orm22#

Functions

void sorm22(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            n1,
    const INT            n2,
    const f32*  restrict Q,
    const INT            ldq,
          f32*  restrict C,
    const INT            ldc,
          f32*  restrict work,
    const INT            lwork,
          INT*           info
);
void sorm22(const char *side, const char *trans, const INT m, const INT n, const INT n1, const INT n2, const f32 *restrict Q, const INT ldq, f32 *restrict C, const INT ldc, f32 *restrict work, const INT lwork, INT *info)#

SORM22 overwrites the general real M-by-N matrix C with. 

            SIDE = 'L'     SIDE = 'R'
TRANS = ‘N’: Q * C C * Q TRANS = ‘T’: Q**T * C C * Q**T

where Q is a real orthogonal matrix of order NQ, with NQ = M if SIDE = ‘L’ and NQ = N if SIDE = ‘R’. The orthogonal 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**T from the Left; = ‘R’: apply Q or Q**T from the Right.

in
trans

= ‘N’: apply Q (No transpose); = ‘T’: apply Q**T (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

Array of dimension (ldq, M) if SIDE = ‘L’, (ldq, N) if SIDE = ‘R’.

in
ldq

The leading dimension of Q. ldq >= max(1,M) if SIDE = ‘L’; ldq >= max(1,N) if SIDE = ‘R’.

inout
C

Array of dimension (ldc, n). On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

in
ldc

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

out
work

Workspace array of dimension (lwork).

in
lwork

The dimension of work. If SIDE = ‘L’, lwork >= max(1,n); if SIDE = ‘R’, lwork >= max(1,m). For optimum performance lwork >= m*n.

out
info

  • = 0: successful exit

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

Functions

void dorm22(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            n1,
    const INT            n2,
    const f64*  restrict Q,
    const INT            ldq,
          f64*  restrict C,
    const INT            ldc,
          f64*  restrict work,
    const INT            lwork,
          INT*           info
);
void dorm22(const char *side, const char *trans, const INT m, const INT n, const INT n1, const INT n2, const f64 *restrict Q, const INT ldq, f64 *restrict C, const INT ldc, f64 *restrict work, const INT lwork, INT *info)#

DORM22 overwrites the general real M-by-N matrix C with. 

            SIDE = 'L'     SIDE = 'R'
TRANS = ‘N’: Q * C C * Q TRANS = ‘T’: Q**T * C C * Q**T

where Q is a real orthogonal matrix of order NQ, with NQ = M if SIDE = ‘L’ and NQ = N if SIDE = ‘R’. The orthogonal 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**T from the Left; = ‘R’: apply Q or Q**T from the Right.

in
trans

= ‘N’: apply Q (No transpose); = ‘T’: apply Q**T (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

Array of dimension (ldq, M) if SIDE = ‘L’, (ldq, N) if SIDE = ‘R’.

in
ldq

The leading dimension of Q. ldq >= max(1,M) if SIDE = ‘L’; ldq >= max(1,N) if SIDE = ‘R’.

inout
C

Array of dimension (ldc, n). On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.

in
ldc

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

out
work

Workspace array of dimension (lwork).

in
lwork

The dimension of work. If SIDE = ‘L’, lwork >= max(1,n); if SIDE = ‘R’, lwork >= max(1,m). For optimum performance lwork >= m*n.

out
info

  • = 0: successful exit

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

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