Multiplies a complex matrix by the complex unitary matrix Q determined by ?hetrd.

## Syntax

lapack_int LAPACKE_cunmtr (int matrix_layout, char side, char uplo, char trans, lapack_int m, lapack_int n, const lapack_complex_float* a, lapack_int lda, const lapack_complex_float* tau, lapack_complex_float* c, lapack_int ldc);

lapack_int LAPACKE_zunmtr (int matrix_layout, char side, char uplo, char trans, lapack_int m, lapack_int n, const lapack_complex_double* a, lapack_int lda, const lapack_complex_double* tau, lapack_complex_double* c, lapack_int ldc);

• mkl.h

## Description

The routine multiplies a complex matrix C by Q or QH, where Q is the unitary matrix Q formed by hetrd when reducing a complex Hermitian matrix A to tridiagonal form: A = Q*T*QH. Use this routine after a call to ?hetrd.

Depending on the parameters side and trans, the routine can form one of the matrix products Q*C, QH*C, C*Q, or C*QH (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 QH is applied to C from the left.

If side = 'R', Q or QH is applied to C from the right.

uplo

Must be 'U' or 'L'.

Use the same uplo as supplied to ?hetrd.

trans

Must be either 'N' or 'T'.

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

If trans = 'C', the routine multiplies C by QH.

m

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

n

The number of columns in C (n 0).

a, c, tau

a (size max(1, lda*r)) and tau are the arrays returned by ?hetrd.

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.

lda

The leading dimension of a; lda max(1, r).

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, QH*C, C*Q, or C*QH (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 8*m2*n if side = 'L' or 8*n2*m if side = 'R'.

The real counterpart of this routine is ormtr.