gesdd - Man Page

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

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

Definition at line 219 of file cgesdd.f.

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

Definition at line 211 of file dgesdd.f.

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

Definition at line 211 of file sgesdd.f.

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

Definition at line 219 of file zgesdd.f.