unmbr(3) Library Functions Manual unmbr(3)

unmbr - {un,or}mbr: multiply by Q, P from gebrd


subroutine cunmbr (vect, side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
CUNMBR subroutine dormbr (vect, side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
DORMBR subroutine sormbr (vect, side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
SORMBR subroutine zunmbr (vect, side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
ZUNMBR

CUNMBR

Purpose:

 If VECT = 'Q', CUNMBR 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
 If VECT = 'P', CUNMBR overwrites the general complex M-by-N matrix C
 with
                 SIDE = 'L'     SIDE = 'R'
 TRANS = 'N':      P * C          C * P
 TRANS = 'C':      P**H * C       C * P**H
 Here Q and P**H are the unitary matrices determined by CGEBRD when
 reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q
 and P**H are defined as products of elementary reflectors H(i) and
 G(i) respectively.
 Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
 order of the unitary matrix Q or P**H that is applied.
 If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
 if nq >= k, Q = H(1) H(2) . . . H(k);
 if nq < k, Q = H(1) H(2) . . . H(nq-1).
 If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
 if k < nq, P = G(1) G(2) . . . G(k);
 if k >= nq, P = G(1) G(2) . . . G(nq-1).

Parameters

VECT 
          VECT is CHARACTER*1
          = 'Q': apply Q or Q**H;
          = 'P': apply P or P**H.

SIDE

          SIDE is CHARACTER*1
          = 'L': apply Q, Q**H, P or P**H from the Left;
          = 'R': apply Q, Q**H, P or P**H from the Right.

TRANS

          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q or P;
          = 'C':  Conjugate transpose, apply Q**H or P**H.

M

          M is INTEGER
          The number of rows of the matrix C. M >= 0.

N

          N is INTEGER
          The number of columns of the matrix C. N >= 0.

K

          K is INTEGER
          If VECT = 'Q', the number of columns in the original
          matrix reduced by CGEBRD.
          If VECT = 'P', the number of rows in the original
          matrix reduced by CGEBRD.
          K >= 0.

A

          A is COMPLEX array, dimension
                                (LDA,min(nq,K)) if VECT = 'Q'
                                (LDA,nq)        if VECT = 'P'
          The vectors which define the elementary reflectors H(i) and
          G(i), whose products determine the matrices Q and P, as
          returned by CGEBRD.

LDA

          LDA is INTEGER
          The leading dimension of the array A.
          If VECT = 'Q', LDA >= max(1,nq);
          if VECT = 'P', LDA >= max(1,min(nq,K)).

TAU

          TAU is COMPLEX array, dimension (min(nq,K))
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i) or G(i) which determines Q or P, as returned
          by CGEBRD in the array argument TAUQ or TAUP.

C

          C is 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
          or P*C or P**H*C or C*P or C*P**H.

LDC

          LDC is INTEGER
          The leading dimension of the array C. LDC >= max(1,M).

WORK

          WORK is COMPLEX array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If SIDE = 'L', LWORK >= max(1,N);
          if SIDE = 'R', LWORK >= max(1,M);
          if N = 0 or M = 0, LWORK >= 1.
          For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L',
          and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the
          optimal blocksize. (NB = 0 if M = 0 or N = 0.)
          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

INFO

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 195 of file cunmbr.f.

DORMBR

Purpose:

 If VECT = 'Q', DORMBR 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
 If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C
 with
                 SIDE = 'L'     SIDE = 'R'
 TRANS = 'N':      P * C          C * P
 TRANS = 'T':      P**T * C       C * P**T
 Here Q and P**T are the orthogonal matrices determined by DGEBRD when
 reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
 P**T are defined as products of elementary reflectors H(i) and G(i)
 respectively.
 Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
 order of the orthogonal matrix Q or P**T that is applied.
 If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
 if nq >= k, Q = H(1) H(2) . . . H(k);
 if nq < k, Q = H(1) H(2) . . . H(nq-1).
 If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
 if k < nq, P = G(1) G(2) . . . G(k);
 if k >= nq, P = G(1) G(2) . . . G(nq-1).

Parameters

VECT 
          VECT is CHARACTER*1
          = 'Q': apply Q or Q**T;
          = 'P': apply P or P**T.

SIDE

          SIDE is CHARACTER*1
          = 'L': apply Q, Q**T, P or P**T from the Left;
          = 'R': apply Q, Q**T, P or P**T from the Right.

TRANS

          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q  or P;
          = 'T':  Transpose, apply Q**T or P**T.

M

          M is INTEGER
          The number of rows of the matrix C. M >= 0.

N

          N is INTEGER
          The number of columns of the matrix C. N >= 0.

K

          K is INTEGER
          If VECT = 'Q', the number of columns in the original
          matrix reduced by DGEBRD.
          If VECT = 'P', the number of rows in the original
          matrix reduced by DGEBRD.
          K >= 0.

A

          A is DOUBLE PRECISION array, dimension
                                (LDA,min(nq,K)) if VECT = 'Q'
                                (LDA,nq)        if VECT = 'P'
          The vectors which define the elementary reflectors H(i) and
          G(i), whose products determine the matrices Q and P, as
          returned by DGEBRD.

LDA

          LDA is INTEGER
          The leading dimension of the array A.
          If VECT = 'Q', LDA >= max(1,nq);
          if VECT = 'P', LDA >= max(1,min(nq,K)).

TAU

          TAU is DOUBLE PRECISION array, dimension (min(nq,K))
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i) or G(i) which determines Q or P, as returned
          by DGEBRD in the array argument TAUQ or TAUP.

C

          C is DOUBLE PRECISION array, 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
          or P*C or P**T*C or C*P or C*P**T.

LDC

          LDC is INTEGER
          The leading dimension of the array C. LDC >= max(1,M).

WORK

          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If SIDE = 'L', LWORK >= max(1,N);
          if SIDE = 'R', LWORK >= max(1,M).
          For optimum performance LWORK >= N*NB if SIDE = 'L', and
          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
          blocksize.
          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

INFO

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 193 of file dormbr.f.

SORMBR

Purpose:

 If VECT = 'Q', SORMBR 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
 If VECT = 'P', SORMBR overwrites the general real M-by-N matrix C
 with
                 SIDE = 'L'     SIDE = 'R'
 TRANS = 'N':      P * C          C * P
 TRANS = 'T':      P**T * C       C * P**T
 Here Q and P**T are the orthogonal matrices determined by SGEBRD when
 reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
 P**T are defined as products of elementary reflectors H(i) and G(i)
 respectively.
 Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
 order of the orthogonal matrix Q or P**T that is applied.
 If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
 if nq >= k, Q = H(1) H(2) . . . H(k);
 if nq < k, Q = H(1) H(2) . . . H(nq-1).
 If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
 if k < nq, P = G(1) G(2) . . . G(k);
 if k >= nq, P = G(1) G(2) . . . G(nq-1).

Parameters

VECT 
          VECT is CHARACTER*1
          = 'Q': apply Q or Q**T;
          = 'P': apply P or P**T.

SIDE

          SIDE is CHARACTER*1
          = 'L': apply Q, Q**T, P or P**T from the Left;
          = 'R': apply Q, Q**T, P or P**T from the Right.

TRANS

          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q  or P;
          = 'T':  Transpose, apply Q**T or P**T.

M

          M is INTEGER
          The number of rows of the matrix C. M >= 0.

N

          N is INTEGER
          The number of columns of the matrix C. N >= 0.

K

          K is INTEGER
          If VECT = 'Q', the number of columns in the original
          matrix reduced by SGEBRD.
          If VECT = 'P', the number of rows in the original
          matrix reduced by SGEBRD.
          K >= 0.

A

          A is REAL array, dimension
                                (LDA,min(nq,K)) if VECT = 'Q'
                                (LDA,nq)        if VECT = 'P'
          The vectors which define the elementary reflectors H(i) and
          G(i), whose products determine the matrices Q and P, as
          returned by SGEBRD.

LDA

          LDA is INTEGER
          The leading dimension of the array A.
          If VECT = 'Q', LDA >= max(1,nq);
          if VECT = 'P', LDA >= max(1,min(nq,K)).

TAU

          TAU is REAL array, dimension (min(nq,K))
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i) or G(i) which determines Q or P, as returned
          by SGEBRD in the array argument TAUQ or TAUP.

C

          C is REAL array, 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
          or P*C or P**T*C or C*P or C*P**T.

LDC

          LDC is INTEGER
          The leading dimension of the array C. LDC >= max(1,M).

WORK

          WORK is REAL array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If SIDE = 'L', LWORK >= max(1,N);
          if SIDE = 'R', LWORK >= max(1,M).
          For optimum performance LWORK >= N*NB if SIDE = 'L', and
          LWORK >= M*NB if SIDE = 'R', where NB is the optimal
          blocksize.
          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

INFO

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 194 of file sormbr.f.

ZUNMBR

Purpose:

 If VECT = 'Q', ZUNMBR 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
 If VECT = 'P', ZUNMBR overwrites the general complex M-by-N matrix C
 with
                 SIDE = 'L'     SIDE = 'R'
 TRANS = 'N':      P * C          C * P
 TRANS = 'C':      P**H * C       C * P**H
 Here Q and P**H are the unitary matrices determined by ZGEBRD when
 reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q
 and P**H are defined as products of elementary reflectors H(i) and
 G(i) respectively.
 Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
 order of the unitary matrix Q or P**H that is applied.
 If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
 if nq >= k, Q = H(1) H(2) . . . H(k);
 if nq < k, Q = H(1) H(2) . . . H(nq-1).
 If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
 if k < nq, P = G(1) G(2) . . . G(k);
 if k >= nq, P = G(1) G(2) . . . G(nq-1).

Parameters

VECT 
          VECT is CHARACTER*1
          = 'Q': apply Q or Q**H;
          = 'P': apply P or P**H.

SIDE

          SIDE is CHARACTER*1
          = 'L': apply Q, Q**H, P or P**H from the Left;
          = 'R': apply Q, Q**H, P or P**H from the Right.

TRANS

          TRANS is CHARACTER*1
          = 'N':  No transpose, apply Q or P;
          = 'C':  Conjugate transpose, apply Q**H or P**H.

M

          M is INTEGER
          The number of rows of the matrix C. M >= 0.

N

          N is INTEGER
          The number of columns of the matrix C. N >= 0.

K

          K is INTEGER
          If VECT = 'Q', the number of columns in the original
          matrix reduced by ZGEBRD.
          If VECT = 'P', the number of rows in the original
          matrix reduced by ZGEBRD.
          K >= 0.

A

          A is COMPLEX*16 array, dimension
                                (LDA,min(nq,K)) if VECT = 'Q'
                                (LDA,nq)        if VECT = 'P'
          The vectors which define the elementary reflectors H(i) and
          G(i), whose products determine the matrices Q and P, as
          returned by ZGEBRD.

LDA

          LDA is INTEGER
          The leading dimension of the array A.
          If VECT = 'Q', LDA >= max(1,nq);
          if VECT = 'P', LDA >= max(1,min(nq,K)).

TAU

          TAU is COMPLEX*16 array, dimension (min(nq,K))
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i) or G(i) which determines Q or P, as returned
          by ZGEBRD in the array argument TAUQ or TAUP.

C

          C is COMPLEX*16 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
          or P*C or P**H*C or C*P or C*P**H.

LDC

          LDC is INTEGER
          The leading dimension of the array C. LDC >= max(1,M).

WORK

          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER
          The dimension of the array WORK.
          If SIDE = 'L', LWORK >= max(1,N);
          if SIDE = 'R', LWORK >= max(1,M);
          if N = 0 or M = 0, LWORK >= 1.
          For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L',
          and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the
          optimal blocksize. (NB = 0 if M = 0 or N = 0.)
          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.

INFO

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 194 of file zunmbr.f.

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