.TH "ptsv" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME ptsv \- ptsv: factor and solve .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBcptsv\fP (n, nrhs, d, e, b, ldb, info)" .br .RI "\fB CPTSV computes the solution to system of linear equations A * X = B for PT matrices\fP " .ti -1c .RI "subroutine \fBdptsv\fP (n, nrhs, d, e, b, ldb, info)" .br .RI "\fB DPTSV computes the solution to system of linear equations A * X = B for PT matrices\fP " .ti -1c .RI "subroutine \fBsptsv\fP (n, nrhs, d, e, b, ldb, info)" .br .RI "\fB SPTSV computes the solution to system of linear equations A * X = B for PT matrices\fP " .ti -1c .RI "subroutine \fBzptsv\fP (n, nrhs, d, e, b, ldb, info)" .br .RI "\fB ZPTSV computes the solution to system of linear equations A * X = B for PT matrices\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine cptsv (integer n, integer nrhs, real, dimension( * ) d, complex, dimension( * ) e, complex, dimension( ldb, * ) b, integer ldb, integer info)" .PP \fB CPTSV computes the solution to system of linear equations A * X = B for PT matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CPTSV computes the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices\&. A is factored as A = L*D*L**H, and the factored form of A is then used to solve the system of equations\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fINRHS\fP .PP .nf NRHS is INTEGER The number of right hand sides, i\&.e\&., the number of columns of the matrix B\&. NRHS >= 0\&. .fi .PP .br \fID\fP .PP .nf D is REAL array, dimension (N) On entry, the n diagonal elements of the tridiagonal matrix A\&. On exit, the n diagonal elements of the diagonal matrix D from the factorization A = L*D*L**H\&. .fi .PP .br \fIE\fP .PP .nf E is COMPLEX array, dimension (N-1) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A\&. On exit, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**H factorization of A\&. E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U**H*D*U factorization of A\&. .fi .PP .br \fIB\fP .PP .nf B is COMPLEX array, dimension (LDB,NRHS) On entry, the N-by-NRHS right hand side matrix B\&. On exit, if INFO = 0, the N-by-NRHS solution matrix X\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER The leading dimension of the array B\&. LDB >= max(1,N)\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading principal minor of order i is not positive, and the solution has not been computed\&. The factorization has not been completed unless i = N\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SS "subroutine dptsv (integer n, integer nrhs, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldb, * ) b, integer ldb, integer info)" .PP \fB DPTSV computes the solution to system of linear equations A * X = B for PT matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DPTSV computes the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices\&. A is factored as A = L*D*L**T, and the factored form of A is then used to solve the system of equations\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fINRHS\fP .PP .nf NRHS is INTEGER The number of right hand sides, i\&.e\&., the number of columns of the matrix B\&. NRHS >= 0\&. .fi .PP .br \fID\fP .PP .nf D is DOUBLE PRECISION array, dimension (N) On entry, the n diagonal elements of the tridiagonal matrix A\&. On exit, the n diagonal elements of the diagonal matrix D from the factorization A = L*D*L**T\&. .fi .PP .br \fIE\fP .PP .nf E is DOUBLE PRECISION array, dimension (N-1) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A\&. On exit, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**T factorization of A\&. (E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U**T*D*U factorization of A\&.) .fi .PP .br \fIB\fP .PP .nf B is DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the N-by-NRHS right hand side matrix B\&. On exit, if INFO = 0, the N-by-NRHS solution matrix X\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER The leading dimension of the array B\&. LDB >= max(1,N)\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading principal minor of order i is not positive, and the solution has not been computed\&. The factorization has not been completed unless i = N\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SS "subroutine sptsv (integer n, integer nrhs, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldb, * ) b, integer ldb, integer info)" .PP \fB SPTSV computes the solution to system of linear equations A * X = B for PT matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SPTSV computes the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices\&. A is factored as A = L*D*L**T, and the factored form of A is then used to solve the system of equations\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fINRHS\fP .PP .nf NRHS is INTEGER The number of right hand sides, i\&.e\&., the number of columns of the matrix B\&. NRHS >= 0\&. .fi .PP .br \fID\fP .PP .nf D is REAL array, dimension (N) On entry, the n diagonal elements of the tridiagonal matrix A\&. On exit, the n diagonal elements of the diagonal matrix D from the factorization A = L*D*L**T\&. .fi .PP .br \fIE\fP .PP .nf E is REAL array, dimension (N-1) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A\&. On exit, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**T factorization of A\&. (E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U**T*D*U factorization of A\&.) .fi .PP .br \fIB\fP .PP .nf B is REAL array, dimension (LDB,NRHS) On entry, the N-by-NRHS right hand side matrix B\&. On exit, if INFO = 0, the N-by-NRHS solution matrix X\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER The leading dimension of the array B\&. LDB >= max(1,N)\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading principal minor of order i is not positive, and the solution has not been computed\&. The factorization has not been completed unless i = N\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SS "subroutine zptsv (integer n, integer nrhs, double precision, dimension( * ) d, complex*16, dimension( * ) e, complex*16, dimension( ldb, * ) b, integer ldb, integer info)" .PP \fB ZPTSV computes the solution to system of linear equations A * X = B for PT matrices\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZPTSV computes the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices\&. A is factored as A = L*D*L**H, and the factored form of A is then used to solve the system of equations\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fINRHS\fP .PP .nf NRHS is INTEGER The number of right hand sides, i\&.e\&., the number of columns of the matrix B\&. NRHS >= 0\&. .fi .PP .br \fID\fP .PP .nf D is DOUBLE PRECISION array, dimension (N) On entry, the n diagonal elements of the tridiagonal matrix A\&. On exit, the n diagonal elements of the diagonal matrix D from the factorization A = L*D*L**H\&. .fi .PP .br \fIE\fP .PP .nf E is COMPLEX*16 array, dimension (N-1) On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A\&. On exit, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**H factorization of A\&. E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U**H*D*U factorization of A\&. .fi .PP .br \fIB\fP .PP .nf B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the N-by-NRHS right hand side matrix B\&. On exit, if INFO = 0, the N-by-NRHS solution matrix X\&. .fi .PP .br \fILDB\fP .PP .nf LDB is INTEGER The leading dimension of the array B\&. LDB >= max(1,N)\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading principal minor of order i is not positive, and the solution has not been computed\&. The factorization has not been completed unless i = N\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.