gesdd(3)

NAME
gesdd - gesdd: SVD, divide and conquer

SYNOPSIS

  Functions

subroutine cgesdd (jobz, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, rwork, iwork, info)
CGESDD
subroutine dgesdd (jobz, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, iwork, info)
DGESDD
subroutine sgesdd (jobz, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, iwork, info)
SGESDD
subroutine zgesdd (jobz, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, rwork, iwork, info)
ZGESDD

Detailed Description

Function Documentation

  subroutine cgesdd (character jobz, integer m, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) s, complex, dimension( ldu, * ) u, integer ldu, complex, dimension( ldvt, * ) vt, integer ldvt, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer, dimension( * ) iwork, integer info)

CGESDD

Purpose:

    !>
    !> CGESDD computes the singular value decomposition (SVD) of a complex
    !> M-by-N matrix A, optionally computing the left and/or right singular
    !> vectors, by using divide-and-conquer method. The SVD is written
    !>
    !>      A = U * SIGMA * conjugate-transpose(V)
    !>
    !> where SIGMA is an M-by-N matrix which is zero except for its
    !> min(m,n) diagonal elements, U is an M-by-M unitary matrix, and
    !> V is an N-by-N unitary matrix.  The diagonal elements of SIGMA
    !> are the singular values of A; they are real and non-negative, and
    !> are returned in descending order.  The first min(m,n) columns of
    !> U and V are the left and right singular vectors of A.
    !>
    !> Note that the routine returns VT = V**H, not V.
    !>
    !>

Parameters
    JOBZ

    !>          JOBZ is CHARACTER*1
    !>          Specifies options for computing all or part of the matrix U:
    !>          = 'A':  all M columns of U and all N rows of V**H are
    !>                  returned in the arrays U and VT;
    !>          = 'S':  the first min(M,N) columns of U and the first
    !>                  min(M,N) rows of V**H are returned in the arrays U
    !>                  and VT;
    !>          = 'O':  If M >= N, the first N columns of U are overwritten
    !>                  in the array A and all rows of V**H are returned in
    !>                  the array VT;
    !>                  otherwise, all columns of U are returned in the
    !>                  array U and the first M rows of V**H are overwritten
    !>                  in the array A;
    !>          = 'N':  no columns of U or rows of V**H are computed.
    !>

    M

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

    N

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

    A

    !>          A is COMPLEX array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix A.
    !>          On exit,
    !>          if JOBZ = 'O',  A is overwritten with the first N columns
    !>                          of U (the left singular vectors, stored
    !>                          columnwise) if M >= N;
    !>                          A is overwritten with the first M rows
    !>                          of V**H (the right singular vectors, stored
    !>                          rowwise) otherwise.
    !>          if JOBZ .ne. 'O', the contents of A are destroyed.
    !>

    LDA

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

    S

    !>          S is REAL array, dimension (min(M,N))
    !>          The singular values of A, sorted so that S(i) >= S(i+1).
    !>

    U

    !>          U is COMPLEX array, dimension (LDU,UCOL)
    !>          UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
    !>          UCOL = min(M,N) if JOBZ = 'S'.
    !>          If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
    !>          unitary matrix U;
    !>          if JOBZ = 'S', U contains the first min(M,N) columns of U
    !>          (the left singular vectors, stored columnwise);
    !>          if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.
    !>

    LDU

    !>          LDU is INTEGER
    !>          The leading dimension of the array U.  LDU >= 1;
    !>          if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
    !>

    VT

    !>          VT is COMPLEX array, dimension (LDVT,N)
    !>          If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the
    !>          N-by-N unitary matrix V**H;
    !>          if JOBZ = 'S', VT contains the first min(M,N) rows of
    !>          V**H (the right singular vectors, stored rowwise);
    !>          if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.
    !>

    LDVT

    !>          LDVT is INTEGER
    !>          The leading dimension of the array VT.  LDVT >= 1;
    !>          if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N;
    !>          if JOBZ = 'S', LDVT >= min(M,N).
    !>

    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 >= 1.
    !>          If LWORK = -1, a workspace query is assumed.  The optimal
    !>          size for the WORK array is calculated and stored in WORK(1),
    !>          and no other work except argument checking is performed.
    !>
    !>          Let mx = max(M,N) and mn = min(M,N).
    !>          If JOBZ = 'N', LWORK >= 2*mn + mx.
    !>          If JOBZ = 'O', LWORK >= 2*mn*mn + 2*mn + mx.
    !>          If JOBZ = 'S', LWORK >=   mn*mn + 3*mn.
    !>          If JOBZ = 'A', LWORK >=   mn*mn + 2*mn + mx.
    !>          These are not tight minimums in all cases; see comments inside code.
    !>          For good performance, LWORK should generally be larger;
    !>          a query is recommended.
    !>

    RWORK

    !>          RWORK is REAL array, dimension (MAX(1,LRWORK))
    !>          Let mx = max(M,N) and mn = min(M,N).
    !>          If JOBZ = 'N',    LRWORK >= 5*mn (LAPACK <= 3.6 needs 7*mn);
    !>          else if mx >> mn, LRWORK >= 5*mn*mn + 5*mn;
    !>          else              LRWORK >= max( 5*mn*mn + 5*mn,
    !>                                           2*mx*mn + 2*mn*mn + mn ).
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (8*min(M,N))
    !>

    INFO

    !>          INFO is INTEGER
    !>          <  0:  if INFO = -i, the i-th argument had an illegal value.
    !>          = -4:  if A had a NAN entry.
    !>          >  0:  The updating process of SBDSDC did not converge.
    !>          =  0:  successful exit.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

  subroutine dgesdd (character jobz, integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( ldvt, * ) vt, integer ldvt, double precision, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer info)

DGESDD

Purpose:

    !>
    !> DGESDD computes the singular value decomposition (SVD) of a real
    !> M-by-N matrix A, optionally computing the left and right singular
    !> vectors.  If singular vectors are desired, it uses a
    !> divide-and-conquer algorithm.
    !>
    !> The SVD is written
    !>
    !>      A = U * SIGMA * transpose(V)
    !>
    !> where SIGMA is an M-by-N matrix which is zero except for its
    !> min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
    !> V is an N-by-N orthogonal matrix.  The diagonal elements of SIGMA
    !> are the singular values of A; they are real and non-negative, and
    !> are returned in descending order.  The first min(m,n) columns of
    !> U and V are the left and right singular vectors of A.
    !>
    !> Note that the routine returns VT = V**T, not V.
    !>
    !>

Parameters
    JOBZ

    !>          JOBZ is CHARACTER*1
    !>          Specifies options for computing all or part of the matrix U:
    !>          = 'A':  all M columns of U and all N rows of V**T are
    !>                  returned in the arrays U and VT;
    !>          = 'S':  the first min(M,N) columns of U and the first
    !>                  min(M,N) rows of V**T are returned in the arrays U
    !>                  and VT;
    !>          = 'O':  If M >= N, the first N columns of U are overwritten
    !>                  on the array A and all rows of V**T are returned in
    !>                  the array VT;
    !>                  otherwise, all columns of U are returned in the
    !>                  array U and the first M rows of V**T are overwritten
    !>                  in the array A;
    !>          = 'N':  no columns of U or rows of V**T are computed.
    !>

    M

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

    N

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

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix A.
    !>          On exit,
    !>          if JOBZ = 'O',  A is overwritten with the first N columns
    !>                          of U (the left singular vectors, stored
    !>                          columnwise) if M >= N;
    !>                          A is overwritten with the first M rows
    !>                          of V**T (the right singular vectors, stored
    !>                          rowwise) otherwise.
    !>          if JOBZ .ne. 'O', the contents of A are destroyed.
    !>

    LDA

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

    S

    !>          S is DOUBLE PRECISION array, dimension (min(M,N))
    !>          The singular values of A, sorted so that S(i) >= S(i+1).
    !>

    U

    !>          U is DOUBLE PRECISION array, dimension (LDU,UCOL)
    !>          UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
    !>          UCOL = min(M,N) if JOBZ = 'S'.
    !>          If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
    !>          orthogonal matrix U;
    !>          if JOBZ = 'S', U contains the first min(M,N) columns of U
    !>          (the left singular vectors, stored columnwise);
    !>          if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.
    !>

    LDU

    !>          LDU is INTEGER
    !>          The leading dimension of the array U.  LDU >= 1; if
    !>          JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
    !>

    VT

    !>          VT is DOUBLE PRECISION array, dimension (LDVT,N)
    !>          If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the
    !>          N-by-N orthogonal matrix V**T;
    !>          if JOBZ = 'S', VT contains the first min(M,N) rows of
    !>          V**T (the right singular vectors, stored rowwise);
    !>          if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.
    !>

    LDVT

    !>          LDVT is INTEGER
    !>          The leading dimension of the array VT.  LDVT >= 1;
    !>          if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N;
    !>          if JOBZ = 'S', LDVT >= min(M,N).
    !>

    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 >= 1.
    !>          If LWORK = -1, a workspace query is assumed.  The optimal
    !>          size for the WORK array is calculated and stored in WORK(1),
    !>          and no other work except argument checking is performed.
    !>
    !>          Let mx = max(M,N) and mn = min(M,N).
    !>          If JOBZ = 'N', LWORK >= 3*mn + max( mx, 7*mn ).
    !>          If JOBZ = 'O', LWORK >= 3*mn + max( mx, 5*mn*mn + 4*mn ).
    !>          If JOBZ = 'S', LWORK >= 4*mn*mn + 7*mn.
    !>          If JOBZ = 'A', LWORK >= 4*mn*mn + 6*mn + mx.
    !>          These are not tight minimums in all cases; see comments inside code.
    !>          For good performance, LWORK should generally be larger;
    !>          a query is recommended.
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (8*min(M,N))
    !>

    INFO

    !>          INFO is INTEGER
    !>          <  0:  if INFO = -i, the i-th argument had an illegal value.
    !>          = -4:  if A had a NAN entry.
    !>          >  0:  DBDSDC did not converge, updating process failed.
    !>          =  0:  successful exit.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

  subroutine sgesdd (character jobz, integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) s, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldvt, * ) vt, integer ldvt, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer info)

SGESDD

Purpose:

    !>
    !> SGESDD computes the singular value decomposition (SVD) of a real
    !> M-by-N matrix A, optionally computing the left and right singular
    !> vectors.  If singular vectors are desired, it uses a
    !> divide-and-conquer algorithm.
    !>
    !> The SVD is written
    !>
    !>      A = U * SIGMA * transpose(V)
    !>
    !> where SIGMA is an M-by-N matrix which is zero except for its
    !> min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
    !> V is an N-by-N orthogonal matrix.  The diagonal elements of SIGMA
    !> are the singular values of A; they are real and non-negative, and
    !> are returned in descending order.  The first min(m,n) columns of
    !> U and V are the left and right singular vectors of A.
    !>
    !> Note that the routine returns VT = V**T, not V.
    !>
    !>

Parameters
    JOBZ

    !>          JOBZ is CHARACTER*1
    !>          Specifies options for computing all or part of the matrix U:
    !>          = 'A':  all M columns of U and all N rows of V**T are
    !>                  returned in the arrays U and VT;
    !>          = 'S':  the first min(M,N) columns of U and the first
    !>                  min(M,N) rows of V**T are returned in the arrays U
    !>                  and VT;
    !>          = 'O':  If M >= N, the first N columns of U are overwritten
    !>                  on the array A and all rows of V**T are returned in
    !>                  the array VT;
    !>                  otherwise, all columns of U are returned in the
    !>                  array U and the first M rows of V**T are overwritten
    !>                  in the array A;
    !>          = 'N':  no columns of U or rows of V**T are computed.
    !>

    M

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

    N

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

    A

    !>          A is REAL array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix A.
    !>          On exit,
    !>          if JOBZ = 'O',  A is overwritten with the first N columns
    !>                          of U (the left singular vectors, stored
    !>                          columnwise) if M >= N;
    !>                          A is overwritten with the first M rows
    !>                          of V**T (the right singular vectors, stored
    !>                          rowwise) otherwise.
    !>          if JOBZ .ne. 'O', the contents of A are destroyed.
    !>

    LDA

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

    S

    !>          S is REAL array, dimension (min(M,N))
    !>          The singular values of A, sorted so that S(i) >= S(i+1).
    !>

    U

    !>          U is REAL array, dimension (LDU,UCOL)
    !>          UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
    !>          UCOL = min(M,N) if JOBZ = 'S'.
    !>          If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
    !>          orthogonal matrix U;
    !>          if JOBZ = 'S', U contains the first min(M,N) columns of U
    !>          (the left singular vectors, stored columnwise);
    !>          if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.
    !>

    LDU

    !>          LDU is INTEGER
    !>          The leading dimension of the array U.  LDU >= 1; if
    !>          JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
    !>

    VT

    !>          VT is REAL array, dimension (LDVT,N)
    !>          If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the
    !>          N-by-N orthogonal matrix V**T;
    !>          if JOBZ = 'S', VT contains the first min(M,N) rows of
    !>          V**T (the right singular vectors, stored rowwise);
    !>          if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.
    !>

    LDVT

    !>          LDVT is INTEGER
    !>          The leading dimension of the array VT.  LDVT >= 1;
    !>          if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N;
    !>          if JOBZ = 'S', LDVT >= min(M,N).
    !>

    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 >= 1.
    !>          If LWORK = -1, a workspace query is assumed.  The optimal
    !>          size for the WORK array is calculated and stored in WORK(1),
    !>          and no other work except argument checking is performed.
    !>
    !>          Let mx = max(M,N) and mn = min(M,N).
    !>          If JOBZ = 'N', LWORK >= 3*mn + max( mx, 7*mn ).
    !>          If JOBZ = 'O', LWORK >= 3*mn + max( mx, 5*mn*mn + 4*mn ).
    !>          If JOBZ = 'S', LWORK >= 4*mn*mn + 7*mn.
    !>          If JOBZ = 'A', LWORK >= 4*mn*mn + 6*mn + mx.
    !>          These are not tight minimums in all cases; see comments inside code.
    !>          For good performance, LWORK should generally be larger;
    !>          a query is recommended.
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (8*min(M,N))
    !>

    INFO

    !>          INFO is INTEGER
    !>          <  0:  if INFO = -i, the i-th argument had an illegal value.
    !>          = -4:  if A had a NAN entry.
    !>          >  0:  SBDSDC did not converge, updating process failed.
    !>          =  0:  successful exit.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

  subroutine zgesdd (character jobz, integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) s, complex*16, dimension( ldu, * ) u, integer ldu, complex*16, dimension( ldvt, * ) vt, integer ldvt, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer, dimension( * ) iwork, integer info)

ZGESDD

Purpose:

    !>
    !> ZGESDD computes the singular value decomposition (SVD) of a complex
    !> M-by-N matrix A, optionally computing the left and/or right singular
    !> vectors, by using divide-and-conquer method. The SVD is written
    !>
    !>      A = U * SIGMA * conjugate-transpose(V)
    !>
    !> where SIGMA is an M-by-N matrix which is zero except for its
    !> min(m,n) diagonal elements, U is an M-by-M unitary matrix, and
    !> V is an N-by-N unitary matrix.  The diagonal elements of SIGMA
    !> are the singular values of A; they are real and non-negative, and
    !> are returned in descending order.  The first min(m,n) columns of
    !> U and V are the left and right singular vectors of A.
    !>
    !> Note that the routine returns VT = V**H, not V.
    !>
    !>

Parameters
    JOBZ

    !>          JOBZ is CHARACTER*1
    !>          Specifies options for computing all or part of the matrix U:
    !>          = 'A':  all M columns of U and all N rows of V**H are
    !>                  returned in the arrays U and VT;
    !>          = 'S':  the first min(M,N) columns of U and the first
    !>                  min(M,N) rows of V**H are returned in the arrays U
    !>                  and VT;
    !>          = 'O':  If M >= N, the first N columns of U are overwritten
    !>                  in the array A and all rows of V**H are returned in
    !>                  the array VT;
    !>                  otherwise, all columns of U are returned in the
    !>                  array U and the first M rows of V**H are overwritten
    !>                  in the array A;
    !>          = 'N':  no columns of U or rows of V**H are computed.
    !>

    M

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

    N

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

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix A.
    !>          On exit,
    !>          if JOBZ = 'O',  A is overwritten with the first N columns
    !>                          of U (the left singular vectors, stored
    !>                          columnwise) if M >= N;
    !>                          A is overwritten with the first M rows
    !>                          of V**H (the right singular vectors, stored
    !>                          rowwise) otherwise.
    !>          if JOBZ .ne. 'O', the contents of A are destroyed.
    !>

    LDA

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

    S

    !>          S is DOUBLE PRECISION array, dimension (min(M,N))
    !>          The singular values of A, sorted so that S(i) >= S(i+1).
    !>

    U

    !>          U is COMPLEX*16 array, dimension (LDU,UCOL)
    !>          UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
    !>          UCOL = min(M,N) if JOBZ = 'S'.
    !>          If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
    !>          unitary matrix U;
    !>          if JOBZ = 'S', U contains the first min(M,N) columns of U
    !>          (the left singular vectors, stored columnwise);
    !>          if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.
    !>

    LDU

    !>          LDU is INTEGER
    !>          The leading dimension of the array U.  LDU >= 1;
    !>          if JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M.
    !>

    VT

    !>          VT is COMPLEX*16 array, dimension (LDVT,N)
    !>          If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the
    !>          N-by-N unitary matrix V**H;
    !>          if JOBZ = 'S', VT contains the first min(M,N) rows of
    !>          V**H (the right singular vectors, stored rowwise);
    !>          if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced.
    !>

    LDVT

    !>          LDVT is INTEGER
    !>          The leading dimension of the array VT.  LDVT >= 1;
    !>          if JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N;
    !>          if JOBZ = 'S', LDVT >= min(M,N).
    !>

    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 >= 1.
    !>          If LWORK = -1, a workspace query is assumed.  The optimal
    !>          size for the WORK array is calculated and stored in WORK(1),
    !>          and no other work except argument checking is performed.
    !>
    !>          Let mx = max(M,N) and mn = min(M,N).
    !>          If JOBZ = 'N', LWORK >= 2*mn + mx.
    !>          If JOBZ = 'O', LWORK >= 2*mn*mn + 2*mn + mx.
    !>          If JOBZ = 'S', LWORK >=   mn*mn + 3*mn.
    !>          If JOBZ = 'A', LWORK >=   mn*mn + 2*mn + mx.
    !>          These are not tight minimums in all cases; see comments inside code.
    !>          For good performance, LWORK should generally be larger;
    !>          a query is recommended.
    !>

    RWORK

    !>          RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
    !>          Let mx = max(M,N) and mn = min(M,N).
    !>          If JOBZ = 'N',    LRWORK >= 5*mn (LAPACK <= 3.6 needs 7*mn);
    !>          else if mx >> mn, LRWORK >= 5*mn*mn + 5*mn;
    !>          else              LRWORK >= max( 5*mn*mn + 5*mn,
    !>                                           2*mx*mn + 2*mn*mn + mn ).
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (8*min(M,N))
    !>

    INFO

    !>          INFO is INTEGER
    !>          <  0:  if INFO = -i, the i-th argument had an illegal value.
    !>          = -4:  if A had a NAN entry.
    !>          >  0:  The updating process of DBDSDC did not converge.
    !>          =  0:  successful exit.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:
    Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA

Author

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