USAGE: q, info = NumRu::Lapack.zupgtr( uplo, ap, tau, [:usage => usage, :help => help]) FORTRAN MANUAL SUBROUTINE ZUPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO ) * Purpose * ======= * * ZUPGTR generates a complex unitary matrix Q which is defined as the * product of n-1 elementary reflectors H(i) of order n, as returned by * ZHPTRD using packed storage: * * if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), * * if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). * * Arguments * ========= * * UPLO (input) CHARACTER*1 * = 'U': Upper triangular packed storage used in previous * call to ZHPTRD; * = 'L': Lower triangular packed storage used in previous * call to ZHPTRD. * * N (input) INTEGER * The order of the matrix Q. N >= 0. * * AP (input) COMPLEX*16 array, dimension (N*(N+1)/2) * The vectors which define the elementary reflectors, as * returned by ZHPTRD. * * TAU (input) COMPLEX*16 array, dimension (N-1) * TAU(i) must contain the scalar factor of the elementary * reflector H(i), as returned by ZHPTRD. * * Q (output) COMPLEX*16 array, dimension (LDQ,N) * The N-by-N unitary matrix Q. * * LDQ (input) INTEGER * The leading dimension of the array Q. LDQ >= max(1,N). * * WORK (workspace) COMPLEX*16 array, dimension (N-1) * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * * ===================================================================== *go to the page top

USAGE: info, c = NumRu::Lapack.zupmtr( side, uplo, trans, m, ap, tau, c, [:usage => usage, :help => help]) FORTRAN MANUAL SUBROUTINE ZUPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK, INFO ) * Purpose * ======= * * ZUPMTR 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 unitary matrix of order nq, with nq = m if * SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of * nq-1 elementary reflectors, as returned by ZHPTRD using packed * storage: * * if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1); * * if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1). * * Arguments * ========= * * SIDE (input) CHARACTER*1 * = 'L': apply Q or Q**H from the Left; * = 'R': apply Q or Q**H from the Right. * * UPLO (input) CHARACTER*1 * = 'U': Upper triangular packed storage used in previous * call to ZHPTRD; * = 'L': Lower triangular packed storage used in previous * call to ZHPTRD. * * TRANS (input) CHARACTER*1 * = 'N': No transpose, apply Q; * = 'C': Conjugate transpose, apply Q**H. * * M (input) INTEGER * The number of rows of the matrix C. M >= 0. * * N (input) INTEGER * The number of columns of the matrix C. N >= 0. * * AP (input) COMPLEX*16 array, dimension * (M*(M+1)/2) if SIDE = 'L' * (N*(N+1)/2) if SIDE = 'R' * The vectors which define the elementary reflectors, as * returned by ZHPTRD. AP is modified by the routine but * restored on exit. * * TAU (input) COMPLEX*16 array, dimension (M-1) if SIDE = 'L' * or (N-1) if SIDE = 'R' * TAU(i) must contain the scalar factor of the elementary * reflector H(i), as returned by ZHPTRD. * * C (input/output) 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 (input) INTEGER * The leading dimension of the array C. LDC >= max(1,M). * * WORK (workspace) COMPLEX*16 array, dimension * (N) if SIDE = 'L' * (M) if SIDE = 'R' * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * * ===================================================================== *go to the page top

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