ungtsqr(3)

Library Functions Manual

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

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

          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 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 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 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

Definition at line 174 of file cungtsqr.f.

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

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

          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 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 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 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

Definition at line 174 of file dorgtsqr.f.

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

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

          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 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 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 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

Definition at line 174 of file sorgtsqr.f.

subroutine zungtsqr (integer m, integer n, integer mb, integer nb, complex16, dimension( lda, ) a, integer lda, complex16, dimension( ldt, ) t, integer ldt, complex16, 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 is INTEGER
          The number of rows of the matrix A.  M >= 0.

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

          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 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 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 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

Definition at line 174 of file zungtsqr.f.

Author

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