# dgesdd.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dgesdd.f

## SYNOPSIS

### Functions/Subroutines

subroutine dgesdd (JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, IWORK, INFO)
DGESDD

## Function/Subroutine Documentation

### 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.

The divide and conquer algorithm makes very mild assumptions about
floating point arithmetic. It will work on machines with a guard
digit in add/subtract, or on those binary machines without guard
digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
Cray-2. It could conceivably fail on hexadecimal or decimal machines
without guard digits, but we know of none.
```

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:  successful exit.
< 0:  if INFO = -i, the i-th argument had an illegal value.
> 0:  DBDSDC did not converge, updating process failed.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

June 2016

Contributors:

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

Definition at line 220 of file dgesdd.f.

## Author

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