getsqrhrt - getsqrhrt: tall-skinny QR factor, with Householder reconstruction

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subroutinecgetsqrhrt(integerm,integern,integermb1,integernb1,integernb2,complex,dimension(lda,*)a,integerlda,complex,dimension(ldt,*)t,integerldt,complex,dimension(*)work,integerlwork,integerinfo)CGETSQRHRTPurpose: CGETSQRHRT computes a NB2-sized column blocked QR-factorization of a complex M-by-N matrix A with M >= N, A = Q * R. The routine uses internally a NB1-sized column blocked and MB1-sized row blocked TSQR-factorization and perfors the reconstruction of the Householder vectors from the TSQR output. The routine also converts the R_tsqr factor from the TSQR-factorization output into the R factor that corresponds to the Householder QR-factorization, A = Q_tsqr * R_tsqr = Q * R. The output Q and R factors are stored in the same format as in CGEQRT (Q is in blocked compact WY-representation). See the documentation of CGEQRT for more details on the format. ParametersM 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. MB1 MB1 is INTEGER The row block size to be used in the blocked TSQR. MB1 > N. NB1 NB1 is INTEGER The column block size to be used in the blocked TSQR. N >= NB1 >= 1. NB2 NB2 is INTEGER The block size to be used in the blocked QR that is output. NB2 >= 1. A A is COMPLEX*16 array, dimension (LDA,N) On entry: an M-by-N matrix A. On exit: a) the elements on and above the diagonal of the array contain the N-by-N upper-triangular matrix R corresponding to the Householder QR; b) the elements below the diagonal represent Q by the columns of blocked V (compact WY-representation). LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). T T is COMPLEX array, dimension (LDT,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. LDT LDT is INTEGER The leading dimension of the array T. LDT >= NB2. 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. If MIN(M,N) = 0, LWORK >= 1, else LWORK >= MAX( 1, LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ), where NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)), NB1LOCAL = MIN(NB1,N). LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL, LW1 = NB1LOCAL * N, LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ). 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 subroutinedgetsqrhrt(integerm,integern,integermb1,integernb1,integernb2,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(ldt,*)t,integerldt,doubleprecision,dimension(*)work,integerlwork,integerinfo)DGETSQRHRTPurpose: DGETSQRHRT computes a NB2-sized column blocked QR-factorization of a real M-by-N matrix A with M >= N, A = Q * R. The routine uses internally a NB1-sized column blocked and MB1-sized row blocked TSQR-factorization and perfors the reconstruction of the Householder vectors from the TSQR output. The routine also converts the R_tsqr factor from the TSQR-factorization output into the R factor that corresponds to the Householder QR-factorization, A = Q_tsqr * R_tsqr = Q * R. The output Q and R factors are stored in the same format as in DGEQRT (Q is in blocked compact WY-representation). See the documentation of DGEQRT for more details on the format. ParametersM 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. MB1 MB1 is INTEGER The row block size to be used in the blocked TSQR. MB1 > N. NB1 NB1 is INTEGER The column block size to be used in the blocked TSQR. N >= NB1 >= 1. NB2 NB2 is INTEGER The block size to be used in the blocked QR that is output. NB2 >= 1. A A is DOUBLE PRECISION array, dimension (LDA,N) On entry: an M-by-N matrix A. On exit: a) the elements on and above the diagonal of the array contain the N-by-N upper-triangular matrix R corresponding to the Householder QR; b) the elements below the diagonal represent Q by the columns of blocked V (compact WY-representation). LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). T T is DOUBLE PRECISION array, dimension (LDT,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. LDT LDT is INTEGER The leading dimension of the array T. LDT >= NB2. 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. If MIN(M,N) = 0, LWORK >= 1, else LWORK >= MAX( 1, LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ), where NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)), NB1LOCAL = MIN(NB1,N). LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL, LW1 = NB1LOCAL * N, LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ). 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 subroutinesgetsqrhrt(integerm,integern,integermb1,integernb1,integernb2,real,dimension(lda,*)a,integerlda,real,dimension(ldt,*)t,integerldt,real,dimension(*)work,integerlwork,integerinfo)SGETSQRHRTPurpose: SGETSQRHRT computes a NB2-sized column blocked QR-factorization of a complex M-by-N matrix A with M >= N, A = Q * R. The routine uses internally a NB1-sized column blocked and MB1-sized row blocked TSQR-factorization and perfors the reconstruction of the Householder vectors from the TSQR output. The routine also converts the R_tsqr factor from the TSQR-factorization output into the R factor that corresponds to the Householder QR-factorization, A = Q_tsqr * R_tsqr = Q * R. The output Q and R factors are stored in the same format as in SGEQRT (Q is in blocked compact WY-representation). See the documentation of SGEQRT for more details on the format. ParametersM 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. MB1 MB1 is INTEGER The row block size to be used in the blocked TSQR. MB1 > N. NB1 NB1 is INTEGER The column block size to be used in the blocked TSQR. N >= NB1 >= 1. NB2 NB2 is INTEGER The block size to be used in the blocked QR that is output. NB2 >= 1. A A is REAL array, dimension (LDA,N) On entry: an M-by-N matrix A. On exit: a) the elements on and above the diagonal of the array contain the N-by-N upper-triangular matrix R corresponding to the Householder QR; b) the elements below the diagonal represent Q by the columns of blocked V (compact WY-representation). LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). T T is REAL array, dimension (LDT,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. LDT LDT is INTEGER The leading dimension of the array T. LDT >= NB2. 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. If MIN(M,N) = 0, LWORK >= 1, else LWORK >= MAX( 1, LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ), where NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)), NB1LOCAL = MIN(NB1,N). LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL, LW1 = NB1LOCAL * N, LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ). 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 subroutinezgetsqrhrt(integerm,integern,integermb1,integernb1,integernb2,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(ldt,*)t,integerldt,complex*16,dimension(*)work,integerlwork,integerinfo)ZGETSQRHRTPurpose: ZGETSQRHRT computes a NB2-sized column blocked QR-factorization of a complex M-by-N matrix A with M >= N, A = Q * R. The routine uses internally a NB1-sized column blocked and MB1-sized row blocked TSQR-factorization and perfors the reconstruction of the Householder vectors from the TSQR output. The routine also converts the R_tsqr factor from the TSQR-factorization output into the R factor that corresponds to the Householder QR-factorization, A = Q_tsqr * R_tsqr = Q * R. The output Q and R factors are stored in the same format as in ZGEQRT (Q is in blocked compact WY-representation). See the documentation of ZGEQRT for more details on the format. ParametersM 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. MB1 MB1 is INTEGER The row block size to be used in the blocked TSQR. MB1 > N. NB1 NB1 is INTEGER The column block size to be used in the blocked TSQR. N >= NB1 >= 1. NB2 NB2 is INTEGER The block size to be used in the blocked QR that is output. NB2 >= 1. A A is COMPLEX*16 array, dimension (LDA,N) On entry: an M-by-N matrix A. On exit: a) the elements on and above the diagonal of the array contain the N-by-N upper-triangular matrix R corresponding to the Householder QR; b) the elements below the diagonal represent Q by the columns of blocked V (compact WY-representation). LDA LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). T T is COMPLEX*16 array, dimension (LDT,N)) The upper triangular block reflectors stored in compact form as a sequence of upper triangular blocks. LDT LDT is INTEGER The leading dimension of the array T. LDT >= NB2. 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. If MIN(M,N) = 0, LWORK >= 1, else LWORK >= MAX( 1, LWT + LW1, MAX( LWT+N*N+LW2, LWT+N*N+N ) ), where NUM_ALL_ROW_BLOCKS = CEIL((M-N)/(MB1-N)), NB1LOCAL = MIN(NB1,N). LWT = NUM_ALL_ROW_BLOCKS * N * NB1LOCAL, LW1 = NB1LOCAL * N, LW2 = NB1LOCAL * MAX( NB1LOCAL, ( N - NB1LOCAL ) ). 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

getsqrhrt - getsqrhrt: tall-skinny QR factor, with Householder reconstruction

Functions subroutine cgetsqrhrt (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info) CGETSQRHRT subroutine dgetsqrhrt (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info) DGETSQRHRT subroutine sgetsqrhrt (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info) SGETSQRHRT subroutine zgetsqrhrt (m, n, mb1, nb1, nb2, a, lda, t, ldt, work, lwork, info) ZGETSQRHRT