?opmtr

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 11/07/2023

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?opmtr

Multiplies a real matrix by the real orthogonal matrix Q determined by ?sptrd.

Syntax

lapack_int LAPACKE_sopmtr (int matrix_layout, char side, char uplo, char trans, lapack_int m, lapack_int n, const float* ap, const float* tau, float* c, lapack_int ldc);

lapack_int LAPACKE_dopmtr (int matrix_layout, char side, char uplo, char trans, lapack_int m, lapack_int n, const double* ap, const double* tau, double* c, lapack_int ldc);

Include Files

mkl.h

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

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

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

matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).

side

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

Must be 'U' or 'L'.

Use the same uplo as supplied to ?sptrd.

trans

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

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

n

The number of columns in C (n≥ 0).

ap, tau, c

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(size max(1, ldc*n) for column major layout and max(1, ldc*m) for row major layout) contains the matrix C.

ldc

The leading dimension of c; ldc≥ max(1, n) for column major layout and ldc≥ max(1, m) for row major layout .

Output Parameters

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

Return Values

This function returns a value info.

If info=0, the execution is successful.

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

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.

Parent topic: Symmetric Eigenvalue Problems: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?opmtr

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

Application Notes