gemqrt - gemqrt: multiply by Q from geqrt

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Sun Jul 20 2025 01:40:05 gemqrt(3)

subroutinecgemqrt(characterside,charactertrans,integerm,integern,integerk,integernb,complex,dimension(ldv,*)v,integerldv,complex,dimension(ldt,*)t,integerldt,complex,dimension(ldc,*)c,integerldc,complex,dimension(*)work,integerinfo)CGEMQRTPurpose: CGEMQRT overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q C C Q TRANS = 'C': Q**H C C Q**H where Q is a complex orthogonal matrix defined as the product of K elementary reflectors: Q = H(1) H(2) . . . H(K) = I - V T V**H generated using the compact WY representation as returned by CGEQRT. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'. ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right. TRANS TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'C': Conjugate transpose, apply Q**H. M M is INTEGER The number of rows of the matrix C. M >= 0. N N is INTEGER The number of columns of the matrix C. N >= 0. K K is INTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0. NB NB is INTEGER The block size used for the storage of T. K >= NB >= 1. This must be the same value of NB used to generate T in CGEQRT. V V is COMPLEX array, dimension (LDV,K) The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGEQRT in the first K columns of its array argument A. LDV LDV is INTEGER The leading dimension of the array V. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N). T T is COMPLEX array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by CGEQRT, stored as a NB-by-N matrix. LDT LDT is INTEGER The leading dimension of the array T. LDT >= NB. C C is COMPLEX array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q C, Q**H C, C Q**H or C Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK WORK is COMPLEX array. The dimension of WORK is N*NB if SIDE = 'L', or M*NB if SIDE = 'R'. 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. subroutinedgemqrt(characterside,charactertrans,integerm,integern,integerk,integernb,doubleprecision,dimension(ldv,*)v,integerldv,doubleprecision,dimension(ldt,*)t,integerldt,doubleprecision,dimension(ldc,*)c,integerldc,doubleprecision,dimension(*)work,integerinfo)DGEMQRTPurpose: DGEMQRT overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q C C Q TRANS = 'T': Q**T C C Q**T where Q is a real orthogonal matrix defined as the product of K elementary reflectors: Q = H(1) H(2) . . . H(K) = I - V T V**T generated using the compact WY representation as returned by DGEQRT. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'. ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right. TRANS TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'C': Transpose, apply Q**T. M M is INTEGER The number of rows of the matrix C. M >= 0. N N is INTEGER The number of columns of the matrix C. N >= 0. K K is INTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0. NB NB is INTEGER The block size used for the storage of T. K >= NB >= 1. This must be the same value of NB used to generate T in DGEQRT. V V is DOUBLE PRECISION array, dimension (LDV,K) The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGEQRT in the first K columns of its array argument A. LDV LDV is INTEGER The leading dimension of the array V. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N). T T is DOUBLE PRECISION array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by DGEQRT, stored as a NB-by-N matrix. LDT LDT is INTEGER The leading dimension of the array T. LDT >= NB. C C is DOUBLE PRECISION array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q C, Q**T C, C Q**T or C Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK WORK is DOUBLE PRECISION array. The dimension of WORK is N*NB if SIDE = 'L', or M*NB if SIDE = 'R'. 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. subroutinesgemqrt(characterside,charactertrans,integerm,integern,integerk,integernb,real,dimension(ldv,*)v,integerldv,real,dimension(ldt,*)t,integerldt,real,dimension(ldc,*)c,integerldc,real,dimension(*)work,integerinfo)SGEMQRTPurpose: SGEMQRT overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q C C Q TRANS = 'T': Q**T C C Q**T where Q is a real orthogonal matrix defined as the product of K elementary reflectors: Q = H(1) H(2) . . . H(K) = I - V T V**T generated using the compact WY representation as returned by SGEQRT. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'. ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**T from the Left; = 'R': apply Q or Q**T from the Right. TRANS TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'T': Transpose, apply Q**T. M M is INTEGER The number of rows of the matrix C. M >= 0. N N is INTEGER The number of columns of the matrix C. N >= 0. K K is INTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0. NB NB is INTEGER The block size used for the storage of T. K >= NB >= 1. This must be the same value of NB used to generate T in SGEQRT. V V is REAL array, dimension (LDV,K) The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGEQRT in the first K columns of its array argument A. LDV LDV is INTEGER The leading dimension of the array V. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N). T T is REAL array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by SGEQRT, stored as a NB-by-N matrix. LDT LDT is INTEGER The leading dimension of the array T. LDT >= NB. C C is REAL array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q C, Q**T C, C Q**T or C Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK WORK is REAL array. The dimension of WORK is N*NB if SIDE = 'L', or M*NB if SIDE = 'R'. 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. subroutinezgemqrt(characterside,charactertrans,integerm,integern,integerk,integernb,complex*16,dimension(ldv,*)v,integerldv,complex*16,dimension(ldt,*)t,integerldt,complex*16,dimension(ldc,*)c,integerldc,complex*16,dimension(*)work,integerinfo)ZGEMQRTPurpose: ZGEMQRT overwrites the general complex M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q C C Q TRANS = 'C': Q**H C C Q**H where Q is a complex orthogonal matrix defined as the product of K elementary reflectors: Q = H(1) H(2) . . . H(K) = I - V T V**H generated using the compact WY representation as returned by ZGEQRT. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'. ParametersSIDE SIDE is CHARACTER*1 = 'L': apply Q or Q**H from the Left; = 'R': apply Q or Q**H from the Right. TRANS TRANS is CHARACTER*1 = 'N': No transpose, apply Q; = 'C': Conjugate transpose, apply Q**H. M M is INTEGER The number of rows of the matrix C. M >= 0. N N is INTEGER The number of columns of the matrix C. N >= 0. K K is INTEGER The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >= 0. NB NB is INTEGER The block size used for the storage of T. K >= NB >= 1. This must be the same value of NB used to generate T in ZGEQRT. V V is COMPLEX*16 array, dimension (LDV,K) The i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGEQRT in the first K columns of its array argument A. LDV LDV is INTEGER The leading dimension of the array V. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N). T T is COMPLEX*16 array, dimension (LDT,K) The upper triangular factors of the block reflectors as returned by ZGEQRT, stored as a NB-by-N matrix. LDT LDT is INTEGER The leading dimension of the array T. LDT >= NB. C C is COMPLEX*16 array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q C, Q**H C, C Q**H or C Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK WORK is COMPLEX*16 array. The dimension of WORK is N*NB if SIDE = 'L', or M*NB if SIDE = 'R'. 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.

gemqrt - gemqrt: multiply by Q from geqrt

Functions subroutine cgemqrt (side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info) CGEMQRT subroutine dgemqrt (side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info) DGEMQRT subroutine sgemqrt (side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info) SGEMQRT subroutine zgemqrt (side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info) ZGEMQRT