?opmtr

Syntax

FORTRAN 77:

call sopmtr(side, uplo, trans, m, n, ap, tau, c, ldc, work, info)

call dopmtr(side, uplo, trans, m, n, ap, tau, c, ldc, work, info)

Fortran 95:

call opmtr(ap, tau, c [,side] [,uplo] [,trans] [,info])

C:

lapack_int LAPACKE_<?>opmtr( int matrix_order, char side, char uplo, char trans, lapack_int m, lapack_int n, const <datatype>* ap, const <datatype>* tau, <datatype>* c, lapack_int ldc );

Include Files

The FORTRAN 77 interfaces are specified in the mkl_lapack.fi and mkl_lapack.h include files, the Fortran 95 interfaces are specified in the lapack.f90 include file, and the C interfaces are specified in the mkl_lapacke.h include file.

Description

The routine multiplies a real matrix C by Q or Q^T, where Q is the orthogonal matrix Q formed by ?sptrd when reducing a packed real symmetric matrix A to tridiagonal form: A = Q*T*Q^T. Use this routine after a call to ?sptrd.

Depending on the parameters side and trans, the routine can form one of the matrix products Q*C, Q^T*C, C*Q, or C*Q^T (overwriting the result on C).

Input Parameters

The data types are given for the Fortran interface. A <datatype> placeholder, if present, is used for the C interface data types in the C interface section above. See C Interface Conventions for the C interface principal conventions and type definitions.

In the descriptions below, r denotes the order of Q:

If side = 'L', r = m; if side = 'R', r = n.

side

CHARACTER*1. Must be either 'L' or 'R'.

If side = 'L', Q or Q^T is applied to C from the left.

If side = 'R', Q or Q^T is applied to C from the right.

uplo

CHARACTER*1. Must be 'U' or 'L'.

Use the same uplo as supplied to ?sptrd.

trans

CHARACTER*1. Must be either 'N' or 'T'.

If trans = 'N', the routine multiplies C by Q.

If trans = 'T', the routine multiplies C by Q^T.

m

INTEGER. The number of rows in the matrix C (m ≥ 0).

n

INTEGER. The number of columns in C (n ≥ 0).

ap, tau, c, work

REAL for sopmtr

DOUBLE PRECISION for dopmtr.

ap and tau are the arrays returned by ?sptrd.

The dimension of ap must be at least max(1, r(r+1)/2).

The dimension of tau must be at least max(1, r-1).

c(ldc,*) contains the matrix C.

The second dimension of c must be at least max(1, n)

work(*) is a workspace array.

The dimension of work must be at least

max(1, n) if side = 'L';

max(1, m) if side = 'R'.

ldc

INTEGER. The leading dimension of c; ldc ≥ max(1, n).

Output Parameters

c

Overwritten by the product Q*C, Q^T*C, C*Q, or C*Q^T (as specified by side and trans).

info

INTEGER.

If info = 0, the execution is successful.

If info = -i, the i-th parameter had an illegal value.

Fortran 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see Fortran 95 Interface Conventions.

Specific details for the routine opmtr interface are the following:

ap

Holds the array A of size (r*(r+1)/2), where

r = m if side = 'L'.

r = n if side = 'R'.

tau

Holds the vector with the number of elements r - 1.

c

Holds the matrix C of size (m,n).

side

Must be 'L' or 'R'. The default value is 'L'.

uplo

Must be 'U' or 'L'. The default value is 'U'.

trans

Must be 'N', 'C', or 'T'. The default value is 'N'.

Application Notes

The computed product differs from the exact product by a matrix E such that ||E||₂ = O(ε) ||C||₂, where ε is the machine precision.

The total number of floating-point operations is approximately 2*m²*n if side = 'L', or 2*n²*m if side = 'R'.

The complex counterpart of this routine is ?upmtr.