ung2r - {un,or}g2r: generate explicit Q from geqrf, level 2

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subroutinecung2r(integerm,integern,integerk,complex,dimension(lda,*)a,integerlda,complex,dimension(*)tau,complex,dimension(*)work,integerinfo)CUNG2RPurpose: CUNG2R 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 (N) 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. subroutinedorg2r(integerm,integern,integerk,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(*)tau,doubleprecision,dimension(*)work,integerinfo)DORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm). Purpose: DORG2R 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 (N) 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. subroutinesorg2r(integerm,integern,integerk,real,dimension(lda,*)a,integerlda,real,dimension(*)tau,real,dimension(*)work,integerinfo)SORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm). Purpose: SORG2R 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 (N) 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. subroutinezung2r(integerm,integern,integerk,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(*)tau,complex*16,dimension(*)work,integerinfo)ZUNG2RPurpose: ZUNG2R 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 (N) 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.

ung2r - {un,or}g2r: generate explicit Q from geqrf, level 2

Functions subroutine cung2r (m, n, k, a, lda, tau, work, info) CUNG2R subroutine dorg2r (m, n, k, a, lda, tau, work, info) DORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm). subroutine sorg2r (m, n, k, a, lda, tau, work, info) SORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm). subroutine zung2r (m, n, k, a, lda, tau, work, info) ZUNG2R