Scroll to navigation

ungtsqr(3) LAPACK ungtsqr(3)

NAME

ungtsqr - {un,or}gtsqr: generate Q from latsqr

SYNOPSIS

Functions


subroutine cungtsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
CUNGTSQR subroutine dorgtsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
DORGTSQR subroutine sorgtsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
SORGTSQR subroutine zungtsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
ZUNGTSQR

Detailed Description

Function Documentation

subroutine cungtsqr (integer m, integer n, integer mb, integer nb, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( * ) work, integer lwork, integer info)

CUNGTSQR

Purpose:



 CUNGTSQR generates an M-by-N complex matrix Q_out with orthonormal


 columns, which are the first N columns of a product of comlpex unitary


 matrices of order M which are returned by CLATSQR


      Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).


 See the documentation for CLATSQR.

Parameters

M 



          M is INTEGER


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

N



          N is INTEGER


          The number of columns of the matrix A. M >= N >= 0.

MB



          MB is INTEGER


          The row block size used by CLATSQR to return


          arrays A and T. MB > N.


          (Note that if MB > M, then M is used instead of MB


          as the row block size).

NB



          NB is INTEGER


          The column block size used by CLATSQR to return


          arrays A and T. NB >= 1.


          (Note that if NB > N, then N is used instead of NB


          as the column block size).

A



          A is COMPLEX array, dimension (LDA,N)


          On entry:


             The elements on and above the diagonal are not accessed.


             The elements below the diagonal represent the unit


             lower-trapezoidal blocked matrix V computed by CLATSQR


             that defines the input matrices Q_in(k) (ones on the


             diagonal are not stored) (same format as the output A


             below the diagonal in CLATSQR).


          On exit:


             The array A contains an M-by-N orthonormal matrix Q_out,


             i.e the columns of A are orthogonal unit vectors.

LDA



          LDA is INTEGER


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

T



          T is COMPLEX array,


          dimension (LDT, N * NIRB)


          where NIRB = Number_of_input_row_blocks


                     = MAX( 1, CEIL((M-N)/(MB-N)) )


          Let NICB = Number_of_input_col_blocks


                   = CEIL(N/NB)


          The upper-triangular block reflectors used to define the


          input matrices Q_in(k), k=(1:NIRB*NICB). The block


          reflectors are stored in compact form in NIRB block


          reflector sequences. Each of NIRB block reflector sequences


          is stored in a larger NB-by-N column block of T and consists


          of NICB smaller NB-by-NB upper-triangular column blocks.


          (same format as the output T in CLATSQR).

LDT



          LDT is INTEGER


          The leading dimension of the array T.


          LDT >= max(1,min(NB1,N)).

WORK



          (workspace) COMPLEX array, dimension (MAX(2,LWORK))


          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK



          LWORK is INTEGER


          The dimension of the array WORK.  LWORK >= (M+NB)*N.


          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.

Contributors:



 November 2019, Igor Kozachenko,


                Computer Science Division,


                University of California, Berkeley

subroutine dorgtsqr (integer m, integer n, integer mb, integer nb, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( * ) work, integer lwork, integer info)

DORGTSQR

Purpose:



 DORGTSQR generates an M-by-N real matrix Q_out with orthonormal columns,


 which are the first N columns of a product of real orthogonal


 matrices of order M which are returned by DLATSQR


      Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).


 See the documentation for DLATSQR.

Parameters

M 



          M is INTEGER


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

N



          N is INTEGER


          The number of columns of the matrix A. M >= N >= 0.

MB



          MB is INTEGER


          The row block size used by DLATSQR to return


          arrays A and T. MB > N.


          (Note that if MB > M, then M is used instead of MB


          as the row block size).

NB



          NB is INTEGER


          The column block size used by DLATSQR to return


          arrays A and T. NB >= 1.


          (Note that if NB > N, then N is used instead of NB


          as the column block size).

A



          A is DOUBLE PRECISION array, dimension (LDA,N)


          On entry:


             The elements on and above the diagonal are not accessed.


             The elements below the diagonal represent the unit


             lower-trapezoidal blocked matrix V computed by DLATSQR


             that defines the input matrices Q_in(k) (ones on the


             diagonal are not stored) (same format as the output A


             below the diagonal in DLATSQR).


          On exit:


             The array A contains an M-by-N orthonormal matrix Q_out,


             i.e the columns of A are orthogonal unit vectors.

LDA



          LDA is INTEGER


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

T



          T is DOUBLE PRECISION array,


          dimension (LDT, N * NIRB)


          where NIRB = Number_of_input_row_blocks


                     = MAX( 1, CEIL((M-N)/(MB-N)) )


          Let NICB = Number_of_input_col_blocks


                   = CEIL(N/NB)


          The upper-triangular block reflectors used to define the


          input matrices Q_in(k), k=(1:NIRB*NICB). The block


          reflectors are stored in compact form in NIRB block


          reflector sequences. Each of NIRB block reflector sequences


          is stored in a larger NB-by-N column block of T and consists


          of NICB smaller NB-by-NB upper-triangular column blocks.


          (same format as the output T in DLATSQR).

LDT



          LDT is INTEGER


          The leading dimension of the array T.


          LDT >= max(1,min(NB1,N)).

WORK



          (workspace) DOUBLE PRECISION array, dimension (MAX(2,LWORK))


          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK



          LWORK is INTEGER


          The dimension of the array WORK.  LWORK >= (M+NB)*N.


          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.

Contributors:



 November 2019, Igor Kozachenko,


                Computer Science Division,


                University of California, Berkeley

subroutine sorgtsqr (integer m, integer n, integer mb, integer nb, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, real, dimension( * ) work, integer lwork, integer info)

SORGTSQR

Purpose:



 SORGTSQR generates an M-by-N real matrix Q_out with orthonormal columns,


 which are the first N columns of a product of real orthogonal


 matrices of order M which are returned by SLATSQR


      Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).


 See the documentation for SLATSQR.

Parameters

M 



          M is INTEGER


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

N



          N is INTEGER


          The number of columns of the matrix A. M >= N >= 0.

MB



          MB is INTEGER


          The row block size used by SLATSQR to return


          arrays A and T. MB > N.


          (Note that if MB > M, then M is used instead of MB


          as the row block size).

NB



          NB is INTEGER


          The column block size used by SLATSQR to return


          arrays A and T. NB >= 1.


          (Note that if NB > N, then N is used instead of NB


          as the column block size).

A



          A is REAL array, dimension (LDA,N)


          On entry:


             The elements on and above the diagonal are not accessed.


             The elements below the diagonal represent the unit


             lower-trapezoidal blocked matrix V computed by SLATSQR


             that defines the input matrices Q_in(k) (ones on the


             diagonal are not stored) (same format as the output A


             below the diagonal in SLATSQR).


          On exit:


             The array A contains an M-by-N orthonormal matrix Q_out,


             i.e the columns of A are orthogonal unit vectors.

LDA



          LDA is INTEGER


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

T



          T is REAL array,


          dimension (LDT, N * NIRB)


          where NIRB = Number_of_input_row_blocks


                     = MAX( 1, CEIL((M-N)/(MB-N)) )


          Let NICB = Number_of_input_col_blocks


                   = CEIL(N/NB)


          The upper-triangular block reflectors used to define the


          input matrices Q_in(k), k=(1:NIRB*NICB). The block


          reflectors are stored in compact form in NIRB block


          reflector sequences. Each of NIRB block reflector sequences


          is stored in a larger NB-by-N column block of T and consists


          of NICB smaller NB-by-NB upper-triangular column blocks.


          (same format as the output T in SLATSQR).

LDT



          LDT is INTEGER


          The leading dimension of the array T.


          LDT >= max(1,min(NB1,N)).

WORK



          (workspace) REAL array, dimension (MAX(2,LWORK))


          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK



          LWORK is INTEGER


          The dimension of the array WORK.  LWORK >= (M+NB)*N.


          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.

Contributors:



 November 2019, Igor Kozachenko,


                Computer Science Division,


                University of California, Berkeley

subroutine zungtsqr (integer m, integer n, integer mb, integer nb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( * ) work, integer lwork, integer info)

ZUNGTSQR

Purpose:



 ZUNGTSQR generates an M-by-N complex matrix Q_out with orthonormal


 columns, which are the first N columns of a product of comlpex unitary


 matrices of order M which are returned by ZLATSQR


      Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).


 See the documentation for ZLATSQR.

Parameters

M 



          M is INTEGER


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

N



          N is INTEGER


          The number of columns of the matrix A. M >= N >= 0.

MB



          MB is INTEGER


          The row block size used by ZLATSQR to return


          arrays A and T. MB > N.


          (Note that if MB > M, then M is used instead of MB


          as the row block size).

NB



          NB is INTEGER


          The column block size used by ZLATSQR to return


          arrays A and T. NB >= 1.


          (Note that if NB > N, then N is used instead of NB


          as the column block size).

A



          A is COMPLEX*16 array, dimension (LDA,N)


          On entry:


             The elements on and above the diagonal are not accessed.


             The elements below the diagonal represent the unit


             lower-trapezoidal blocked matrix V computed by ZLATSQR


             that defines the input matrices Q_in(k) (ones on the


             diagonal are not stored) (same format as the output A


             below the diagonal in ZLATSQR).


          On exit:


             The array A contains an M-by-N orthonormal matrix Q_out,


             i.e the columns of A are orthogonal unit vectors.

LDA



          LDA is INTEGER


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

T



          T is COMPLEX*16 array,


          dimension (LDT, N * NIRB)


          where NIRB = Number_of_input_row_blocks


                     = MAX( 1, CEIL((M-N)/(MB-N)) )


          Let NICB = Number_of_input_col_blocks


                   = CEIL(N/NB)


          The upper-triangular block reflectors used to define the


          input matrices Q_in(k), k=(1:NIRB*NICB). The block


          reflectors are stored in compact form in NIRB block


          reflector sequences. Each of NIRB block reflector sequences


          is stored in a larger NB-by-N column block of T and consists


          of NICB smaller NB-by-NB upper-triangular column blocks.


          (same format as the output T in ZLATSQR).

LDT



          LDT is INTEGER


          The leading dimension of the array T.


          LDT >= max(1,min(NB1,N)).

WORK



          (workspace) COMPLEX*16 array, dimension (MAX(2,LWORK))


          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK



          LWORK is INTEGER


          The dimension of the array WORK.  LWORK >= (M+NB)*N.


          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.

Contributors:



 November 2019, Igor Kozachenko,


                Computer Science Division,


                University of California, Berkeley

Author

Generated automatically by Doxygen for LAPACK from the source code.

Sat Dec 9 2023 21:42:18 Version 3.12.0