table of contents
upgtr(3) | Library Functions Manual | 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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 113 of file cupgtr.f.
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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 113 of file dopgtr.f.
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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 113 of file sopgtr.f.
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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 113 of file zupgtr.f.
Author¶
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