CUNGBR generates one of the complex unitary matrices Q or P**H
 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) or G(i) respectively.
 If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
 is of order M:
 if m >= k, Q = H(1) H(2) . . . H(k) and CUNGBR returns the first n
 columns of Q, where m >= n >= k;
 if m < k, Q = H(1) H(2) . . . H(m-1) and CUNGBR returns Q as an
 M-by-M matrix.
 If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H
 is of order N:
 if k < n, P**H = G(k) . . . G(2) G(1) and CUNGBR returns the first m
 rows of P**H, where n >= m >= k;
 if k >= n, P**H = G(n-1) . . . G(2) G(1) and CUNGBR returns P**H as
 an N-by-N matrix.

VECT

          VECT is CHARACTER*1
          Specifies whether the matrix Q or the matrix P**H is
          required, as defined in the transformation applied by CGEBRD:
          = 'Q':  generate Q;
          = 'P':  generate P**H.

M

          M is INTEGER
          The number of rows of the matrix Q or P**H to be returned.
          M >= 0.

N

          N is INTEGER
          The number of columns of the matrix Q or P**H to be returned.
          N >= 0.
          If VECT = 'Q', M >= N >= min(M,K);
          if VECT = 'P', N >= M >= min(N,K).

K

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

A

          A is COMPLEX array, dimension (LDA,N)
          On entry, the vectors which define the elementary reflectors,
          as returned by CGEBRD.
          On exit, the M-by-N matrix Q or P**H.

LDA

          LDA is INTEGER
          The leading dimension of the array A. LDA >= M.

TAU

          TAU is COMPLEX array, dimension
                                (min(M,K)) if VECT = 'Q'
                                (min(N,K)) if VECT = 'P'
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i) or G(i), which determines Q or P**H, as
          returned by CGEBRD in its array argument TAUQ or TAUP.

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. LWORK >= max(1,min(M,N)).
          For optimum performance LWORK >= min(M,N)*NB, 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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

 DORGBR generates one of the real orthogonal matrices Q or P**T
 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) or G(i) respectively.
 If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
 is of order M:
 if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n
 columns of Q, where m >= n >= k;
 if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an
 M-by-M matrix.
 If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T
 is of order N:
 if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m
 rows of P**T, where n >= m >= k;
 if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as
 an N-by-N matrix.

VECT

          VECT is CHARACTER*1
          Specifies whether the matrix Q or the matrix P**T is
          required, as defined in the transformation applied by DGEBRD:
          = 'Q':  generate Q;
          = 'P':  generate P**T.

M

          M is INTEGER
          The number of rows of the matrix Q or P**T to be returned.
          M >= 0.

N

          N is INTEGER
          The number of columns of the matrix Q or P**T to be returned.
          N >= 0.
          If VECT = 'Q', M >= N >= min(M,K);
          if VECT = 'P', N >= M >= min(N,K).

K

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

A

          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the vectors which define the elementary reflectors,
          as returned by DGEBRD.
          On exit, the M-by-N matrix Q or P**T.

LDA

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

TAU

          TAU is DOUBLE PRECISION array, dimension
                                (min(M,K)) if VECT = 'Q'
                                (min(N,K)) if VECT = 'P'
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i) or G(i), which determines Q or P**T, as
          returned by DGEBRD in its array argument TAUQ or TAUP.

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. LWORK >= max(1,min(M,N)).
          For optimum performance LWORK >= min(M,N)*NB, 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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

 SORGBR generates one of the real orthogonal matrices Q or P**T
 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) or G(i) respectively.
 If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
 is of order M:
 if m >= k, Q = H(1) H(2) . . . H(k) and SORGBR returns the first n
 columns of Q, where m >= n >= k;
 if m < k, Q = H(1) H(2) . . . H(m-1) and SORGBR returns Q as an
 M-by-M matrix.
 If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T
 is of order N:
 if k < n, P**T = G(k) . . . G(2) G(1) and SORGBR returns the first m
 rows of P**T, where n >= m >= k;
 if k >= n, P**T = G(n-1) . . . G(2) G(1) and SORGBR returns P**T as
 an N-by-N matrix.

VECT

          VECT is CHARACTER*1
          Specifies whether the matrix Q or the matrix P**T is
          required, as defined in the transformation applied by SGEBRD:
          = 'Q':  generate Q;
          = 'P':  generate P**T.

M

          M is INTEGER
          The number of rows of the matrix Q or P**T to be returned.
          M >= 0.

N

          N is INTEGER
          The number of columns of the matrix Q or P**T to be returned.
          N >= 0.
          If VECT = 'Q', M >= N >= min(M,K);
          if VECT = 'P', N >= M >= min(N,K).

K

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

A

          A is REAL array, dimension (LDA,N)
          On entry, the vectors which define the elementary reflectors,
          as returned by SGEBRD.
          On exit, the M-by-N matrix Q or P**T.

LDA

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

TAU

          TAU is REAL array, dimension
                                (min(M,K)) if VECT = 'Q'
                                (min(N,K)) if VECT = 'P'
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i) or G(i), which determines Q or P**T, as
          returned by SGEBRD in its array argument TAUQ or TAUP.

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. LWORK >= max(1,min(M,N)).
          For optimum performance LWORK >= min(M,N)*NB, 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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

 ZUNGBR generates one of the complex unitary matrices Q or P**H
 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) or G(i) respectively.
 If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
 is of order M:
 if m >= k, Q = H(1) H(2) . . . H(k) and ZUNGBR returns the first n
 columns of Q, where m >= n >= k;
 if m < k, Q = H(1) H(2) . . . H(m-1) and ZUNGBR returns Q as an
 M-by-M matrix.
 If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H
 is of order N:
 if k < n, P**H = G(k) . . . G(2) G(1) and ZUNGBR returns the first m
 rows of P**H, where n >= m >= k;
 if k >= n, P**H = G(n-1) . . . G(2) G(1) and ZUNGBR returns P**H as
 an N-by-N matrix.

VECT

          VECT is CHARACTER*1
          Specifies whether the matrix Q or the matrix P**H is
          required, as defined in the transformation applied by ZGEBRD:
          = 'Q':  generate Q;
          = 'P':  generate P**H.

M

          M is INTEGER
          The number of rows of the matrix Q or P**H to be returned.
          M >= 0.

N

          N is INTEGER
          The number of columns of the matrix Q or P**H to be returned.
          N >= 0.
          If VECT = 'Q', M >= N >= min(M,K);
          if VECT = 'P', N >= M >= min(N,K).

K

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

A

          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the vectors which define the elementary reflectors,
          as returned by ZGEBRD.
          On exit, the M-by-N matrix Q or P**H.

LDA

          LDA is INTEGER
          The leading dimension of the array A. LDA >= M.

TAU

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

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. LWORK >= max(1,min(M,N)).
          For optimum performance LWORK >= min(M,N)*NB, 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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.