NCOEF, COEF, B, LDB)

Double:          The double precision name is DPOLRG.

Description

Let m = NCOEF and c = COEF.

The routine POLRG computes the matrix polynomial

using Horner's scheme

where I is the N ´ N identity matrix.

Comments

Workspace may be explicitly provided, if desired, by use of P2LRG/DP2LRG. The reference is

CALL P2LRG (N, A, LDA, NCOEF, COEF, B, LDB, WORK)

The additional argument is

WORK — Work vector of length N * N.

Example

This example evaluates the matrix polynomial 3I + A + 2A2, where A is a 3 ´ 3 matrix.

 

      USE POLRG_INT

      USE WRRRN_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    LDA, LDB, N, NCOEF

      PARAMETER  (N=3, NCOEF=3, LDA=N, LDB=N)

!

      REAL       A(LDA,N), B(LDB,N), COEF(NCOEF)

!                                 Set values of A and COEF

!

!                                 A = (  1.0    3.0    2.0  )

!                                     ( -5.0    1.0    7.0  )

!                                     (  1.0    5.0   -4.0  )

!

!                                 COEF = (3.0, 1.0, 2.0)

!

      DATA A/1.0, -5.0, 1.0, 3.0, 1.0, 5.0, 2.0, 7.0, -4.0/

      DATA COEF/3.0, 1.0, 2.0/

!

!                                 Evaluate B = 3I + A + 2*A**2

      CALL POLRG (A, COEF, B)

!                                 Print B

      CALL WRRRN ('B = 3I + A + 2*A**2', B)

      END

Output

 

    B = 3I + A + 2*A**2
        1       2       3
1   -20.0    35.0    32.0
2   -11.0    46.0   -55.0
3   -55.0   -19.0   105.0

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