# zgesdd.f man page

zgesdd.f —

## Synopsis

### Functions/Subroutines

subroutinezgesdd(JOBZ, M, N, A, LDA, S, U, LDU, VT, LDVT, WORK, LWORK, RWORK, IWORK, INFO)ZGESDD

## Function/Subroutine Documentation

### subroutine zgesdd (characterJOBZ, integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, double precision, dimension( * )S, complex*16, dimension( ldu, * )U, integerLDU, complex*16, dimension( ldvt, * )VT, integerLDVT, complex*16, dimension( * )WORK, integerLWORK, double precision, dimension( * )RWORK, integer, dimension( * )IWORK, integerINFO)

**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.
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**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 JOBZ = 'N', LWORK >= 2*min(M,N)+max(M,N).
if JOBZ = 'O',
LWORK >= 2*min(M,N)*min(M,N)+2*min(M,N)+max(M,N).
if JOBZ = 'S' or 'A',
LWORK >= min(M,N)*min(M,N)+2*min(M,N)+max(M,N).
For good performance, LWORK should generally be larger.
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.
```

*RWORK*

```
RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
If JOBZ = 'N', LRWORK >= 5*min(M,N).
Otherwise,
LRWORK >= min(M,N)*max(5*min(M,N)+7,2*max(M,N)+2*min(M,N)+1)
```

*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: The updating process of DBDSDC did not converge.
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

**Contributors:**

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

Definition at line 222 of file zgesdd.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zgesdd(3) is an alias of zgesdd.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK