Man page - ggsvp3(3)

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Manual

ggsvp3

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cggsvp3 (character jobu, character jobv, character jobq, integerm, integer p, integer n, complex, dimension( lda, * ) a, integer lda,complex, dimension( ldb, * ) b, integer ldb, real tola, real tolb,integer k, integer l, complex, dimension( ldu, * ) u, integer ldu,complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldq, *) q, integer ldq, integer, dimension( * ) iwork, real, dimension( * )rwork, complex, dimension( * ) tau, complex, dimension( * ) work,integer lwork, integer info)
subroutine dggsvp3 (character jobu, character jobv, character jobq, integerm, integer p, integer n, double precision, dimension( lda, * ) a,integer lda, double precision, dimension( ldb, * ) b, integer ldb,double precision tola, double precision tolb, integer k, integer l,double precision, dimension( ldu, * ) u, integer ldu, double precision,dimension( ldv, * ) v, integer ldv, double precision, dimension( ldq, *) q, integer ldq, integer, dimension( * ) iwork, double precision,dimension( * ) tau, double precision, dimension( * ) work, integerlwork, integer info)
subroutine sggsvp3 (character jobu, character jobv, character jobq, integerm, integer p, integer n, real, dimension( lda, * ) a, integer lda,real, dimension( ldb, * ) b, integer ldb, real tola, real tolb, integerk, integer l, real, dimension( ldu, * ) u, integer ldu, real,dimension( ldv, * ) v, integer ldv, real, dimension( ldq, * ) q,integer ldq, integer, dimension( * ) iwork, real, dimension( * ) tau,real, dimension( * ) work, integer lwork, integer info)
subroutine zggsvp3 (character jobu, character jobv, character jobq, integerm, integer p, integer n, complex*16, dimension( lda, * ) a, integerlda, complex*16, dimension( ldb, * ) b, integer ldb, double precisiontola, double precision tolb, integer k, integer l, complex*16,dimension( ldu, * ) u, integer ldu, complex*16, dimension( ldv, * ) v,integer ldv, complex*16, dimension( ldq, * ) q, integer ldq, integer,dimension( * ) iwork, double precision, dimension( * ) rwork,complex*16, dimension( * ) tau, complex*16, dimension( * ) work,integer lwork, integer info)
Author

NAME

ggsvp3 - ggsvp3: step in ggsvd

SYNOPSIS

Functions

subroutine cggsvp3 (jobu, jobv, jobq, m, p, n, a, lda, b, ldb, tola, tolb, k, l, u, ldu, v, ldv, q, ldq, iwork, rwork, tau, work, lwork, info)
CGGSVP3
subroutine dggsvp3 (jobu, jobv, jobq, m, p, n, a, lda, b, ldb, tola, tolb, k, l, u, ldu, v, ldv, q, ldq, iwork, tau, work, lwork, info)
DGGSVP3
subroutine sggsvp3 (jobu, jobv, jobq, m, p, n, a, lda, b, ldb, tola, tolb, k, l, u, ldu, v, ldv, q, ldq, iwork, tau, work, lwork, info)
SGGSVP3
subroutine zggsvp3 (jobu, jobv, jobq, m, p, n, a, lda, b, ldb, tola, tolb, k, l, u, ldu, v, ldv, q, ldq, iwork, rwork, tau, work, lwork, info)
ZGGSVP3

Detailed Description

Function Documentation

subroutine cggsvp3 (character jobu, character jobv, character jobq, integerm, integer p, integer n, complex, dimension( lda, * ) a, integer lda,complex, dimension( ldb, * ) b, integer ldb, real tola, real tolb,integer k, integer l, complex, dimension( ldu, * ) u, integer ldu,complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldq, *) q, integer ldq, integer, dimension( * ) iwork, real, dimension( * )rwork, complex, dimension( * ) tau, complex, dimension( * ) work,integer lwork, integer info)

CGGSVP3

Purpose:

CGGSVP3 computes unitary matrices U, V and Q such that

N-K-L K L
U**H*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0;
L ( 0 0 A23 )
M-K-L ( 0 0 0 )

N-K-L K L
= K ( 0 A12 A13 ) if M-K-L < 0;
M-K ( 0 0 A23 )

N-K-L K L
V**H*B*Q = L ( 0 0 B13 )
P-L ( 0 0 0 )

where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective
numerical rank of the (M+P)-by-N matrix (A**H,B**H)**H.

This decomposition is the preprocessing step for computing the
Generalized Singular Value Decomposition (GSVD), see subroutine
CGGSVD3.

Parameters

JOBU

JOBU is CHARACTER*1
= ā€™Uā€™: Unitary matrix U is computed;
= ā€™Nā€™: U is not computed.

JOBV

JOBV is CHARACTER*1
= ā€™Vā€™: Unitary matrix V is computed;
= ā€™Nā€™: V is not computed.

JOBQ

JOBQ is CHARACTER*1
= ā€™Qā€™: Unitary matrix Q is computed;
= ā€™Nā€™: Q is not computed.

M

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

P

P is INTEGER
The number of rows of the matrix B. P >= 0.

N

N is INTEGER
The number of columns of the matrices A and B. N >= 0.

A

A is COMPLEX array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, A contains the triangular (or trapezoidal) matrix
described in the Purpose section.

LDA

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

B

B is COMPLEX array, dimension (LDB,N)
On entry, the P-by-N matrix B.
On exit, B contains the triangular matrix described in
the Purpose section.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,P).

TOLA

TOLA is REAL

TOLB

TOLB is REAL

TOLA and TOLB are the thresholds to determine the effective
numerical rank of matrix B and a subblock of A. Generally,
they are set to
TOLA = MAX(M,N)*norm(A)*MACHEPS,
TOLB = MAX(P,N)*norm(B)*MACHEPS.
The size of TOLA and TOLB may affect the size of backward
errors of the decomposition.

K

K is INTEGER

L

L is INTEGER

On exit, K and L specify the dimension of the subblocks
described in Purpose section.
K + L = effective numerical rank of (A**H,B**H)**H.

U

U is COMPLEX array, dimension (LDU,M)
If JOBU = ā€™Uā€™, U contains the unitary matrix U.
If JOBU = ā€™Nā€™, U is not referenced.

LDU

LDU is INTEGER
The leading dimension of the array U. LDU >= max(1,M) if
JOBU = ā€™Uā€™; LDU >= 1 otherwise.

V

V is COMPLEX array, dimension (LDV,P)
If JOBV = ā€™Vā€™, V contains the unitary matrix V.
If JOBV = ā€™Nā€™, V is not referenced.

LDV

LDV is INTEGER
The leading dimension of the array V. LDV >= max(1,P) if
JOBV = ā€™Vā€™; LDV >= 1 otherwise.

Q

Q is COMPLEX array, dimension (LDQ,N)
If JOBQ = ā€™Qā€™, Q contains the unitary matrix Q.
If JOBQ = ā€™Nā€™, Q is not referenced.

LDQ

LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,N) if
JOBQ = ā€™Qā€™; LDQ >= 1 otherwise.

IWORK

IWORK is INTEGER array, dimension (N)

RWORK

RWORK is REAL array, dimension (2*N)

TAU

TAU is COMPLEX array, dimension (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, 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.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The subroutine uses LAPACK subroutine CGEQP3 for the QR factorization
with column pivoting to detect the effective numerical rank of the
a matrix. It may be replaced by a better rank determination strategy.

CGGSVP3 replaces the deprecated subroutine CGGSVP.

subroutine dggsvp3 (character jobu, character jobv, character jobq, integerm, integer p, integer n, double precision, dimension( lda, * ) a,integer lda, double precision, dimension( ldb, * ) b, integer ldb,double precision tola, double precision tolb, integer k, integer l,double precision, dimension( ldu, * ) u, integer ldu, double precision,dimension( ldv, * ) v, integer ldv, double precision, dimension( ldq, *) q, integer ldq, integer, dimension( * ) iwork, double precision,dimension( * ) tau, double precision, dimension( * ) work, integerlwork, integer info)

DGGSVP3

Purpose:

DGGSVP3 computes orthogonal matrices U, V and Q such that

N-K-L K L
U**T*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0;
L ( 0 0 A23 )
M-K-L ( 0 0 0 )

N-K-L K L
= K ( 0 A12 A13 ) if M-K-L < 0;
M-K ( 0 0 A23 )

N-K-L K L
V**T*B*Q = L ( 0 0 B13 )
P-L ( 0 0 0 )

where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective
numerical rank of the (M+P)-by-N matrix (A**T,B**T)**T.

This decomposition is the preprocessing step for computing the
Generalized Singular Value Decomposition (GSVD), see subroutine
DGGSVD3.

Parameters

JOBU

JOBU is CHARACTER*1
= ā€™Uā€™: Orthogonal matrix U is computed;
= ā€™Nā€™: U is not computed.

JOBV

JOBV is CHARACTER*1
= ā€™Vā€™: Orthogonal matrix V is computed;
= ā€™Nā€™: V is not computed.

JOBQ

JOBQ is CHARACTER*1
= ā€™Qā€™: Orthogonal matrix Q is computed;
= ā€™Nā€™: Q is not computed.

M

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

P

P is INTEGER
The number of rows of the matrix B. P >= 0.

N

N is INTEGER
The number of columns of the matrices A and B. N >= 0.

A

A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, A contains the triangular (or trapezoidal) matrix
described in the Purpose section.

LDA

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

B

B is DOUBLE PRECISION array, dimension (LDB,N)
On entry, the P-by-N matrix B.
On exit, B contains the triangular matrix described in
the Purpose section.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,P).

TOLA

TOLA is DOUBLE PRECISION

TOLB

TOLB is DOUBLE PRECISION

TOLA and TOLB are the thresholds to determine the effective
numerical rank of matrix B and a subblock of A. Generally,
they are set to
TOLA = MAX(M,N)*norm(A)*MACHEPS,
TOLB = MAX(P,N)*norm(B)*MACHEPS.
The size of TOLA and TOLB may affect the size of backward
errors of the decomposition.

K

K is INTEGER

L

L is INTEGER

On exit, K and L specify the dimension of the subblocks
described in Purpose section.
K + L = effective numerical rank of (A**T,B**T)**T.

U

U is DOUBLE PRECISION array, dimension (LDU,M)
If JOBU = ā€™Uā€™, U contains the orthogonal matrix U.
If JOBU = ā€™Nā€™, U is not referenced.

LDU

LDU is INTEGER
The leading dimension of the array U. LDU >= max(1,M) if
JOBU = ā€™Uā€™; LDU >= 1 otherwise.

V

V is DOUBLE PRECISION array, dimension (LDV,P)
If JOBV = ā€™Vā€™, V contains the orthogonal matrix V.
If JOBV = ā€™Nā€™, V is not referenced.

LDV

LDV is INTEGER
The leading dimension of the array V. LDV >= max(1,P) if
JOBV = ā€™Vā€™; LDV >= 1 otherwise.

Q

Q is DOUBLE PRECISION array, dimension (LDQ,N)
If JOBQ = ā€™Qā€™, Q contains the orthogonal matrix Q.
If JOBQ = ā€™Nā€™, Q is not referenced.

LDQ

LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,N) if
JOBQ = ā€™Qā€™; LDQ >= 1 otherwise.

IWORK

IWORK is INTEGER array, dimension (N)

TAU

TAU is DOUBLE PRECISION array, dimension (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, 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.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The subroutine uses LAPACK subroutine DGEQP3 for the QR factorization
with column pivoting to detect the effective numerical rank of the
a matrix. It may be replaced by a better rank determination strategy.

DGGSVP3 replaces the deprecated subroutine DGGSVP.

subroutine sggsvp3 (character jobu, character jobv, character jobq, integerm, integer p, integer n, real, dimension( lda, * ) a, integer lda,real, dimension( ldb, * ) b, integer ldb, real tola, real tolb, integerk, integer l, real, dimension( ldu, * ) u, integer ldu, real,dimension( ldv, * ) v, integer ldv, real, dimension( ldq, * ) q,integer ldq, integer, dimension( * ) iwork, real, dimension( * ) tau,real, dimension( * ) work, integer lwork, integer info)

SGGSVP3

Purpose:

SGGSVP3 computes orthogonal matrices U, V and Q such that

N-K-L K L
U**T*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0;
L ( 0 0 A23 )
M-K-L ( 0 0 0 )

N-K-L K L
= K ( 0 A12 A13 ) if M-K-L < 0;
M-K ( 0 0 A23 )

N-K-L K L
V**T*B*Q = L ( 0 0 B13 )
P-L ( 0 0 0 )

where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective
numerical rank of the (M+P)-by-N matrix (A**T,B**T)**T.

This decomposition is the preprocessing step for computing the
Generalized Singular Value Decomposition (GSVD), see subroutine
SGGSVD3.

Parameters

JOBU

JOBU is CHARACTER*1
= ā€™Uā€™: Orthogonal matrix U is computed;
= ā€™Nā€™: U is not computed.

JOBV

JOBV is CHARACTER*1
= ā€™Vā€™: Orthogonal matrix V is computed;
= ā€™Nā€™: V is not computed.

JOBQ

JOBQ is CHARACTER*1
= ā€™Qā€™: Orthogonal matrix Q is computed;
= ā€™Nā€™: Q is not computed.

M

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

P

P is INTEGER
The number of rows of the matrix B. P >= 0.

N

N is INTEGER
The number of columns of the matrices A and B. N >= 0.

A

A is REAL array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, A contains the triangular (or trapezoidal) matrix
described in the Purpose section.

LDA

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

B

B is REAL array, dimension (LDB,N)
On entry, the P-by-N matrix B.
On exit, B contains the triangular matrix described in
the Purpose section.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,P).

TOLA

TOLA is REAL

TOLB

TOLB is REAL

TOLA and TOLB are the thresholds to determine the effective
numerical rank of matrix B and a subblock of A. Generally,
they are set to
TOLA = MAX(M,N)*norm(A)*MACHEPS,
TOLB = MAX(P,N)*norm(B)*MACHEPS.
The size of TOLA and TOLB may affect the size of backward
errors of the decomposition.

K

K is INTEGER

L

L is INTEGER

On exit, K and L specify the dimension of the subblocks
described in Purpose section.
K + L = effective numerical rank of (A**T,B**T)**T.

U

U is REAL array, dimension (LDU,M)
If JOBU = ā€™Uā€™, U contains the orthogonal matrix U.
If JOBU = ā€™Nā€™, U is not referenced.

LDU

LDU is INTEGER
The leading dimension of the array U. LDU >= max(1,M) if
JOBU = ā€™Uā€™; LDU >= 1 otherwise.

V

V is REAL array, dimension (LDV,P)
If JOBV = ā€™Vā€™, V contains the orthogonal matrix V.
If JOBV = ā€™Nā€™, V is not referenced.

LDV

LDV is INTEGER
The leading dimension of the array V. LDV >= max(1,P) if
JOBV = ā€™Vā€™; LDV >= 1 otherwise.

Q

Q is REAL array, dimension (LDQ,N)
If JOBQ = ā€™Qā€™, Q contains the orthogonal matrix Q.
If JOBQ = ā€™Nā€™, Q is not referenced.

LDQ

LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,N) if
JOBQ = ā€™Qā€™; LDQ >= 1 otherwise.

IWORK

IWORK is INTEGER array, dimension (N)

TAU

TAU is REAL array, dimension (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, 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.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The subroutine uses LAPACK subroutine SGEQP3 for the QR factorization
with column pivoting to detect the effective numerical rank of the
a matrix. It may be replaced by a better rank determination strategy.

SGGSVP3 replaces the deprecated subroutine SGGSVP.

subroutine zggsvp3 (character jobu, character jobv, character jobq, integerm, integer p, integer n, complex*16, dimension( lda, * ) a, integerlda, complex*16, dimension( ldb, * ) b, integer ldb, double precisiontola, double precision tolb, integer k, integer l, complex*16,dimension( ldu, * ) u, integer ldu, complex*16, dimension( ldv, * ) v,integer ldv, complex*16, dimension( ldq, * ) q, integer ldq, integer,dimension( * ) iwork, double precision, dimension( * ) rwork,complex*16, dimension( * ) tau, complex*16, dimension( * ) work,integer lwork, integer info)

ZGGSVP3

Purpose:

ZGGSVP3 computes unitary matrices U, V and Q such that

N-K-L K L
U**H*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0;
L ( 0 0 A23 )
M-K-L ( 0 0 0 )

N-K-L K L
= K ( 0 A12 A13 ) if M-K-L < 0;
M-K ( 0 0 A23 )

N-K-L K L
V**H*B*Q = L ( 0 0 B13 )
P-L ( 0 0 0 )

where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular
upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0,
otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective
numerical rank of the (M+P)-by-N matrix (A**H,B**H)**H.

This decomposition is the preprocessing step for computing the
Generalized Singular Value Decomposition (GSVD), see subroutine
ZGGSVD3.

Parameters

JOBU

JOBU is CHARACTER*1
= ā€™Uā€™: Unitary matrix U is computed;
= ā€™Nā€™: U is not computed.

JOBV

JOBV is CHARACTER*1
= ā€™Vā€™: Unitary matrix V is computed;
= ā€™Nā€™: V is not computed.

JOBQ

JOBQ is CHARACTER*1
= ā€™Qā€™: Unitary matrix Q is computed;
= ā€™Nā€™: Q is not computed.

M

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

P

P is INTEGER
The number of rows of the matrix B. P >= 0.

N

N is INTEGER
The number of columns of the matrices A and B. N >= 0.

A

A is COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, A contains the triangular (or trapezoidal) matrix
described in the Purpose section.

LDA

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

B

B is COMPLEX*16 array, dimension (LDB,N)
On entry, the P-by-N matrix B.
On exit, B contains the triangular matrix described in
the Purpose section.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,P).

TOLA

TOLA is DOUBLE PRECISION

TOLB

TOLB is DOUBLE PRECISION

TOLA and TOLB are the thresholds to determine the effective
numerical rank of matrix B and a subblock of A. Generally,
they are set to
TOLA = MAX(M,N)*norm(A)*MAZHEPS,
TOLB = MAX(P,N)*norm(B)*MAZHEPS.
The size of TOLA and TOLB may affect the size of backward
errors of the decomposition.

K

K is INTEGER

L

L is INTEGER

On exit, K and L specify the dimension of the subblocks
described in Purpose section.
K + L = effective numerical rank of (A**H,B**H)**H.

U

U is COMPLEX*16 array, dimension (LDU,M)
If JOBU = ā€™Uā€™, U contains the unitary matrix U.
If JOBU = ā€™Nā€™, U is not referenced.

LDU

LDU is INTEGER
The leading dimension of the array U. LDU >= max(1,M) if
JOBU = ā€™Uā€™; LDU >= 1 otherwise.

V

V is COMPLEX*16 array, dimension (LDV,P)
If JOBV = ā€™Vā€™, V contains the unitary matrix V.
If JOBV = ā€™Nā€™, V is not referenced.

LDV

LDV is INTEGER
The leading dimension of the array V. LDV >= max(1,P) if
JOBV = ā€™Vā€™; LDV >= 1 otherwise.

Q

Q is COMPLEX*16 array, dimension (LDQ,N)
If JOBQ = ā€™Qā€™, Q contains the unitary matrix Q.
If JOBQ = ā€™Nā€™, Q is not referenced.

LDQ

LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,N) if
JOBQ = ā€™Qā€™; LDQ >= 1 otherwise.

IWORK

IWORK is INTEGER array, dimension (N)

RWORK

RWORK is DOUBLE PRECISION array, dimension (2*N)

TAU

TAU is COMPLEX*16 array, dimension (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, 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.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The subroutine uses LAPACK subroutine ZGEQP3 for the QR factorization
with column pivoting to detect the effective numerical rank of the
a matrix. It may be replaced by a better rank determination strategy.

ZGGSVP3 replaces the deprecated subroutine ZGGSVP.

Author

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