!>
!> CGEBRD reduces a general complex M-by-N matrix A to upper or lower
!> bidiagonal form B by a unitary transformation: Q**H * A * P = B.
!>
!> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
!> 

M

!>          M is INTEGER
!>          The number of rows in the matrix A.  M >= 0.
!> 

N

!>          N is INTEGER
!>          The number of columns in the matrix A.  N >= 0.
!> 

A

!>          A is COMPLEX array, dimension (LDA,N)
!>          On entry, the M-by-N general matrix to be reduced.
!>          On exit,
!>          if m >= n, the diagonal and the first superdiagonal are
!>            overwritten with the upper bidiagonal matrix B; the
!>            elements below the diagonal, with the array TAUQ, represent
!>            the unitary matrix Q as a product of elementary
!>            reflectors, and the elements above the first superdiagonal,
!>            with the array TAUP, represent the unitary matrix P as
!>            a product of elementary reflectors;
!>          if m < n, the diagonal and the first subdiagonal are
!>            overwritten with the lower bidiagonal matrix B; the
!>            elements below the first subdiagonal, with the array TAUQ,
!>            represent the unitary matrix Q as a product of
!>            elementary reflectors, and the elements above the diagonal,
!>            with the array TAUP, represent the unitary matrix P as
!>            a product of elementary reflectors.
!>          See Further Details.
!> 

LDA

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

D

!>          D is REAL array, dimension (min(M,N))
!>          The diagonal elements of the bidiagonal matrix B:
!>          D(i) = A(i,i).
!> 

E

!>          E is REAL array, dimension (min(M,N)-1)
!>          The off-diagonal elements of the bidiagonal matrix B:
!>          if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1;
!>          if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.
!> 

TAUQ

!>          TAUQ is COMPLEX array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors which
!>          represent the unitary matrix Q. See Further Details.
!> 

TAUP

!>          TAUP is COMPLEX array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors which
!>          represent the unitary matrix P. See Further Details.
!> 

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 length of the array WORK.  LWORK >= max(1,M,N).
!>          For optimum performance LWORK >= (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.

!>
!>  The matrices Q and P are represented as products of elementary
!>  reflectors:
!>
!>  If m >= n,
!>
!>     Q = H(1) H(2) . . . H(n)  and  P = G(1) G(2) . . . G(n-1)
!>
!>  Each H(i) and G(i) has the form:
!>
!>     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
!>
!>  where tauq and taup are complex scalars, and v and u are complex
!>  vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in
!>  A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in
!>  A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
!>
!>  If m < n,
!>
!>     Q = H(1) H(2) . . . H(m-1)  and  P = G(1) G(2) . . . G(m)
!>
!>  Each H(i) and G(i) has the form:
!>
!>     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
!>
!>  where tauq and taup are complex scalars, and v and u are complex
!>  vectors; v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in
!>  A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in
!>  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
!>
!>  The contents of A on exit are illustrated by the following examples:
!>
!>  m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):
!>
!>    (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 )
!>    (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 )
!>    (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 )
!>    (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 )
!>    (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 )
!>    (  v1  v2  v3  v4  v5 )
!>
!>  where d and e denote diagonal and off-diagonal elements of B, vi
!>  denotes an element of the vector defining H(i), and ui an element of
!>  the vector defining G(i).
!> 

!>
!> DGEBRD reduces a general real M-by-N matrix A to upper or lower
!> bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.
!>
!> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
!> 

M

!>          M is INTEGER
!>          The number of rows in the matrix A.  M >= 0.
!> 

N

!>          N is INTEGER
!>          The number of columns in the matrix A.  N >= 0.
!> 

A

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, the M-by-N general matrix to be reduced.
!>          On exit,
!>          if m >= n, the diagonal and the first superdiagonal are
!>            overwritten with the upper bidiagonal matrix B; the
!>            elements below the diagonal, with the array TAUQ, represent
!>            the orthogonal matrix Q as a product of elementary
!>            reflectors, and the elements above the first superdiagonal,
!>            with the array TAUP, represent the orthogonal matrix P as
!>            a product of elementary reflectors;
!>          if m < n, the diagonal and the first subdiagonal are
!>            overwritten with the lower bidiagonal matrix B; the
!>            elements below the first subdiagonal, with the array TAUQ,
!>            represent the orthogonal matrix Q as a product of
!>            elementary reflectors, and the elements above the diagonal,
!>            with the array TAUP, represent the orthogonal matrix P as
!>            a product of elementary reflectors.
!>          See Further Details.
!> 

LDA

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

D

!>          D is DOUBLE PRECISION array, dimension (min(M,N))
!>          The diagonal elements of the bidiagonal matrix B:
!>          D(i) = A(i,i).
!> 

E

!>          E is DOUBLE PRECISION array, dimension (min(M,N)-1)
!>          The off-diagonal elements of the bidiagonal matrix B:
!>          if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1;
!>          if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.
!> 

TAUQ

!>          TAUQ is DOUBLE PRECISION array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors which
!>          represent the orthogonal matrix Q. See Further Details.
!> 

TAUP

!>          TAUP is DOUBLE PRECISION array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors which
!>          represent the orthogonal matrix P. See Further Details.
!> 

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 length of the array WORK.  LWORK >= max(1,M,N).
!>          For optimum performance LWORK >= (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.

!>
!>  The matrices Q and P are represented as products of elementary
!>  reflectors:
!>
!>  If m >= n,
!>
!>     Q = H(1) H(2) . . . H(n)  and  P = G(1) G(2) . . . G(n-1)
!>
!>  Each H(i) and G(i) has the form:
!>
!>     H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T
!>
!>  where tauq and taup are real scalars, and v and u are real vectors;
!>  v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i);
!>  u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n);
!>  tauq is stored in TAUQ(i) and taup in TAUP(i).
!>
!>  If m < n,
!>
!>     Q = H(1) H(2) . . . H(m-1)  and  P = G(1) G(2) . . . G(m)
!>
!>  Each H(i) and G(i) has the form:
!>
!>     H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T
!>
!>  where tauq and taup are real scalars, and v and u are real vectors;
!>  v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
!>  u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n);
!>  tauq is stored in TAUQ(i) and taup in TAUP(i).
!>
!>  The contents of A on exit are illustrated by the following examples:
!>
!>  m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):
!>
!>    (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 )
!>    (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 )
!>    (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 )
!>    (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 )
!>    (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 )
!>    (  v1  v2  v3  v4  v5 )
!>
!>  where d and e denote diagonal and off-diagonal elements of B, vi
!>  denotes an element of the vector defining H(i), and ui an element of
!>  the vector defining G(i).
!> 

!>
!> SGEBRD reduces a general real M-by-N matrix A to upper or lower
!> bidiagonal form B by an orthogonal transformation: Q**T * A * P = B.
!>
!> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
!> 

M

!>          M is INTEGER
!>          The number of rows in the matrix A.  M >= 0.
!> 

N

!>          N is INTEGER
!>          The number of columns in the matrix A.  N >= 0.
!> 

A

!>          A is REAL array, dimension (LDA,N)
!>          On entry, the M-by-N general matrix to be reduced.
!>          On exit,
!>          if m >= n, the diagonal and the first superdiagonal are
!>            overwritten with the upper bidiagonal matrix B; the
!>            elements below the diagonal, with the array TAUQ, represent
!>            the orthogonal matrix Q as a product of elementary
!>            reflectors, and the elements above the first superdiagonal,
!>            with the array TAUP, represent the orthogonal matrix P as
!>            a product of elementary reflectors;
!>          if m < n, the diagonal and the first subdiagonal are
!>            overwritten with the lower bidiagonal matrix B; the
!>            elements below the first subdiagonal, with the array TAUQ,
!>            represent the orthogonal matrix Q as a product of
!>            elementary reflectors, and the elements above the diagonal,
!>            with the array TAUP, represent the orthogonal matrix P as
!>            a product of elementary reflectors.
!>          See Further Details.
!> 

LDA

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

D

!>          D is REAL array, dimension (min(M,N))
!>          The diagonal elements of the bidiagonal matrix B:
!>          D(i) = A(i,i).
!> 

E

!>          E is REAL array, dimension (min(M,N)-1)
!>          The off-diagonal elements of the bidiagonal matrix B:
!>          if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1;
!>          if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.
!> 

TAUQ

!>          TAUQ is REAL array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors which
!>          represent the orthogonal matrix Q. See Further Details.
!> 

TAUP

!>          TAUP is REAL array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors which
!>          represent the orthogonal matrix P. See Further Details.
!> 

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 length of the array WORK.  LWORK >= max(1,M,N).
!>          For optimum performance LWORK >= (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.

!>
!>  The matrices Q and P are represented as products of elementary
!>  reflectors:
!>
!>  If m >= n,
!>
!>     Q = H(1) H(2) . . . H(n)  and  P = G(1) G(2) . . . G(n-1)
!>
!>  Each H(i) and G(i) has the form:
!>
!>     H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T
!>
!>  where tauq and taup are real scalars, and v and u are real vectors;
!>  v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in A(i+1:m,i);
!>  u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in A(i,i+2:n);
!>  tauq is stored in TAUQ(i) and taup in TAUP(i).
!>
!>  If m < n,
!>
!>     Q = H(1) H(2) . . . H(m-1)  and  P = G(1) G(2) . . . G(m)
!>
!>  Each H(i) and G(i) has the form:
!>
!>     H(i) = I - tauq * v * v**T  and G(i) = I - taup * u * u**T
!>
!>  where tauq and taup are real scalars, and v and u are real vectors;
!>  v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
!>  u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n);
!>  tauq is stored in TAUQ(i) and taup in TAUP(i).
!>
!>  The contents of A on exit are illustrated by the following examples:
!>
!>  m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):
!>
!>    (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 )
!>    (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 )
!>    (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 )
!>    (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 )
!>    (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 )
!>    (  v1  v2  v3  v4  v5 )
!>
!>  where d and e denote diagonal and off-diagonal elements of B, vi
!>  denotes an element of the vector defining H(i), and ui an element of
!>  the vector defining G(i).
!> 

!>
!> ZGEBRD reduces a general complex M-by-N matrix A to upper or lower
!> bidiagonal form B by a unitary transformation: Q**H * A * P = B.
!>
!> If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.
!> 

M

!>          M is INTEGER
!>          The number of rows in the matrix A.  M >= 0.
!> 

N

!>          N is INTEGER
!>          The number of columns in the matrix A.  N >= 0.
!> 

A

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the M-by-N general matrix to be reduced.
!>          On exit,
!>          if m >= n, the diagonal and the first superdiagonal are
!>            overwritten with the upper bidiagonal matrix B; the
!>            elements below the diagonal, with the array TAUQ, represent
!>            the unitary matrix Q as a product of elementary
!>            reflectors, and the elements above the first superdiagonal,
!>            with the array TAUP, represent the unitary matrix P as
!>            a product of elementary reflectors;
!>          if m < n, the diagonal and the first subdiagonal are
!>            overwritten with the lower bidiagonal matrix B; the
!>            elements below the first subdiagonal, with the array TAUQ,
!>            represent the unitary matrix Q as a product of
!>            elementary reflectors, and the elements above the diagonal,
!>            with the array TAUP, represent the unitary matrix P as
!>            a product of elementary reflectors.
!>          See Further Details.
!> 

LDA

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

D

!>          D is DOUBLE PRECISION array, dimension (min(M,N))
!>          The diagonal elements of the bidiagonal matrix B:
!>          D(i) = A(i,i).
!> 

E

!>          E is DOUBLE PRECISION array, dimension (min(M,N)-1)
!>          The off-diagonal elements of the bidiagonal matrix B:
!>          if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1;
!>          if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.
!> 

TAUQ

!>          TAUQ is COMPLEX*16 array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors which
!>          represent the unitary matrix Q. See Further Details.
!> 

TAUP

!>          TAUP is COMPLEX*16 array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors which
!>          represent the unitary matrix P. See Further Details.
!> 

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 length of the array WORK.  LWORK >= max(1,M,N).
!>          For optimum performance LWORK >= (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.

!>
!>  The matrices Q and P are represented as products of elementary
!>  reflectors:
!>
!>  If m >= n,
!>
!>     Q = H(1) H(2) . . . H(n)  and  P = G(1) G(2) . . . G(n-1)
!>
!>  Each H(i) and G(i) has the form:
!>
!>     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
!>
!>  where tauq and taup are complex scalars, and v and u are complex
!>  vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in
!>  A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in
!>  A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
!>
!>  If m < n,
!>
!>     Q = H(1) H(2) . . . H(m-1)  and  P = G(1) G(2) . . . G(m)
!>
!>  Each H(i) and G(i) has the form:
!>
!>     H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H
!>
!>  where tauq and taup are complex scalars, and v and u are complex
!>  vectors; v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in
!>  A(i+2:m,i); u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in
!>  A(i,i+1:n); tauq is stored in TAUQ(i) and taup in TAUP(i).
!>
!>  The contents of A on exit are illustrated by the following examples:
!>
!>  m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):
!>
!>    (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 )
!>    (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 )
!>    (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 )
!>    (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 )
!>    (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 )
!>    (  v1  v2  v3  v4  v5 )
!>
!>  where d and e denote diagonal and off-diagonal elements of B, vi
!>  denotes an element of the vector defining H(i), and ui an element of
!>  the vector defining G(i).
!>