unm22#

Functions

void cunm22(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            n1,
    const INT            n2,
    const c64*  restrict Q,
    const INT            ldq,
          c64*  restrict C,
    const INT            ldc,
          c64*  restrict work,
    const INT            lwork,
          INT*           info
);
void cunm22(const char *side, const char *trans, const INT m, const INT n, const INT n1, const INT n2, const c64 *restrict Q, const INT ldq, c64 *restrict C, const INT ldc, c64 *restrict work, const INT lwork, INT *info)#

CUNM22 overwrites the general complex M-by-N matrix C with. 

           SIDE = 'L'     SIDE = 'R'
TRANS = ‘N’: Q * C C * Q TRANS = ‘C’: Q**H * C C * Q**H

where Q is a complex unitary matrix of order NQ, with NQ = M if SIDE = ‘L’ and NQ = N if SIDE = ‘R’. The unitary matrix Q processes a 2-by-2 block structure 

    [  Q11  Q12  ]
Q = [            ]
    [  Q21  Q22  ],
where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an N2-by-N2 upper triangular matrix.

Parameters

in
side

= ‘L’: apply Q or Q**H from the Left; = ‘R’: apply Q or Q**H from the Right.

in
trans

= ‘N’: apply Q (No transpose); = ‘C’: apply Q**H (Conjugate transpose).

in
m

The number of rows of the matrix C. m >= 0.

in
n

The number of columns of the matrix C. n >= 0.

in
n1

The dimension of Q12. n1 >= 0.

in
n2

The dimension of Q21. n2 >= 0. n1 + n2 = m if SIDE = ‘L’ and n1 + n2 = n if SIDE = ‘R’.

in
Q

Single complex array, dimension (ldq, m) if SIDE = ‘L’, (ldq, n) if SIDE = ‘R’.

in
ldq

The leading dimension of the array Q. ldq >= max(1, m) if SIDE = ‘L’; ldq >= max(1, n) if SIDE = ‘R’.

inout
C

Single complex array, dimension (ldc, n). On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.

in
ldc

The leading dimension of the array C. ldc >= max(1, m).

out
work

Single complex array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

in
lwork

The dimension of the array work. If SIDE = ‘L’, lwork >= max(1, n); if SIDE = ‘R’, lwork >= max(1, m). For optimum performance lwork >= m*n. If lwork = -1, then a workspace query is assumed.

out
info

= 0: successful exit < 0: if info = -i, the i-th argument had an illegal value

Functions

void zunm22(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            n1,
    const INT            n2,
    const c128* restrict Q,
    const INT            ldq,
          c128* restrict C,
    const INT            ldc,
          c128* restrict work,
    const INT            lwork,
          INT*           info
);
void zunm22(const char *side, const char *trans, const INT m, const INT n, const INT n1, const INT n2, const c128 *restrict Q, const INT ldq, c128 *restrict C, const INT ldc, c128 *restrict work, const INT lwork, INT *info)#

ZUNM22 overwrites the general complex M-by-N matrix C with. 

           SIDE = 'L'     SIDE = 'R'
TRANS = ‘N’: Q * C C * Q TRANS = ‘C’: Q**H * C C * Q**H

where Q is a complex unitary matrix of order NQ, with NQ = M if SIDE = ‘L’ and NQ = N if SIDE = ‘R’. The unitary matrix Q processes a 2-by-2 block structure 

    [  Q11  Q12  ]
Q = [            ]
    [  Q21  Q22  ],
where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an N2-by-N2 upper triangular matrix.

Parameters

in
side

= ‘L’: apply Q or Q**H from the Left; = ‘R’: apply Q or Q**H from the Right.

in
trans

= ‘N’: apply Q (No transpose); = ‘C’: apply Q**H (Conjugate transpose).

in
m

The number of rows of the matrix C. m >= 0.

in
n

The number of columns of the matrix C. n >= 0.

in
n1

The dimension of Q12. n1 >= 0.

in
n2

The dimension of Q21. n2 >= 0. n1 + n2 = m if SIDE = ‘L’ and n1 + n2 = n if SIDE = ‘R’.

in
Q

Double complex array, dimension (ldq, m) if SIDE = ‘L’, (ldq, n) if SIDE = ‘R’.

in
ldq

The leading dimension of the array Q. ldq >= max(1, m) if SIDE = ‘L’; ldq >= max(1, n) if SIDE = ‘R’.

inout
C

Double complex array, dimension (ldc, n). On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.

in
ldc

The leading dimension of the array C. ldc >= max(1, m).

out
work

Double complex array, dimension (max(1, lwork)). On exit, if info = 0, work[0] returns the optimal lwork.

in
lwork

The dimension of the array work. If SIDE = ‘L’, lwork >= max(1, n); if SIDE = ‘R’, lwork >= max(1, m). For optimum performance lwork >= m*n. If lwork = -1, then a workspace query is assumed.

out
info

= 0: successful exit < 0: if info = -i, the i-th argument had an illegal value

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