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Text File | 1994-01-13 | 16.8 KB | 405 lines

FUNCTION INDEX ============== In the descriptions below, matrices are represented by capital letters, vectors by lower case letters and scalars by alpha. Function Description band2mat() Convert band matrix to dense matrix bd_free() Deallocate (destroy) band matrix bd_get() Allocate and initialise band matrix bd_transp() Transpose band matrix bd_resize() Resize band matrix bdLDLfactor() Band LDL^T factorisation bdLDLsolve() Solve Ax=b using band LDL^T factors bdLUfactor() Band LU factorisation bdLUsolve() Solve Ax=b using band LU factors bisvd() SVD of bi-diagonal matrix BKPfactor() Bunch-Kaufman-Parlett factorisation BKPsolve() Bunch-Kaufman-Parlett solver catch() Catch a raised error (macro) catchall() Catch any raised error (macro) catch_FPE() Catch floating point error (sets flag) CHfactor() Dense Cholesky factorisation CHsolve() Cholesky solver d_save() Save real in MATLAB format Dsolve() Solve Dx=y , D diagonal ERRABORT() Abort on error (sets flag, macro) ERREXIT() Exit on error (sets flag, macro) error() Raise an error (macro, see ev_err()) err_list_attach() Attach new list of errors err_list_free() Discard list of errors err_is_list_attached() Checks for an error list ev_err() Raise an error (function) fft() Computes Fast Fourier Transform finput() Input a simple data item from a stream fprompter() Print prompt to stderr get_col() Extract a column from a matrix get_row() Extract a row from a matrix givens() Compute Givens parameters hhtrcols() Compute AP^T where P is a Householder matrix hhtrrows() Compute PA where P is a Householder matrix hhtrvec() Compute Px where P is a Householder matrix hhvec() Compute parameters for a Householder matrix ifft() Computes inverse FFT in_prod() Inner product of vectors input() Input a simple data item from stdin (macro) iter_arnoldi() Arnoldi iterative method iter_arnoldi_iref() Arnoldi iterative method with refinement iter_ATx() Set A^T in ITER structure iter_Ax() Set A in ITER structure iter_Bx() Set preconditioner in ITER structure iter_cg() Conjugate gradients iterative method iter_cgne() Conjugate gradients for normal equations iter_cgs() CGS iterative method iter_copy() Copy ITER data structures iter_copy2() Shallow copy of ITER data structures iter_dump() Dump ITER data structure to a stream iter_free() Free (deallocate) ITER structure iter_get() Allocate ITER structure iter_gmres() GMRES iterative method iter_lanczos() Lanczos iterative method iter_lanczos2() Lanczos method with Cullum and Willoughby extensions iter_lsqr() LSQR iterative method iter_mgcr() MGCR iterative method iter_resize() Resize vectors in an ITER data structure iter_spcg() Sparse matrix CG method iter_spcgne() Sparse matrix CG method for normal equations iter_spcgs() Sparse matrix CGS method iter_spgmres() Sparse matrix GMRES method iter_splsqr() Sparse matrix LSQR method iter_spmgcr() Sparse matrix MGCR method iv_add() Add integer vectors iv_copy() Copy integer vector iv_dump() Dump integer vector to a stream iv_finput() Input integer vector from a stream iv_foutput() Output integer vector to a stream IV_FREE() Free (deallocate) an integer vector (macro) iv_free() Free (deallocate) integer vector (function) iv_free_vars() Free a list of integer vectors iv_get() Allocate and initialise an integer vector iv_get_vars() Allocate list of integer vectors iv_input() Input integer vector from stdin (macro) iv_output() Output integer vector to stdout (macro) iv_resize() Resize an integer vector iv_resize_vars() Resize a list of integer vectors iv_sub() Subtract integer vectors LDLfactor() LDL^T factorisation LDLsolve() LDL^T solver LDLupdate() Update LDL^T factorisation Lsolve() Solve Lx=y , L lower triangular LTsolve() Solve L^Tx=y , L lower triangular LUcondest() Estimate a condition number using LU factors LUfactor() Compute LU factors with implicit scaled partial pivoting LUsolve() Solve Ax=b using LU factors LUTsolve() Solve A^Tx=b usng LU factors m_add() Add matrices makeQ() Form Q matrix for QR factorisation makeR() Form R matrix for QR factorisation mat2band() Extract band matrix from dense matrix MCHfactor() Modified Cholesky factorisation (actually factors A+D, D diagonal, instead of A) m_copy() Copy dense matrix m_dump() Dump matrix data structure to a stream mem_attach_list() Adds a new family of types mem_bytes() Notify change in memory usage (macro) mem_bytes_list() Notify change in memory usage mem_free_list() Frees a family of types mem_info_bytes() Number of bytes used by a type mem_info_numvar() Number of structures of a type mem_info_file() Print memory info to a stream mem_info_is_on() Is memory data being accumulated? mem_info_on() Turns memory info system on/off mem_is_list_attached() Is list of types attached? mem_numvar() Notify change in number of structures allocated (macro) mem_numvar_list() Notify change in number of structures allocated mem_stat_dump() Prints information on registered workspace mem_stat_free() Frees (deallocates) static workspace mem_stat_mark() Sets mark for workspace MEM_STAT_REG() Register static workspace (macro) mem_stat_show_mark() Current workspace group m_exp() Computes matrix exponential m_finput() Input matrix from a stream m_foutput() Output matrix to a stream M_FREE() Free (deallocate) a matrix (macro) m_free() Free (deallocate) matrix (function) m_free_vars() Free a list of matrices m_get() Allocate and initialise a matrix m_get_vars() Allocate list of matrices m_ident() Sets matrix to identity matrix m_input() Input matrix from stdin (macro) m_inverse() Invert matrix m_load() Load matrix in MATLAB format m_mlt() Multiplies matrices mmtr_mlt() Computes AB^T m_norm1() Computes ||A||_1 of a matrix m_norm_frob() Computes the Frobenius norm of a matrix m_norm_inf() Computes ||A||_inf of a matrix m_ones() Set matrix to all 1's m_output() Output matrix to stdout (macro) m_poly() Computes a matrix polynomial m_pow() Computes integer power of a matrix mrand() Generates pseudo-random real number m_rand() Randomise entries of a matrix mrandlist() Generates array of pseudo-random numbers m_resize() Resize matrix m_resize_vars() Resize a list of matrices m_save() Save matrix in MATLAB format m_sub() Subtract matrices m_transp() Transpose matrix mtrm_mlt() Computes A^TB mv_mlt() Computes Ax mv_mltadd() Computes y <- Ax+y m_zero() Zero a matrix ON_ERROR() Error handler (macro) prompter() Print prompt message to stdout px_cols() Permute the columns of a matrix px_copy() Copy permutation px_dump() Dump permutation data structure to a stream px_finput() Input permutation from a stream px_foutput() Output permutation to a stream PX_FREE() Free (deallocate) a permutation (macro) px_free() Free (deallocate) permutation (function) px_free_vars() Free a list of permutations px_get() Allocate and initialise a permutation px_get_vars() Allocate a list of permutations px_ident() Sets permutation to identity px_input() Input permutation from stdin (macro) px_inv() Invert permutation pxinv_vec() Computes P^Tx where P is a permutation matrix pxinv_zvec() Computes P^Tx where P is a permutation matrix (complex) px_mlt() Multiply permutations px_output() Output permutation to stdout (macro) px_resize() Resize a permutation px_resize_vars() Resize a list of permutations px_rows() Permute the rows of a matrix px_sign() Returns the sign of the permutation px_transp() Transpose a pair of entries px_vec() Computes Px where P is a permutation matrix px_zvec() Computes Px where P is a permutation matrix (complex) QRCPfactor() QR factorisation with column pivoting QRfactor() QR factorisation QRsolve() Solve Ax=b using QR factorisation QRTsolve() Solve A^Tx=b using QR factorisation QRupdate() Update explicit QR factors rot_cols() Apply Givens rotation to the columns of a matrix rot_rows() Apply Givens rotation to the rows of a matrix rot_vec() Apply Givens rotation to a vector rot_zvec() Apply complex Givens rotation to a vector schur() Compute real Schur form schur_evals() Compute eigenvalues from the real Schur form schur_vecs() Compute eigenvectors from the real Schur form set_col() Set the column of a matrix to a given vector set_err_flag() Control behaviour of ev_err() set_row() Set the row of a matrix to a given vector sm_mlt() Scalar-matrix multiplication smrand() Set seed for mrand() spBKPfactor() Sparse symmetric indefinite factorsiation spBKPsolve() Sparse symmetric indefinite solver spCHfactor() Sparse Cholesky factorisation spCHsolve() Sparse Cholesky solver spCHsymb() Symbolic sparse Cholesky factorisation (no floating point operations) sp_col_access() Sets up column access paths for a sparse matrix sp_compact() Eliminates zero entries in a sparse matrix sp_copy() Copies a sparse matrix sp_copy2() Copies a sparse matrix into another sp_diag_access() Sets up diagonal access paths for a sparse matrix sp_dump() Dump sparse matrix data structure to a stream sp_finput() Input sparse matrix from a stream sp_foutput() Output a sparse matrix to a stream sp_free() Free (deallocate) a sparse matrix sp_get() Allocate and initialise a sparse matrix sp_get_val() Get the (i,j) entry of a sparse matrix spICHfactor() Sparse incomplete Cholesky factorisation sp_input() Input a sparse matrix form stdin spLUfactor() Sparse LU factorisation using partial pivoting spLUsolve() Solves Ax=b using sparse LU factors spLUTsolve() Solves A^Tx=b using sparse LU factors sp_mv_mlt() Computes Ax for sparse A sp_output() Outputs a sparse matrix to a stream (macro) sp_resize() Resize a sparse matrix sprow_add() Adds a pair of sparse rows sprow_foutput() Output sparse row to a stream sprow_get() Allocate and initialise a sparse row sprow_get_idx() Get location of an entry in a sparse row sprow_merge() Merge two sparse rows sprow_mltadd() Sparse row vector multiply-and-add sprow_set_val() Set an entry in a sparse row sprow_smlt() Multiplies a sparse row by a scalar sprow_sub() Subtracts a sparse row from another sprow_xpd() Expand a sparse row sp_set_val() Set the (i,j) entry of a sparse matrix sp_vm_mlt() Compute x^TA for sparse A sp_zero() Zero (but do not remove) all entries of a sparse matrix svd() Compute the SVD of a matrix sv_mlt() Scalar-vector multiply symmeig() Compute eigenvalues/vectors of a symmetric matrix tracecatch() Catch and re-raise errors (macro) trieig() Compute eigenvalues/vectors of a symmetric tridiagonal matrix Usolve() Solve Ux=b where U is upper triangular UTsolve() Solve U^Tx=b where U is upper triangular v_add() Add vectors v_conv() Convolution product of vectors v_copy() Copy vector v_dump() Dump vector data structure to a stream v_finput() Input vector from a stream v_foutput() Output vector to a stream V_FREE() Free (deallocate) a vector (macro) v_free() Free (deallocate) vector (function) v_free_vars() Free a list of vectors v_get() Allocate and initialise a vector v_get_vars() Allocate list of vectors v_input() Input vector from stdin (macro) v_lincomb() Compute sum of a_i x_i for an array of vectors v_linlist() Compute sum of a_i x_i for a list of vectors v_map() Apply function componentwise to a vector v_max() Computes max vector entry and index v_min() Computes min vector entry and index v_mltadd() Computes y <- alpha*x+y for vectors x , y vm_mlt() Computes x^TA vm_mltadd() Computes y^T <- y^T+x^TA v_norm1() Computes ||x||_1 for a vector v_norm2() Computes ||x||_2 (the Euclidean norm) of a vector v_norm_inf() Computes ||x||_inf for a vector v_ones() Set vector to all 1's v_output() Output vector to stdout (macro) v_pconv() Periodic convolution of two vectors v_rand() Randomise entries of a vector v_resize() Resize a vector v_resize_vars() Resize a list of vectors v_save() Save a vector in MATLAB format v_slash() Computes componentwise ratio of vectors v_sort() Sorts vector components v_star() Componentwise vector product v_sub() Subtract two vectors v_sum() Sum of components of a vector v_zero() Zero a vector zabs() Complex absolute value (modulus) zadd() Add complex numbers zconj() Conjugate complex number zdiv() Divide complex numbers zexp() Complex exponential z_finput() Read complex number from file or stream z_foutput() Prints complex number to file or stream zgivens() Compute complex Givens' rotation zhhtrcols() Apply Householder transformation: PA (complex) zhhtrrows() Apply Householder transformation: AP (complex) zhhtrvec() Apply Householder transformation: Px (complex) zhhvec() Compute Householder transformation zin_prod() Complex inner product z_input() Read complex number from stdin zinv() Computes 1/z (complex) zLAsolve() Solve L^*x=b , L complex lower triangular zlog() Complex logarithm zLsolve() Solve Lx=b , L complex lower triangular zLUAsolve() Solve A^*x=b using complex LU factorisation (A^* - adjoint of A, A is complex) zLUcondest() Complex LU condition estimate zLUfactor() Complex LU factorisation zLUsolve() Solve Ax=b using complex LU factorisation zm_add() Add complex matrices zm_adjoint() Computes adjoint of complex matrix zmake() Construct complex number from real and imaginary parts zmakeQ() Construct Q matrix for complex QR zmakeR() Construct R matrix for complex QR zmam_mlt() Computes A^*B (complex) zm_dump() Dump complex matrix to stream zm_finput() Input complex matrix from stream ZM_FREE() Free (deallocate) complex matrix (macro) zm_free() Free (deallocate) complex matrix (function) zm_free_vars() Free a list of complex matrices zm_get() Allocate complex matrix zm_get_vars() Allocate a list of complex matrices zm_input() Input complex matrix from stdin zm_inverse() Compute inverse of complex matrix zm_load() Load complex matrix in MATLAB format zmlt() Multiply complex numbers zmma_mlt() Computes AB^* (complex) zm_mlt() Multiply complex matrices zm_norm1() Complex matrix 1-norm zm_norm_frob() Complex matrix Frobenius norm zm_norm_inf() Complex matrix infinity-norm zm_rand() Randomise complex matrix zm_resize() Resize complex matrix zm_resize_vars() Resize a list of complex matrices zm_save() Save complex matrix in MATLAB format zm_sub() Subtract complex matrices zmv_mlt() Complex matrix-vector multiply zmv_mltadd() Complex matrix-vector multiply and add zm_zero() Zero complex matrix zneg() Computes -z (complex) z_output() Print complex number to stdout zQRCPfactor() Complex QR factorisation with column pivoting zQRCPsolve() Solve Ax = b using complex QR factorisation zQRfactor() Complex QR factorisation zQRAsolve() Solve A^*x = b using complex QR factorisation zQRsolve() Solve Ax = b using complex QR factorisation zrot_cols() Complex Givens' rotation of columns zrot_rows() Complex Givens' rotation of rows z_save() Save complex number in MATLAB format zschur() Complex Schur factorisation zset_col() Set column of complex matrix zset_row() Set row of complex matrix zsm_mlt() Complex scalar-matrix product zsqrt() Square root z (complex) zsub() Subtract complex numbers zUAsolve() Solve U^*x=b , U complex upper triangular zUsolve() Solve Ux=b , U complex upper triangular zv_add() Add complex vectors zv_copy() Copy complex vector zv_dump() Dump complex vector to a stream zv_finput() Input complex vector from a stream ZV_FREE() Free (deallocate) complex vector (macro) zv_free() Free (deallocate) complex vector (function) zv_free_vars() Free a list of complex vectors zv_get() Allocate complex vector zv_get_vars() Allocate a list of complex vectors zv_input() Input complex vector from a stdin zv_lincomb() Compute sum of a_i x_i for an array of vectors zv_linlist() Compute sum of a_i x_i for a list of vectors zv_map() Apply function componentwise to a complex vector zv_mlt() Complex scalar-vector product zv_mltadd() Complex scalar-vector multiply and add zvm_mlt() Computes A^*x (complex) zvm_mltadd() Computes A^*x+y (complex) zv_norm1() Complex vector 1-norm vnorm1() zv_norm2() Complex vector 2-norm (Euclidean norm) zv_norm_inf() Complex vector infinity- (or supremum) norm zv_rand() Randomise complex vector zv_resize() Resize complex vector zv_resize_vars() Resize a list of complex vectors zv_save() Save complex vector in MATLAB format zv_slash() Componentwise ratio of complex vectors zv_star() Componentwise product of complex vectors zv_sub() Subtract complex vectors zv_sum() Sum of components of a complex vector zv_zero() Zero complex vector Low level routines Function Description __add__() Add arrays __ip__() Inner product of arrays MEM_COPY() Copy memory (macro) MEM_ZERO() Zero memory (macro) __mltadd__() Forms x+ alpha*y for arrays __smlt__() Scalar-vector multiplication for arrays __sub__() Subtract an array from another __zadd__() Add complex arrays __zconj__() Conjugate complex array __zero__() Zero an array __zip__() Complex inner product of arrays __zmlt__() Complex array scalar product __zmltadd__() Complex array saxpy __zsub__() Subtract complex arrays __zzero__() Zero a complex array