### Computational Routines for Linear Equations

Routine NameOperation
sgetrf, dgetrf
cgetrf, zgetrf
Computes an LU factorization of a general matrix, using partial pivoting with row interchanges
sgetrs, dgetrs
cgetrs, zgetrs
Solves a general system of linear equations AX=B, A**T X=B or A**H X=B, using the LU factorization computed by SGETRF/CGETRF
sgecon, dgecon
cgecon, zgecon
Estimates the reciprocal of the condition number of a general matrix, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGETRF/CGETRF
sgerfs, dgerfs
cgerfs, zgerfs
Improves the computed solution to a general system of linear equations AX=B, A**T X=B or A**H X=B, and provides forward and backward error bounds for the solution
sgetri, dgetri
cgetri, zgetri
Computes the inverse of a general matrix, using the LU factorization computed by SGETRF/CGETRF
sgeequ, dgeequ
cgeequ, zgeequ
Computes row and column scalings to equilibrate a general rectangular matrix and reduce its condition number
sgbtrf, dgbtrf
cgbtrf, zgbtrf
Computes an LU factorization of a general band matrix, using partial pivoting with row interchanges
sgbtrs, dgbtrs
cgbtrs, zgbtrs
Solves a general banded system of linear equations AX=B, A**T X=B or A**H X=B, using the LU factorization computed by SGBTRF/CGBTRF
sgbcon, dgbcon
cgbcon, zgbcon
Estimates the reciprocal of the condition number of a general band matrix, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGBTRF/CGBTRF
sgbrfs, dgbrfs
cgbrfs, zgbrfs
Improves the computed solution to a general banded system of linear equations AX=B, A**T X=B or A**H X=B, and provides forward and backward error bounds for the solution
sgbequ, dgbequ
cgbequ, zgbequ
Computes row and column scalings to equilibrate a general band matrix and reduce its condition number
sgttrf, dgttrf
cgttrf, zgttrf
Computes an LU factorization of a general tridiagonal matrix, using partial pivoting with row interchanges
sgttrs, dgttrs
cgttrs, zgttrs
Solves a general tridiagonal system of linear equations AX=B, A**T X=B or A**H X=B, using the LU factorization computed by SGTTRF/CGTTRF
sgtcon, dgtcon
cgtcon, zgtcon
Estimates the reciprocal of the condition number of a general tridiagonal matrix, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGTTRF/CGTTRF
sgtrfs, dgtrfs
cgtrfs, zgtrfs
Improves the computed solution to a general tridiagonal system of linear equations AX=B, A**T X=B or A**H X=B, and providesforward and backward error bounds for the solution
spotrf, dpotrf
cpotrf, zpotrf
Computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix
spotrs, dpotrs
cpotrs, zpotrs
Solves a symmetric/Hermitian positive definite system of linear equations AX=B, using the Cholesky factorization computed by SPOTRF/CPOTRF
spocon, dpocon
cpocon, zpocon
Estimates the reciprocal of the condition number of a symmetric/Hermitian positive definite matrix, using the Cholesky factorization computed by SPOTRF/CPOTRF
sporfs, dporfs
cporfs, zporfs
Improves the computed solution to a symmetric/Hermitian positive definite system of linear equations AX=B, and provides forward and backward error bounds for the solution
spotri, dpotri
cpotri, zpotri
Computes the inverse of a symmetric/Hermitian positive definite matrix, using the Cholesky factorization computed by SPOTRF/CPOTRF
spoequ, dpoequ
cpoequ, zpoequ
Computes row and column scalings to equilibrate a symmetric/Hermitian positive definite matrix and reduce its condition number
spptrf, dpptrf
cpptrf, zpptrf
Computes the Cholesky factorization of a symmetric/Hermitian positive definite matrix in packed storage
spptrs, dpptrs
cpptrs, zpptrs
Solves a symmetric/Hermitian positive definite system of linear equations AX=B, where A is held in packed storage, using the Cholesky factorization computed by SPPTRF/CPPTRF
sppcon, dppcon
cppcon, zppcon
Estimates the reciprocal of the condition number of a symmetric/Hermitian positive definite matrix in packed storage, using the Cholesky factorization computed by SPPTRF/CPPTRF
spprfs, dpprfs
cpprfs, zpprfs
Improves the computed solution to a symmetric/Hermitian positive definite system of linear equations AX=B, where A is held in packed storage, and provides forward and backward error bounds for the solution
spptri, dpptri
cpptri, zpptri
Computes the inverse of a symmetric/Hermitian positive definite matrix in packed storage, using the Cholesky factorization computed by SPPTRF/CPPTRF
sppequ, dppequ
cppequ, zppequ
Computes row and column scalings to equilibrate a symmetric/hermitian positive definite matrix in packed storage and reduce its condition number
spbtrf, dpbtrf
cpbtrf, zpbtrf
Computes the Cholesky factorization of a symmetric/Hermitian positive definite band matrix
spbtrs, dpbtrs
cpbtrs, zpbtrs
Solves a symmetric/Hermitian positive definite banded system of linear equations AX=B, using the Cholesky factorization computed by SPBTRF/CPBTRF
spbcon, dpbcon
cpbcon, zpbcon
Estimates the reciprocal of the condition number of a symmetric/Hermitian positive definite band matrix, using the Cholesky factorization computed by SPBTRF/CPBTRF
spbrfs, dpbrfs
cpbrfs, zpbrfs
Improves the computed solution to a symmetric/Hermitian positive definite banded system of linear equations AX=B, and provides forward and backward error bounds for the solution
spbequ, dpbequ
cpbequ, zpbequ
Computes row and column scalings to equilibrate a symmetric/Hermitian positive definite band matrix and reduce its condition number
spttrf, dpttrf
cpttrf, zpttrf
Computes the LDL**H factorization of a symmetric/Hermitian positive definite tridiagonal matrix
spttrs, dpttrs
cpttrs, zpttrs
Solves a symmetric/Hermitian positive definite tridiagonal system of linear equations, using the LDL**H factorization computed by SPTTRF/CPTTRF
sptcon, dptcon
cptcon, zptcon
Computes the reciprocal of the condition number of a symmetric/Hermitian positive definite tridiagonal matrix, using the LDL**H factorization computed by SPTTRF/CPTTRF
sptrfs, dptrfs
cptrfs, zptrfs
Improves the computed solution to a symmetric/Hermitian positive definite tridiagonal system of linear equations AX=B, and provides forward and backward error bounds for the solution
ssytrf, dsytrf
csytrf, zsytrf
Computes the factorization of a real/complex symmetric indefinite matrix, using the diagonal pivoting method
ssytrs, dsytrs
csytrs, zsytrs
Solves a real/complex symmetric indefinite system of linear equations AX=B, using the factorization computed by SSPTRF/CSPTRF
ssycon, dsycon
csycon, zsycon
Estimates the reciprocal of the condition number of a real/complex symmetric indefinite matrix, using the factorization computed by SSYTRF/CSYTRF
ssyrfs, dsyrfs
csyrfs, zsyrfs
Improves the computed solution to a real/complex/ symmetric indefinite system of linear equations AX=B, and provides forward and backward error bounds for the solution
ssytri, dsytri
csytri, zsytri
Computes the inverse of a real/complex symmetric indefinite matrix, using the factorization computed by SSYTRF/CSYTRF
chetrf, zhetrf Computes the factorization of a complex Hermitian indefinite matrix, using the diagonal pivoting method
chetrs, zhetrs Solves a complex Hermitian indefinite system of linear equations AX=B, using the factorization computed by CHPTRF
checon, zhecon Estimates the reciprocal of the condition number of a complex Hermitian indefinite matrix, using the factorization computed by CHETRF
cherfs, zherfs Improves the computed solution to a complex Hermitian indefinite system of linear equations AX=B, and provides forward and backward error bounds for the solution
chetri, zhetri Computes the inverse of a complex Hermitian indefinite matrix, using the factorization computed by CHETRF
ssptrf, dsptrf
csptrf, zsptrf
Computes the factorization of a real/complex symmetric indefinite matrix in packed storage, using the diagonal pivoting method
ssptrs, dsptrs
csptrs, zsptrs
Solves a real/complex symmetric indefinite system of linear equations AX=B, where A is held in packed storage, using the factorization computed by SSPTRF/CSPTRF
sspcon, dspcon
cspcon, zspcon
Estimates the reciprocal of the condition number of a real/complex symmetric indefinite matrix in packed storage, using the factorization computed by SSPTRF/CSPTRF
ssprfs, dsprfs
csprfs, zsprfs
Improves the computed solution to a real/complex symmetric indefinite system of linear equations AX=B, where A is held in packed storage, and provides forward and backward error bounds for the solution
ssptri, dsptri
csptri, zsptri
Computes the inverse of a real/complex symmetric indefinite matrix in packed storage, using the factorization computed by SSPTRF/CSPTRF
chptrf, zhptrf Computes the factorization of a complex Hermitian indefinite matrix in packed storage, using the diagonal pivoting method
chptrs, zhptrs Solves a complex Hermitian indefinite system of linear equations AX=B, where A is held in packed storage, using the factorization computed by CHPTRF
chpcon, zhpcon Estimates the reciprocal of the condition number of a complex Hermitian indefinite matrix in packed storage, using the factorization computed by CHPTRF
chprfs, zhprfs Improves the computed solution to a complex Hermitian indefinite system of linear equations AX=B, where A is held in packed storage, and provides forward and backward error bounds for the solution
chptri, zhptri Computes the inverse of a complex Hermitian indefinite matrix in packed storage, using the factorization computed by CHPTRF
strtrs, dtrtrs
ctrtrs, ztrtrs
Solves a triangular system of linear equations AX=B, A**T X=B or A**H X=B
strcon, dtrcon
ctrcon, ztrcon
Estimates the reciprocal of the condition number of a triangular matrix, in either the 1-norm or the infinity-norm
strrfs, dtrrfs
ctrrfs, ztrrfs
Provides forward and backward error bounds for the solution of a triangular system of linear equations A X=B, A**T X=B or A**H X=B
strtri, dtrtri
ctrtri, ztrtri
Computes the inverse of a triangular matrix
stptrs, dtptrs
ctptrs, ztptrs
Solves a triangular system of linear equations AX=B, A**T X=B or A**H X=B, where A is held in packed storage
stpcon, dtpcon
ctpcon, ztpcon
Estimates the reciprocal of the condition number of a triangular matrix in packed storage, in either the 1-norm or the infinity-norm
stprfs, dtprfs
ctprfs, ztprfs
Provides forward and backward error bounds for the solution of a triangular system of linear equations AX=B, A**T X=B or A**H X=B, where A is held in packed storage
stptri, dtptri
ctptri, ztptri
Computes the inverse of a triangular matrix in packed storage
stbtrs, dtbtrs
ctbtrs, ztbtrs
Solves a triangular banded system of linear equations AX=B, A**T X=B or A**H X=B
stbcon, dtbcon
ctbcon, ztbcon
Estimates the reciprocal of the condition number of a triangular band matrix, in either the 1-norm or the infinity-norm
stbrfs, dtbrfs
ctbrfs, ztbrfs
Provides forward and backward error bounds for the solution of a triangular banded system of linear equations AX=B, A**T X=B or A**H X=B

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