zgejsv zgesdd zgesvd zgesvdq zgesvdx zggsvd3

zgesvd() void zgesvd ( char  jobu, char  jobvt, int  m, int  n, int  lda, doublecomplex  a[], double  s[], int  ldu, doublecomplex  u[], int  ldvt, doublecomplex  vt[], doublecomplex  work[], int  lwork, double  rwork[], int *  info  ) (Simple driver) Singular value decomposition (SVD) of a complex matrix Purpose This routine computes the singular value decomposition (SVD) of a complex m x n matrix A, optionally computing the left and/or right singular vectors. The SVD is written A = U * SIGMA * V^H where SIGMA is an m x n matrix which is zero except for its min(m, n) diagonalelements, U is an m x m unitary matrix, and V is an n x n unitary matrix. The diagonal elements of SIGMA are the singular values of A. They are real and non-negative, and are returned in descending order. The first min(m, n) columns of U and V are the left and right singular vectors of A. Note that the routine returns V^H, not V. Parameters [in] jobu Specifies options for computing all or part of the matrix U: = 'A': All m columns of U are returned in array u[][]. = 'S': The first min(m, n) columns of U (the left singular vectors) are returned in the array u[][]. = 'O': The first min(m, n) columns of U (the left singular vectors) are overwritten on the array a[][]. = 'N': No columns of U (no left singular vectors) are computed. [in] jobvt Specifies options for computing all or part of the matrix V^H: = 'A': All n rows of V^H are returned in the array vt[][]. = 'S': The first min(m, n) rows of V^H (the right singular vectors) are returned in the array vt[][]. = 'O': The first min(m, n) rows of V^H (the right singular vectors) are overwritten on the array a[][]. = 'N': No rows of V^H (no right singular vectors) are computed. [in] m Number of rows of the input matrix A. (m >= 0) (If m = 0, returns without computation) [in] n Number of columns of the input matrix A. (n >= 0) (If n = 0, returns without computation) [in] lda Leading dimension of the two dimensional array a[][]. (lda >= max(1, m)) [in,out] a[][] Array a[la][lda] (la >= n) [in] m x n matrix A. [out] jobu = 'O': a[][] is overwritten with the first min(m, n) columns of U (the left singular vectors, stored columnwise).   jobvt = 'O': a[][] is overwritten with the first min(m, n) rows of V^H (the right singular vectors, stored rowwise).   jobu != 'O' and jobvt != 'O': The contents of a[][] are destroyed. [out] s[] Array s[ls] (ls >= min(m, n)) The singular values of A, sorted so that s[i] >= s[i+1]. [in] ldu Leading dimension of the two dimensional array u[][]. (ldu >= 1 if jobu = 'O' or 'N', ldu >= m if jobu = 'A' or 'S') [out] u[][] Array u[lu][ldu] (lu >= m (if jobu = 'A'), lu >= min(m, n) (if jobu = 'S')) jobu = 'A': u[][] contains the m x m unitary matrix U. jobu = 'S': u[][] contains the first min(m, n) columns of U (the left singular vectors, stored columnwise). jobu = 'N' or 'O': u[][] is not referenced. [in] ldvt Leading dimension of the two dimensional array vt[][]. (ldvt >= 1 if jobvt = 'O' or 'N', ldvt >= n if jobvt = 'A', ldvt >= min(m, n) if jobvt = 'S') [out] vt[][] Array vt[lvt][ldvt] (lvt >= n) jobvt = 'A': vt[][] contains the n x n unitary matrix V^H. jobvt = 'S': vt[][] contains the first min(m, n) rows of V^H (the right singular vectors, stored rowwise). jobvt = 'N' or 'O': vt[][] is not referenced. [out] work[] Array work[lwork] Work array On exit, if info = 0, work[0] returns the optimal lwork. [in] lwork The dimension of the array work[] (lwork >= max(1, 2*min(m, n) + max(m, n))) For good performance, lwork must generally be larger. 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] rwork[] Array rwork[lrwork] (lrwork >= 5*min(m, n)) Work array. If info > 0, rwork[0 to min(m, n)-2] contains the unconverged super-diagonal elements of an upper bidiagonal matrix B whose diagonal is in s[] (not necessarily sorted). B satisfies A = U * B * V^H, so it has the same singular values as A, and singular vectors related by U and V^H. [out] info = 0: Successful exit = -1: The argument jobu had an illegal value (jobu != 'A', 'S', 'O' nor 'N') = -2: The argument jobvt had an illegal value (jobvt != 'A', 'S', 'O' nor 'N') = -3: The argument m had an illegal value (m < 0) = -4: The argument n had an illegal value (n < 0) = -5: The argument lda had an illegal value (lda < max(1, m)) = -8: The argument ldu had an illegal value (ldu too small) = -10: The argument ldvt had an illegal value (ldvt too small) = -13: The argument lwork had an illegal value (lwork too small) > 0: If zbdsqr did not converge, info specifies how many super-diagonals of an intermediate bidiagonal form B did not converge to zero. See the description of rwork[] above for details. Reference LAPACK