
complib/zlatzm(3)  applie a Householder matrix generated by ZTZRQF to a matrix

ZLATZM applies a Householder matrix generated by ZTZRQF to a matrix. Let P = I  tau*u*u', u = ( 1 ), ( v ) where v is an (m1) vector if SIDE = 'L', or a (n1) vector if SIDE = 'R'. If SIDE equals 'L', let C = [ C1 ] 1 [ C2 ] m1 n Then C is overwritten by P*C. If SIDE equals 'R', let C = [ C1, C2 ] m 1 n1 Then C is overwritten by C*P. 
complib/zlauu2(3)  compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower trian

ZLAUU2 computes the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A. If UPLO = 'U' or 'u' then the upper triangle of the result is stored, overwriting the factor U in A. If UPLO = 'L' or 'l' then the lower triangle of the result is stored, overwriting the factor L in A. This is the unblocked form of the algorithm, calling Level 2 BLAS.... 

complib/zlauum(3)  compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower trian

ZLAUUM computes the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A. If UPLO = 'U' or 'u' then the upper triangle of the result is stored, overwriting the factor U in A. If UPLO = 'L' or 'l' then the lower triangle of the result is stored, overwriting the factor L in A. This is the blocked form of the algorithm, calling Level 3 BLAS.... 
complib/zpbcon(3)  estimate the reciprocal of the condition number (in the 1norm) of a complex Hermitian positive definite band

ZPBCON estimates the reciprocal of the condition number (in the 1norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPBTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). 
complib/zpbequ(3)  compute row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce

ZPBEQU computes row and column scalings intended to equilibrate a Hermitian positive definite band matrix A and reduce its condition number (with respect to the twonorm). S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings.... 
complib/zpbrfs(3)  when the coefficient matrix is Hermitian positive definite and banded, and provides error bounds and backward

ZPBRFS 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. 
complib/zpbstf(3)  compute a split Cholesky factorization of a complex Hermitian positive definite band matrix A

ZPBSTF computes a split Cholesky factorization of a complex Hermitian positive definite band matrix A. This routine is designed to be used in conjunction with ZHBGST. 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 nm. 
complib/zpbsv(3)  X = B,

ZPBSV computes the solution to a complex system of linear equations A * X = B, where A is an NbyN Hermitian positive definite band matrix and X and B are NbyNRHS 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... 
complib/zpbsvx(3)  compute the solution to a complex system of linear equations A * X = B,

ZPBSVX 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 NbyN Hermitian positive definite band matrix and X and B are NbyNRHS matrices. Error bounds on the solution and a condition estimate are also provided. 
complib/zpbtf2(3)  compute the Cholesky factorization of a complex Hermitian positive definite band matrix A

ZPBTF2 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. 
complib/zpbtrf(3)  compute the Cholesky factorization of a complex Hermitian positive definite band matrix A

ZPBTRF 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. 
complib/zpbtrs(3)  solve a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky

ZPBTRS 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 ZPBTRF. 
complib/zpocon(3)  estimate the reciprocal of the condition number (in the 1norm) of a complex Hermitian positive definite matri

ZPOCON estimates the reciprocal of the condition number (in the 1norm) of a complex Hermitian positive definite matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPOTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). 
complib/zpoequ(3)  compute row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its

ZPOEQU computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the twonorm). S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings.... 
complib/zporfs(3)  when the coefficient matrix is Hermitian positive definite,

ZPORFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite, and provides error bounds and backward error estimates for the solution. 