ungtsqr_row(3) Library Functions Manual ungtsqr_row(3) NAME ungtsqr_row - {un,or}gtsqr_row: generate Q from latsqr SYNOPSIS Functions subroutine cungtsqr_row (m, n, mb, nb, a, lda, t, ldt, work, lwork, info) CUNGTSQR_ROW subroutine dorgtsqr_row (m, n, mb, nb, a, lda, t, ldt, work, lwork, info) DORGTSQR_ROW subroutine sorgtsqr_row (m, n, mb, nb, a, lda, t, ldt, work, lwork, info) SORGTSQR_ROW subroutine zungtsqr_row (m, n, mb, nb, a, lda, t, ldt, work, lwork, info) ZUNGTSQR_ROW Detailed Description Function Documentation subroutine cungtsqr_row (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_ROW Purpose: !> !> CUNGTSQR_ROW generates an M-by-N complex matrix Q_out with !> orthonormal columns from the output of CLATSQR. These N orthonormal !> columns are the first N columns of a product of complex unitary !> matrices Q(k)_in of order M, which are returned by CLATSQR in !> a special format. !> !> Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ). !> !> The input matrices Q(k)_in are stored in row and column blocks in A. !> See the documentation of CLATSQR for more details on the format of !> Q(k)_in, where each Q(k)_in is represented by block Householder !> transformations. This routine calls an auxiliary routine CLARFB_GETT, !> where the computation is performed on each individual block. The !> algorithm first sweeps NB-sized column blocks from the right to left !> starting in the bottom row block and continues to the top row block !> (hence _ROW in the routine name). This sweep is in reverse order of !> the order in which CLATSQR generates the output blocks. !> 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 used as !> input. 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). See CLATSQR for more details. !> !> 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 the 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. See CLATSQR for more details on the format !> of T. !> LDT !> LDT is INTEGER !> The leading dimension of the array T. !> LDT >= max(1,min(NB,N)). !> WORK !> (workspace) 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 >= NBLOCAL * MAX(NBLOCAL,(N-NBLOCAL)), !> where NBLOCAL=MIN(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 2020, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> Definition at line 187 of file cungtsqr_row.f. subroutine dorgtsqr_row (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_ROW Purpose: !> !> DORGTSQR_ROW generates an M-by-N real matrix Q_out with !> orthonormal columns from the output of DLATSQR. These N orthonormal !> columns are the first N columns of a product of complex unitary !> matrices Q(k)_in of order M, which are returned by DLATSQR in !> a special format. !> !> Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ). !> !> The input matrices Q(k)_in are stored in row and column blocks in A. !> See the documentation of DLATSQR for more details on the format of !> Q(k)_in, where each Q(k)_in is represented by block Householder !> transformations. This routine calls an auxiliary routine DLARFB_GETT, !> where the computation is performed on each individual block. The !> algorithm first sweeps NB-sized column blocks from the right to left !> starting in the bottom row block and continues to the top row block !> (hence _ROW in the routine name). This sweep is in reverse order of !> the order in which DLATSQR generates the output blocks. !> 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 used as !> input. 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). See DLATSQR for more details. !> !> 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 the 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. See DLATSQR for more details on the format !> of T. !> LDT !> LDT is INTEGER !> The leading dimension of the array T. !> LDT >= max(1,min(NB,N)). !> WORK !> (workspace) 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 >= NBLOCAL * MAX(NBLOCAL,(N-NBLOCAL)), !> where NBLOCAL=MIN(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 2020, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> Definition at line 187 of file dorgtsqr_row.f. subroutine sorgtsqr_row (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_ROW Purpose: !> !> SORGTSQR_ROW generates an M-by-N real matrix Q_out with !> orthonormal columns from the output of SLATSQR. These N orthonormal !> columns are the first N columns of a product of complex unitary !> matrices Q(k)_in of order M, which are returned by SLATSQR in !> a special format. !> !> Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ). !> !> The input matrices Q(k)_in are stored in row and column blocks in A. !> See the documentation of SLATSQR for more details on the format of !> Q(k)_in, where each Q(k)_in is represented by block Householder !> transformations. This routine calls an auxiliary routine SLARFB_GETT, !> where the computation is performed on each individual block. The !> algorithm first sweeps NB-sized column blocks from the right to left !> starting in the bottom row block and continues to the top row block !> (hence _ROW in the routine name). This sweep is in reverse order of !> the order in which SLATSQR generates the output blocks. !> 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 used as !> input. 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). See SLATSQR for more details. !> !> 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 the 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. See SLATSQR for more details on the format !> of T. !> LDT !> LDT is INTEGER !> The leading dimension of the array T. !> LDT >= max(1,min(NB,N)). !> WORK !> (workspace) 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 >= NBLOCAL * MAX(NBLOCAL,(N-NBLOCAL)), !> where NBLOCAL=MIN(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 2020, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> Definition at line 187 of file sorgtsqr_row.f. subroutine zungtsqr_row (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_ROW Purpose: !> !> ZUNGTSQR_ROW generates an M-by-N complex matrix Q_out with !> orthonormal columns from the output of ZLATSQR. These N orthonormal !> columns are the first N columns of a product of complex unitary !> matrices Q(k)_in of order M, which are returned by ZLATSQR in !> a special format. !> !> Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ). !> !> The input matrices Q(k)_in are stored in row and column blocks in A. !> See the documentation of ZLATSQR for more details on the format of !> Q(k)_in, where each Q(k)_in is represented by block Householder !> transformations. This routine calls an auxiliary routine ZLARFB_GETT, !> where the computation is performed on each individual block. The !> algorithm first sweeps NB-sized column blocks from the right to left !> starting in the bottom row block and continues to the top row block !> (hence _ROW in the routine name). This sweep is in reverse order of !> the order in which ZLATSQR generates the output blocks. !> 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 used as !> input. 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). See ZLATSQR for more details. !> !> 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 the 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. See ZLATSQR for more details on the format !> of T. !> LDT !> LDT is INTEGER !> The leading dimension of the array T. !> LDT >= max(1,min(NB,N)). !> WORK !> (workspace) 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 >= NBLOCAL * MAX(NBLOCAL,(N-NBLOCAL)), !> where NBLOCAL=MIN(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 2020, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> Definition at line 187 of file zungtsqr_row.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 ungtsqr_row(3)