unmbr(3)

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

SYNOPSIS

  Functions

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

Detailed Description

Function Documentation

  subroutine cunmbr (character vect, character side, character trans, integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer lwork, integer info)

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.

  subroutine dormbr (character vect, character side, character trans, integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer lwork, integer info)

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.

  subroutine sormbr (character vect, character side, character trans, integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer lwork, integer info)

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.

  subroutine zunmbr (character vect, character side, character trans, integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer lwork, integer info)

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.

Author

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