--- name: "ungtsqr" section: "3" platform: "linux" package: "lapack-doc" version: "3.12.1-2" release: "Arch Linux 2026-11-01" platforms: ["linux"] url: "https://new.carta.tech/ungtsqr" --- # ungtsqr(3) {un,or}gtsqr: generate Q from latsqr ## 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 !> !> ``` 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* ``` !> 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 !> !> ``` 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* ``` !> 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 !> !> ``` Definition at line **174** of file **sorgtsqr.f**. ### 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 !> !> ``` Definition at line **174** of file **zungtsqr.f**. ## Author Generated automatically by Doxygen for LAPACK from the source code.