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complib/CPBFA(3) -- CPBFA factors a complex Hermitian positive definite matrix stored in band form. CPBFA is usually called by CPB
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On Entry ABD COMPLEX(LDA, N) the matrix to be factored. The columns of the upper triangle are stored in the columns of ABD and the diagonals of the upper triangle are stored in the rows of ABD . See the comments below for details. LDA INTEGER the leading dimension of the array ABD . LDA must be .GE. M + 1 . N INTEGER the order of the matrix A . M INTEGER the number of diagonals above the main diagonal. 0 .LE. M .LT. N . On Return ABD an upper triangular matrix R , stored in band form, so that A ... |
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complib/cpbrfs(3) -- when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward
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CPBRFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward error estimates for the solution. |
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complib/CPBSL(3) -- CPBSL solves the complex Hermitian positive definite band system A*X = B using the factors computed by CPBCO o
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On Entry ABD COMPLEX(LDA, N) the output from CPBCO or CPBFA. LDA INTEGER the leading dimension of the array ABD . N INTEGER the order of the matrix A . M INTEGER the number of diagonals above the main diagonal. B COMPLEX(N) the right hand side vector. On Return B the solution vector X . Error Condition A division by zero will occur if the input factor contains a zero on the diagonal. Technically this indicates singularity but it is usually caused by improper subroutine arguments. It will not occ... |
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complib/cpbstf(3) -- compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A
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CPBSTF computes a split Cholesky factorization of a complex Hermitian positive definite band matrix A. This routine is designed to be used in conjunction with CHBGST. The factorization has the form A = S**H*S where S is a band matrix of the same bandwidth as A and the following structure: S = ( U ) ( M L ) where U is upper triangular of order m = (n+kd)/2, and L is lower triangular of order n-m. |
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complib/cpbsv(3) -- X = B,
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CPBSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite band matrix and X and B are N-by-NRHS matrices. The Cholesky decomposition is used to factor A as A = U**H * U, if UPLO = 'U', or A = L * L**H, if UPLO = 'L', where U is an upper triangular band matrix, and L is a lower triangular band matrix, with the same number of superdiagonals or subdiagonals as A. The factored form of A is then used to solve the system of equa... |
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complib/cpbsvx(3) -- compute the solution to a complex system of linear equations A * X = B,
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CPBSVX uses the Cholesky factorization A = U**H*U or A = L*L**H to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite band matrix and X and B are N-by-NRHS matrices. Error bounds on the solution and a condition estimate are also provided. |
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complib/cpbtf2(3) -- compute the Cholesky factorization of a complex Hermitian positive definite band matrix A
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CPBTF2 computes the Cholesky factorization of a complex Hermitian positive definite band matrix A. The factorization has the form A = U' * U , if UPLO = 'U', or A = L * L', if UPLO = 'L', where U is an upper triangular matrix, U' is the conjugate transpose of U, and L is lower triangular. This is the unblocked version of the algorithm, calling Level 2 BLAS. |
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complib/cpbtrf(3) -- compute the Cholesky factorization of a complex Hermitian positive definite band matrix A
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CPBTRF computes the Cholesky factorization of a complex Hermitian positive definite band matrix A. The factorization has the form A = U**H * U, if UPLO = 'U', or A = L * L**H, if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular. |
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complib/cpbtrs(3) -- solve a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky
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CPBTRS solves a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRF. |
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c++/cplxerr(3) -- error-handling function for the C++ Complex Math Library
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In the following description of the complex error handling routine, - i is of type int and - x is of type c_exception. i = complex_error(x) Invoked by functions in the C++ Complex Mathematics Library when errors are detected. Users may define their own procedures for handling errors, by defining a function named complex_error in their programs. com... |
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c++/cplxexp(3) -- exponential, logarithm, power, square root functions for the C++ complex library
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The following math functions are overloaded by the complex library, where: - x, y, and z are of type complex. z = exp(x) Returns ex. z = log(x) Returns the natural logarithm of x. z = pow(x, y) Returns xy. z = sqrt(x) Returns the square root of x, contained in the first or fourth quadrants of the complex plane.... |
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c++/cplxops(3) -- operators for the C++ complex math library
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The basic arithmetic operators, comparison operators, and assignment operators are overloaded for complex numbers. The operators have their conventional precedences. In the following descriptions for complex operators, - x, y, and z are of type complex. Arithmetic operators: z = x + y Returns a complex which is the arithmetic sum of complex numbers x and y. z = -x Returns a complex which is the arithm... |
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c++/cplxtrig(3) -- trigonometric and hyperbolic functions for the C++ complex library
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The following trigonometric functions are defined for complex, where: - x and y are of type complex. y = sin(x) Returns the sine of x. y = cos(x) Returns the cosine of x. y = sinh(x) Returns the hyperbolic sine of x. y = cosh(x) Returns the hyperbolic cosine of x. |
