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.

Definition at line 195 of file cunmbr.f.

  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.

Definition at line 193 of file dormbr.f.

  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.

Definition at line 194 of file sormbr.f.

  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.

Definition at line 194 of file zunmbr.f.

Author

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