# ungtsqr - Man Page

{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**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.