gemqr - gemqr: multiply by Q from geqr

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Thu Aug 7 2025 17:26:25 gemqr(3)

subroutinecgemqr(characterside,charactertrans,integerm,integern,integerk,complex,dimension(lda,*)a,integerlda,complex,dimension(*)t,integertsize,complex,dimension(ldc,*)c,integerldc,complex,dimension(*)work,integerlwork,integerinfo)CGEMQRPurpose: CGEMQR overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**H * C C * Q**H where Q is a complex unitary matrix defined as the product of blocked elementary reflectors computed by tall skinny QR factorization (CGEQR) 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 A. 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. A A is COMPLEX array, dimension (LDA,K) Part of the data structure to represent Q as returned by CGEQR. LDA LDA is INTEGER The leading dimension of the array A. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N). T T is COMPLEX array, dimension (MAX(5,TSIZE)). Part of the data structure to represent Q as returned by CGEQR. TSIZE TSIZE is INTEGER The dimension of the array T. TSIZE >= 5. C C is COMPLEX array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK (workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the minimal LWORK. LWORK LWORK is INTEGER The dimension of the array WORK. LWORK >= 1. If LWORK = -1, then a workspace query is assumed. The routine only calculates the size of the WORK array, returns this value as WORK(1), and no error message related to WORK 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. FurtherDetails These details are particular for this LAPACK implementation. Users should not take them for granted. These details may change in the future, and are not likely true for another LAPACK implementation. These details are relevant if one wants to try to understand the code. They are not part of the interface. In this version, T(2): row block size (MB) T(3): column block size (NB) T(6:TSIZE): data structure needed for Q, computed by CLATSQR or CGEQRT Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, CGEQR will use either CLATSQR (if the matrix is tall-and-skinny) or CGEQRT to compute the QR factorization. This version of CGEMQR will use either CLAMTSQR or CGEMQRT to multiply matrix Q by another matrix. Further Details in CLAMTSQR or CGEMQRT. subroutinedgemqr(characterside,charactertrans,integerm,integern,integerk,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(*)t,integertsize,doubleprecision,dimension(ldc,*)c,integerldc,doubleprecision,dimension(*)work,integerlwork,integerinfo)DGEMQRPurpose: DGEMQR 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 blocked elementary reflectors computed by tall skinny QR factorization (DGEQR) 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 A. 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. A A is DOUBLE PRECISION array, dimension (LDA,K) Part of the data structure to represent Q as returned by DGEQR. LDA LDA is INTEGER The leading dimension of the array A. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N). T T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE)). Part of the data structure to represent Q as returned by DGEQR. TSIZE TSIZE is INTEGER The dimension of the array T. TSIZE >= 5. 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 or Q**T*C or C*Q**T or C*Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the minimal LWORK. LWORK LWORK is INTEGER The dimension of the array WORK. LWORK >= 1. If LWORK = -1, then a workspace query is assumed. The routine only calculates the size of the WORK array, returns this value as WORK(1), and no error message related to WORK 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. FurtherDetails These details are particular for this LAPACK implementation. Users should not take them for granted. These details may change in the future, and are not likely true for another LAPACK implementation. These details are relevant if one wants to try to understand the code. They are not part of the interface. In this version, T(2): row block size (MB) T(3): column block size (NB) T(6:TSIZE): data structure needed for Q, computed by DLATSQR or DGEQRT Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, DGEQR will use either DLATSQR (if the matrix is tall-and-skinny) or DGEQRT to compute the QR factorization. This version of DGEMQR will use either DLAMTSQR or DGEMQRT to multiply matrix Q by another matrix. Further Details in DLATMSQR or DGEMQRT. subroutinesgemqr(characterside,charactertrans,integerm,integern,integerk,real,dimension(lda,*)a,integerlda,real,dimension(*)t,integertsize,real,dimension(ldc,*)c,integerldc,real,dimension(*)work,integerlwork,integerinfo)SGEMQRPurpose: SGEMQR 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 blocked elementary reflectors computed by tall skinny QR factorization (SGEQR) 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 A. 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. A A is REAL array, dimension (LDA,K) Part of the data structure to represent Q as returned by SGEQR. LDA LDA is INTEGER The leading dimension of the array A. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N). T T is REAL array, dimension (MAX(5,TSIZE)). Part of the data structure to represent Q as returned by SGEQR. TSIZE TSIZE is INTEGER The dimension of the array T. TSIZE >= 5. C C is REAL array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK (workspace) REAL array, dimension (MAX(1,LWORK)) LWORK LWORK is INTEGER The dimension of the array WORK. If LWORK = -1, then a workspace query is assumed. The routine only calculates the size of the WORK array, returns this value as WORK(1), and no error message related to WORK 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. FurtherDetails These details are particular for this LAPACK implementation. Users should not take them for granted. These details may change in the future, and are not likely true for another LAPACK implementation. These details are relevant if one wants to try to understand the code. They are not part of the interface. In this version, T(2): row block size (MB) T(3): column block size (NB) T(6:TSIZE): data structure needed for Q, computed by SLATSQR or SGEQRT Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, SGEQR will use either SLATSQR (if the matrix is tall-and-skinny) or SGEQRT to compute the QR factorization. This version of SGEMQR will use either SLAMTSQR or SGEMQRT to multiply matrix Q by another matrix. Further Details in SLAMTSQR or SGEMQRT. subroutinezgemqr(characterside,charactertrans,integerm,integern,integerk,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(*)t,integertsize,complex*16,dimension(ldc,*)c,integerldc,complex*16,dimension(*)work,integerlwork,integerinfo)ZGEMQRPurpose: ZGEMQR overwrites the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C C * Q TRANS = 'T': Q**H * C C * Q**H where Q is a complex unitary matrix defined as the product of blocked elementary reflectors computed by tall skinny QR factorization (ZGEQR) 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 A. 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. A A is COMPLEX*16 array, dimension (LDA,K) Part of the data structure to represent Q as returned by ZGEQR. LDA LDA is INTEGER The leading dimension of the array A. If SIDE = 'L', LDA >= max(1,M); if SIDE = 'R', LDA >= max(1,N). T T is COMPLEX*16 array, dimension (MAX(5,TSIZE)). Part of the data structure to represent Q as returned by ZGEQR. TSIZE TSIZE is INTEGER The dimension of the array T. TSIZE >= 5. 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 or Q**H*C or C*Q**H or C*Q. LDC LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the minimal LWORK. LWORK LWORK is INTEGER The dimension of the array WORK. LWORK >= 1. If LWORK = -1, then a workspace query is assumed. The routine only calculates the size of the WORK array, returns this value as WORK(1), and no error message related to WORK 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. FurtherDetails These details are particular for this LAPACK implementation. Users should not take them for granted. These details may change in the future, and are not likely true for another LAPACK implementation. These details are relevant if one wants to try to understand the code. They are not part of the interface. In this version, T(2): row block size (MB) T(3): column block size (NB) T(6:TSIZE): data structure needed for Q, computed by ZLATSQR or ZGEQRT Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, ZGEQR will use either ZLATSQR (if the matrix is tall-and-skinny) or ZGEQRT to compute the QR factorization. This version of ZGEMQR will use either ZLAMTSQR or ZGEMQRT to multiply matrix Q by another matrix. Further Details in ZLAMTSQR or ZGEMQRT.

gemqr - gemqr: multiply by Q from geqr

Functions subroutine cgemqr (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info) CGEMQR subroutine dgemqr (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info) DGEMQR subroutine sgemqr (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info) SGEMQR subroutine zgemqr (side, trans, m, n, k, a, lda, t, tsize, c, ldc, work, lwork, info) ZGEMQR