.TH "ungtsqr_row" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME ungtsqr_row \- {un,or}gtsqr_row: generate Q from latsqr .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcungtsqr_row\fP (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)" .br .RI "\fBCUNGTSQR_ROW\fP " .ti -1c .RI "subroutine \fBdorgtsqr_row\fP (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)" .br .RI "\fBDORGTSQR_ROW\fP " .ti -1c .RI "subroutine \fBsorgtsqr_row\fP (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)" .br .RI "\fBSORGTSQR_ROW\fP " .ti -1c .RI "subroutine \fBzungtsqr_row\fP (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)" .br .RI "\fBZUNGTSQR_ROW\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "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)" .PP \fBCUNGTSQR_ROW\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> 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\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf !> M is INTEGER !> The number of rows of the matrix A\&. M >= 0\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The number of columns of the matrix A\&. M >= N >= 0\&. !> .fi .PP .br \fIMB\fP .PP .nf !> 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)\&. !> .fi .PP .br \fINB\fP .PP .nf !> 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)\&. !> .fi .PP .br \fIA\fP .PP .nf !> 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\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,M)\&. !> .fi .PP .br \fIT\fP .PP .nf !> 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\&. !> .fi .PP .br \fILDT\fP .PP .nf !> LDT is INTEGER !> The leading dimension of the array T\&. !> LDT >= max(1,min(NB,N))\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> (workspace) COMPLEX array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> 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\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 .PP .nf !> !> November 2020, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> .fi .PP .RE .PP .PP Definition at line \fB187\fP of file \fBcungtsqr_row\&.f\fP\&. .SS "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)" .PP \fBDORGTSQR_ROW\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> 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\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf !> M is INTEGER !> The number of rows of the matrix A\&. M >= 0\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The number of columns of the matrix A\&. M >= N >= 0\&. !> .fi .PP .br \fIMB\fP .PP .nf !> 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)\&. !> .fi .PP .br \fINB\fP .PP .nf !> 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)\&. !> .fi .PP .br \fIA\fP .PP .nf !> 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\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,M)\&. !> .fi .PP .br \fIT\fP .PP .nf !> 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\&. !> .fi .PP .br \fILDT\fP .PP .nf !> LDT is INTEGER !> The leading dimension of the array T\&. !> LDT >= max(1,min(NB,N))\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> 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\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 .PP .nf !> !> November 2020, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> .fi .PP .RE .PP .PP Definition at line \fB187\fP of file \fBdorgtsqr_row\&.f\fP\&. .SS "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)" .PP \fBSORGTSQR_ROW\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> 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\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf !> M is INTEGER !> The number of rows of the matrix A\&. M >= 0\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The number of columns of the matrix A\&. M >= N >= 0\&. !> .fi .PP .br \fIMB\fP .PP .nf !> 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)\&. !> .fi .PP .br \fINB\fP .PP .nf !> 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)\&. !> .fi .PP .br \fIA\fP .PP .nf !> 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\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,M)\&. !> .fi .PP .br \fIT\fP .PP .nf !> 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\&. !> .fi .PP .br \fILDT\fP .PP .nf !> LDT is INTEGER !> The leading dimension of the array T\&. !> LDT >= max(1,min(NB,N))\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> (workspace) REAL array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> 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\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 .PP .nf !> !> November 2020, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> .fi .PP .RE .PP .PP Definition at line \fB187\fP of file \fBsorgtsqr_row\&.f\fP\&. .SS "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)" .PP \fBZUNGTSQR_ROW\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> 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\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIM\fP .PP .nf !> M is INTEGER !> The number of rows of the matrix A\&. M >= 0\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The number of columns of the matrix A\&. M >= N >= 0\&. !> .fi .PP .br \fIMB\fP .PP .nf !> 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)\&. !> .fi .PP .br \fINB\fP .PP .nf !> 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)\&. !> .fi .PP .br \fIA\fP .PP .nf !> 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\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,M)\&. !> .fi .PP .br \fIT\fP .PP .nf !> 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\&. !> .fi .PP .br \fILDT\fP .PP .nf !> LDT is INTEGER !> The leading dimension of the array T\&. !> LDT >= max(1,min(NB,N))\&. !> .fi .PP .br \fIWORK\fP .PP .nf !> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> 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\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 .PP .nf !> !> November 2020, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> .fi .PP .RE .PP .PP Definition at line \fB187\fP of file \fBzungtsqr_row\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.