table of contents
| upgtr(3) | LAPACK | upgtr(3) |
NAME¶
upgtr - {up,op}gtr: generate Q from hetrd
SYNOPSIS¶
Functions¶
subroutine cupgtr (uplo, n, ap, tau, q, ldq, work, info)
CUPGTR subroutine dopgtr (uplo, n, ap, tau, q, ldq, work, info)
DOPGTR subroutine sopgtr (uplo, n, ap, tau, q, ldq, work, info)
SOPGTR subroutine zupgtr (uplo, n, ap, tau, q, ldq, work, info)
ZUPGTR
Detailed Description¶
Function Documentation¶
subroutine cupgtr (character uplo, integer n, complex, dimension( * ) ap, complex, dimension( * ) tau, complex, dimension( ldq, * ) q, integer ldq, complex, dimension( * ) work, integer info)¶
CUPGTR
Purpose:
CUPGTR generates a complex unitary matrix Q which is defined as the
product of n-1 elementary reflectors H(i) of order n, as returned by
CHPTRD using packed storage:
if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': Upper triangular packed storage used in previous
call to CHPTRD;
= 'L': Lower triangular packed storage used in previous
call to CHPTRD.
N
N is INTEGER
The order of the matrix Q. N >= 0.
AP
AP is COMPLEX array, dimension (N*(N+1)/2)
The vectors which define the elementary reflectors, as
returned by CHPTRD.
TAU
TAU is COMPLEX array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by CHPTRD.
Q
Q is COMPLEX array, dimension (LDQ,N)
The N-by-N unitary matrix Q.
LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
WORK
WORK is COMPLEX array, dimension (N-1)
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.
subroutine dopgtr (character uplo, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) tau, double precision, dimension( ldq, * ) q, integer ldq, double precision, dimension( * ) work, integer info)¶
DOPGTR
Purpose:
DOPGTR generates a real orthogonal matrix Q which is defined as the
product of n-1 elementary reflectors H(i) of order n, as returned by
DSPTRD using packed storage:
if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': Upper triangular packed storage used in previous
call to DSPTRD;
= 'L': Lower triangular packed storage used in previous
call to DSPTRD.
N
N is INTEGER
The order of the matrix Q. N >= 0.
AP
AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The vectors which define the elementary reflectors, as
returned by DSPTRD.
TAU
TAU is DOUBLE PRECISION array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DSPTRD.
Q
Q is DOUBLE PRECISION array, dimension (LDQ,N)
The N-by-N orthogonal matrix Q.
LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
WORK
WORK is DOUBLE PRECISION array, dimension (N-1)
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.
subroutine sopgtr (character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) tau, real, dimension( ldq, * ) q, integer ldq, real, dimension( * ) work, integer info)¶
SOPGTR
Purpose:
SOPGTR generates a real orthogonal matrix Q which is defined as the
product of n-1 elementary reflectors H(i) of order n, as returned by
SSPTRD using packed storage:
if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': Upper triangular packed storage used in previous
call to SSPTRD;
= 'L': Lower triangular packed storage used in previous
call to SSPTRD.
N
N is INTEGER
The order of the matrix Q. N >= 0.
AP
AP is REAL array, dimension (N*(N+1)/2)
The vectors which define the elementary reflectors, as
returned by SSPTRD.
TAU
TAU is REAL array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by SSPTRD.
Q
Q is REAL array, dimension (LDQ,N)
The N-by-N orthogonal matrix Q.
LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
WORK
WORK is REAL array, dimension (N-1)
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.
subroutine zupgtr (character uplo, integer n, complex*16, dimension( * ) ap, complex*16, dimension( * ) tau, complex*16, dimension( ldq, * ) q, integer ldq, complex*16, dimension( * ) work, integer info)¶
ZUPGTR
Purpose:
ZUPGTR generates a complex unitary matrix Q which is defined as the
product of n-1 elementary reflectors H(i) of order n, as returned by
ZHPTRD using packed storage:
if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': Upper triangular packed storage used in previous
call to ZHPTRD;
= 'L': Lower triangular packed storage used in previous
call to ZHPTRD.
N
N is INTEGER
The order of the matrix Q. N >= 0.
AP
AP is COMPLEX*16 array, dimension (N*(N+1)/2)
The vectors which define the elementary reflectors, as
returned by ZHPTRD.
TAU
TAU is COMPLEX*16 array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by ZHPTRD.
Q
Q is COMPLEX*16 array, dimension (LDQ,N)
The N-by-N unitary matrix Q.
LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
WORK
WORK is COMPLEX*16 array, dimension (N-1)
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.
Author¶
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| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |