# dgesvdx.f

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

## SYNOPSIS

### Functions/Subroutines

subroutine dgesvdx (JOBU, JOBVT, RANGE, M, N, A, LDA, VL, VU, IL, IU, NS, S, U, LDU, VT, LDVT, WORK, LWORK, IWORK, INFO)
DGESVDX computes the singular value decomposition (SVD) for GE matrices

## Function/Subroutine Documentation

### subroutine dgesvdx (character JOBU, character JOBVT, character RANGE, integer M, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision VL, double precision VU, integer IL, integer IU, integer NS, 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)

DGESVDX computes the singular value decomposition (SVD) for GE matrices

Purpose:

```  DGESVDX computes the singular value decomposition (SVD) of a real
M-by-N matrix A, optionally computing the left and/or right singular
vectors. 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.

DGESVDX uses an eigenvalue problem for obtaining the SVD, which
allows for the computation of a subset of singular values and
vectors. See DBDSVDX for details.

Note that the routine returns V**T, not V.
```

Parameters:

JOBU

```          JOBU is CHARACTER*1
Specifies options for computing all or part of the matrix U:
= 'V':  the first min(m,n) columns of U (the left singular
vectors) or as specified by RANGE are returned in
the array U;
= 'N':  no columns of U (no left singular vectors) are
computed.
```

JOBVT

```          JOBVT is CHARACTER*1
Specifies options for computing all or part of the matrix
V**T:
= 'V':  the first min(m,n) rows of V**T (the right singular
vectors) or as specified by RANGE are returned in
the array VT;
= 'N':  no rows of V**T (no right singular vectors) are
computed.
```

RANGE

```          RANGE is CHARACTER*1
= 'A': all singular values will be found.
= 'V': all singular values in the half-open interval (VL,VU]
will be found.
= 'I': the IL-th through IU-th singular values will be found.
```

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, the contents of A are destroyed.
```

LDA

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

VL

```          VL is DOUBLE PRECISION
If RANGE='V', the lower bound of the interval to
be searched for singular values. VU > VL.
Not referenced if RANGE = 'A' or 'I'.
```

VU

```          VU is DOUBLE PRECISION
If RANGE='V', the upper bound of the interval to
be searched for singular values. VU > VL.
Not referenced if RANGE = 'A' or 'I'.
```

IL

```          IL is INTEGER
If RANGE='I', the index of the
smallest singular value to be returned.
1 <= IL <= IU <= min(M,N), if min(M,N) > 0.
Not referenced if RANGE = 'A' or 'V'.
```

IU

```          IU is INTEGER
If RANGE='I', the index of the
largest singular value to be returned.
1 <= IL <= IU <= min(M,N), if min(M,N) > 0.
Not referenced if RANGE = 'A' or 'V'.
```

NS

```          NS is INTEGER
The total number of singular values found,
0 <= NS <= min(M,N).
If RANGE = 'A', NS = min(M,N); if RANGE = 'I', NS = IU-IL+1.
```

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)
If JOBU = 'V', U contains columns of U (the left singular
vectors, stored columnwise) as specified by RANGE; if
JOBU = 'N', U is not referenced.
Note: The user must ensure that UCOL >= NS; if RANGE = 'V',
the exact value of NS is not known in advance and an upper
bound must be used.
```

LDU

```          LDU is INTEGER
The leading dimension of the array U.  LDU >= 1; if
JOBU = 'V', LDU >= M.
```

VT

```          VT is DOUBLE PRECISION array, dimension (LDVT,N)
If JOBVT = 'V', VT contains the rows of V**T (the right singular
vectors, stored rowwise) as specified by RANGE; if JOBVT = 'N',
VT is not referenced.
Note: The user must ensure that LDVT >= NS; if RANGE = 'V',
the exact value of NS is not known in advance and an upper
bound must be used.
```

LDVT

```          LDVT is INTEGER
The leading dimension of the array VT.  LDVT >= 1; if
JOBVT = 'V', LDVT >= NS (see above).
```

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)*(MIN(M,N)+4)) for the paths (see
- PATH 1  (M much larger than N)
- PATH 1t (N much larger than M)
LWORK >= MAX(1,MIN(M,N)*2+MAX(M,N)) for the other paths.
For good performance, LWORK should generally be larger.

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.
```

IWORK

```          IWORK is INTEGER array, dimension (12*MIN(M,N))
If INFO = 0, the first NS elements of IWORK are zero. If INFO > 0,
then IWORK contains the indices of the eigenvectors that failed
to converge in DBDSVDX/DSTEVX.
```

INFO

```     INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i, then i eigenvectors failed to converge
in DBDSVDX/DSTEVX.
if INFO = N*2 + 1, an internal error occurred in
DBDSVDX
```

Author:

Univ. of Tennessee

Univ. of California Berkeley