ungqr - {un,or}gqr: generate explicit Q from geqrf

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

subroutinecungqr(integerm,integern,integerk,complex,dimension(lda,*)a,integerlda,complex,dimension(*)tau,complex,dimension(*)work,integerlwork,integerinfo)CUNGQRPurpose: CUNGQR generates an M-by-N complex matrix Q with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M Q = H(1) H(2) . . . H(k) as returned by CGEQRF. ParametersM M is INTEGER The number of rows of the matrix Q. M >= 0. N N is INTEGER The number of columns of the matrix Q. M >= N >= 0. K K is INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0. A A is COMPLEX array, dimension (LDA,N) On entry, the i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGEQRF in the first k columns of its array argument A. On exit, the M-by-N matrix Q. LDA LDA is INTEGER The first dimension of the array A. LDA >= max(1,M). TAU TAU is COMPLEX array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGEQRF. WORK WORK is 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. LWORK >= max(1,N). For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. 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 has an illegal value Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinedorgqr(integerm,integern,integerk,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(*)tau,doubleprecision,dimension(*)work,integerlwork,integerinfo)DORGQRPurpose: DORGQR generates an M-by-N real matrix Q with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M Q = H(1) H(2) . . . H(k) as returned by DGEQRF. ParametersM M is INTEGER The number of rows of the matrix Q. M >= 0. N N is INTEGER The number of columns of the matrix Q. M >= N >= 0. K K is INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0. A A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGEQRF in the first k columns of its array argument A. On exit, the M-by-N matrix Q. LDA LDA is INTEGER The first dimension of the array A. LDA >= max(1,M). TAU TAU is DOUBLE PRECISION array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGEQRF. WORK WORK is 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. LWORK >= max(1,N). For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. 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 has an illegal value Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinesorgqr(integerm,integern,integerk,real,dimension(lda,*)a,integerlda,real,dimension(*)tau,real,dimension(*)work,integerlwork,integerinfo)SORGQRPurpose: SORGQR generates an M-by-N real matrix Q with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M Q = H(1) H(2) . . . H(k) as returned by SGEQRF. ParametersM M is INTEGER The number of rows of the matrix Q. M >= 0. N N is INTEGER The number of columns of the matrix Q. M >= N >= 0. K K is INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0. A A is REAL array, dimension (LDA,N) On entry, the i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGEQRF in the first k columns of its array argument A. On exit, the M-by-N matrix Q. LDA LDA is INTEGER The first dimension of the array A. LDA >= max(1,M). TAU TAU is REAL array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGEQRF. WORK WORK is 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. LWORK >= max(1,N). For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. 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 has an illegal value Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. subroutinezungqr(integerm,integern,integerk,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(*)tau,complex*16,dimension(*)work,integerlwork,integerinfo)ZUNGQRPurpose: ZUNGQR generates an M-by-N complex matrix Q with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M Q = H(1) H(2) . . . H(k) as returned by ZGEQRF. ParametersM M is INTEGER The number of rows of the matrix Q. M >= 0. N N is INTEGER The number of columns of the matrix Q. M >= N >= 0. K K is INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0. A A is COMPLEX*16 array, dimension (LDA,N) On entry, the i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGEQRF in the first k columns of its array argument A. On exit, the M-by-N matrix Q. LDA LDA is INTEGER The first dimension of the array A. LDA >= max(1,M). TAU TAU is COMPLEX*16 array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZGEQRF. WORK WORK is 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. LWORK >= max(1,N). For optimum performance LWORK >= N*NB, where NB is the optimal blocksize. 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 has an illegal value Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.

ungqr - {un,or}gqr: generate explicit Q from geqrf

Functions subroutine cungqr (m, n, k, a, lda, tau, work, lwork, info) CUNGQR subroutine dorgqr (m, n, k, a, lda, tau, work, lwork, info) DORGQR subroutine sorgqr (m, n, k, a, lda, tau, work, lwork, info) SORGQR subroutine zungqr (m, n, k, a, lda, tau, work, lwork, info) ZUNGQR