zhbtrd zhetrd zhptrd zpteqr zstedc zstein zstemr zsteqr zungtr zunmtr zupgtr zupmtr

zunmtr() void zunmtr ( char  side, char  uplo, char  trans, int  m, int  n, int  lda, doublecomplex  a[], doublecomplex  tau[], int  ldc, doublecomplex  c[], doublecomplex  work[], int  lwork, int *  info  ) Multiplies by a transform matrix from a complex Hermitian matrix to tridiagonal form Purpose This routine overwrites the general complex m x 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 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 zhetrd: If uplo = 'U', Q = H(nq-1) . . . H(2) H(1). If uplo = 'L', Q = H(1) H(2) . . . H(nq-1). Parameters [in] side = 'L': Apply Q or Q^H from the Left. = 'R': Apply Q or Q^H from the Right. [in] uplo = 'U': Upper triangle of a[][] contains elementary reflectors from zhetrd. = 'L': Lower triangle of a[][] contains elementary reflectors from zhetrd. [in] trans = 'N': No transpose, apply Q. = 'T': Transpose, apply Q^H. [in] m Number of rows of the matrix C. (m >= 0) (If m = 0, returns without computation) [in] n Number of columns of the matrix C. (n >= 0) (If n = 0, returns without computation) [in] lda Leading dimension of the two dimensional array a[][]. (lda >= max(1, m) if side = 'L', lda >= max(1, n) if side = 'R') [in] a[][] Array a[la][lda] (la >= m if side = 'L', la >= n if side = 'R') The vectors which define the elementary reflectors, as returned by zhetrd. [in] tau[] Array tau[ltau] (ltau >= m - 1 if side = 'L', ltau >= n - 1 if side = 'R') tau[i] must contain the scalar factor of the elementary reflector H(i), as returned by zhetrd. [in] ldc Leading dimension of the two dimensional array c[][]. (ldc >= max(1, m)) [in,out] c[][] Array c[lc][ldc] (lc >= n) [in] The m x n matrix C. [out] C is overwritten by Q*C or Q^H*C or C*Q^H or C*Q. [out] work[] Array work[lwork] Work array. On exit, if info = 0, work[0] returns the optimal lwork. [in] lwork The size of work[]. (lwork >= max(1, n) if side = 'L', lwork >= max(1, m) if side = 'R') For optimum performance lwork >= n*nb if side = 'L', and lwork >= m*nb if side = 'R', 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, and returns the value in work[0]. [out] info = 0: Successful exit. = -1: The argument side had an illegal value. (side != 'L' nor 'R') = -2: The argument uplo had an illegal value. (uplo != 'U' nor 'L') = -3: The argument trans had an illegal value. (trans != 'N' nor 'T') = -4: The argument m had an illegal value. (m < 0) = -5: The argument n had an illegal value. (n < 0) = -8: The argument lda had an illegal value. (lda < max(1, m) if side = 'L', lda < max(1, n) if side = 'R') = -9: The argument ldc had an illegal value. (ldc < max(1, m)) = -12: The argument lwork had an illegal value. (lwork too small) Reference LAPACK