Man page - hpsv(3)

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Manual

hpsv

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chpsv (character uplo, integer n, integer nrhs, complex,dimension( * ) ap, integer, dimension( * ) ipiv, complex, dimension(ldb, * ) b, integer ldb, integer info)
subroutine cspsv (character uplo, integer n, integer nrhs, complex,dimension( * ) ap, integer, dimension( * ) ipiv, complex, dimension(ldb, * ) b, integer ldb, integer info)
subroutine dspsv (character uplo, integer n, integer nrhs, doubleprecision, dimension( * ) ap, integer, dimension( * ) ipiv, doubleprecision, dimension( ldb, * ) b, integer ldb, integer info)
subroutine sspsv (character uplo, integer n, integer nrhs, real, dimension(* ) ap, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b,integer ldb, integer info)
subroutine zhpsv (character uplo, integer n, integer nrhs, complex*16,dimension( * ) ap, integer, dimension( * ) ipiv, complex*16, dimension(ldb, * ) b, integer ldb, integer info)
subroutine zspsv (character uplo, integer n, integer nrhs, complex*16,dimension( * ) ap, integer, dimension( * ) ipiv, complex*16, dimension(ldb, * ) b, integer ldb, integer info)
Author

NAME

hpsv - {hp,sp}sv: factor and solve

SYNOPSIS

Functions

subroutine chpsv (uplo, n, nrhs, ap, ipiv, b, ldb, info)
CHPSV computes the solution to system of linear equations A * X = B for OTHER matrices
subroutine cspsv (uplo, n, nrhs, ap, ipiv, b, ldb, info)
CSPSV computes the solution to system of linear equations A * X = B for OTHER matrices
subroutine dspsv (uplo, n, nrhs, ap, ipiv, b, ldb, info)
DSPSV computes the solution to system of linear equations A * X = B for OTHER matrices
subroutine sspsv (uplo, n, nrhs, ap, ipiv, b, ldb, info)
SSPSV computes the solution to system of linear equations A * X = B for OTHER matrices
subroutine zhpsv (uplo, n, nrhs, ap, ipiv, b, ldb, info)
ZHPSV computes the solution to system of linear equations A * X = B for OTHER matrices
subroutine zspsv (uplo, n, nrhs, ap, ipiv, b, ldb, info)
ZSPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Detailed Description

Function Documentation

subroutine chpsv (character uplo, integer n, integer nrhs, complex,dimension( * ) ap, integer, dimension( * ) ipiv, complex, dimension(ldb, * ) b, integer ldb, integer info)

CHPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Purpose:

CHPSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian matrix stored in packed format and X
and B are N-by-NRHS matrices.

The diagonal pivoting method is used to factor A as
A = U * D * U**H, if UPLO = ā€™Uā€™, or
A = L * D * L**H, if UPLO = ā€™Lā€™,
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, D is Hermitian and block diagonal with 1-by-1
and 2-by-2 diagonal blocks. The factored form of A is then used to
solve the system of equations A * X = B.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.

AP

AP is COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.

On exit, the block diagonal matrix D and the multipliers used
to obtain the factor U or L from the factorization
A = U*D*U**H or A = L*D*L**H as computed by CHPTRF, stored as
a packed triangular matrix in the same storage format as A.

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D, as
determined by CHPTRF. If IPIV(k) > 0, then rows and columns
k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
diagonal block. If UPLO = ā€™Uā€™ and IPIV(k) = IPIV(k-1) < 0,
then rows and columns k-1 and -IPIV(k) were interchanged and
D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = ā€™Lā€™ and
IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
-IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
diagonal block.

B

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.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, D(i,i) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular, so the solution could not be
computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The packed storage scheme is illustrated by the following example
when N = 4, UPLO = ā€™Uā€™:

Two-dimensional storage of the Hermitian matrix A:

a11 a12 a13 a14
a22 a23 a24
a33 a34 (aij = conjg(aji))
a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

subroutine cspsv (character uplo, integer n, integer nrhs, complex,dimension( * ) ap, integer, dimension( * ) ipiv, complex, dimension(ldb, * ) b, integer ldb, integer info)

CSPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Purpose:

CSPSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N symmetric matrix stored in packed format and X
and B are N-by-NRHS matrices.

The diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = ā€™Uā€™, or
A = L * D * L**T, if UPLO = ā€™Lā€™,
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, D is symmetric and block diagonal with 1-by-1
and 2-by-2 diagonal blocks. The factored form of A is then used to
solve the system of equations A * X = B.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.

AP

AP is COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.

On exit, the block diagonal matrix D and the multipliers used
to obtain the factor U or L from the factorization
A = U*D*U**T or A = L*D*L**T as computed by CSPTRF, stored as
a packed triangular matrix in the same storage format as A.

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D, as
determined by CSPTRF. If IPIV(k) > 0, then rows and columns
k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
diagonal block. If UPLO = ā€™Uā€™ and IPIV(k) = IPIV(k-1) < 0,
then rows and columns k-1 and -IPIV(k) were interchanged and
D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = ā€™Lā€™ and
IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
-IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
diagonal block.

B

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.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, D(i,i) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular, so the solution could not be
computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The packed storage scheme is illustrated by the following example
when N = 4, UPLO = ā€™Uā€™:

Two-dimensional storage of the symmetric matrix A:

a11 a12 a13 a14
a22 a23 a24
a33 a34 (aij = aji)
a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

subroutine dspsv (character uplo, integer n, integer nrhs, doubleprecision, dimension( * ) ap, integer, dimension( * ) ipiv, doubleprecision, dimension( ldb, * ) b, integer ldb, integer info)

DSPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Purpose:

DSPSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric matrix stored in packed format and X
and B are N-by-NRHS matrices.

The diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = ā€™Uā€™, or
A = L * D * L**T, if UPLO = ā€™Lā€™,
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, D is symmetric and block diagonal with 1-by-1
and 2-by-2 diagonal blocks. The factored form of A is then used to
solve the system of equations A * X = B.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.

AP

AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.

On exit, the block diagonal matrix D and the multipliers used
to obtain the factor U or L from the factorization
A = U*D*U**T or A = L*D*L**T as computed by DSPTRF, stored as
a packed triangular matrix in the same storage format as A.

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D, as
determined by DSPTRF. If IPIV(k) > 0, then rows and columns
k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
diagonal block. If UPLO = ā€™Uā€™ and IPIV(k) = IPIV(k-1) < 0,
then rows and columns k-1 and -IPIV(k) were interchanged and
D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = ā€™Lā€™ and
IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
-IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
diagonal block.

B

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.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, D(i,i) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular, so the solution could not be
computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The packed storage scheme is illustrated by the following example
when N = 4, UPLO = ā€™Uā€™:

Two-dimensional storage of the symmetric matrix A:

a11 a12 a13 a14
a22 a23 a24
a33 a34 (aij = aji)
a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

subroutine sspsv (character uplo, integer n, integer nrhs, real, dimension(* ) ap, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b,integer ldb, integer info)

SSPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Purpose:

SSPSV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N symmetric matrix stored in packed format and X
and B are N-by-NRHS matrices.

The diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = ā€™Uā€™, or
A = L * D * L**T, if UPLO = ā€™Lā€™,
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, D is symmetric and block diagonal with 1-by-1
and 2-by-2 diagonal blocks. The factored form of A is then used to
solve the system of equations A * X = B.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.

AP

AP is REAL array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.

On exit, the block diagonal matrix D and the multipliers used
to obtain the factor U or L from the factorization
A = U*D*U**T or A = L*D*L**T as computed by SSPTRF, stored as
a packed triangular matrix in the same storage format as A.

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D, as
determined by SSPTRF. If IPIV(k) > 0, then rows and columns
k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
diagonal block. If UPLO = ā€™Uā€™ and IPIV(k) = IPIV(k-1) < 0,
then rows and columns k-1 and -IPIV(k) were interchanged and
D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = ā€™Lā€™ and
IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
-IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
diagonal block.

B

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.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, D(i,i) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular, so the solution could not be
computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The packed storage scheme is illustrated by the following example
when N = 4, UPLO = ā€™Uā€™:

Two-dimensional storage of the symmetric matrix A:

a11 a12 a13 a14
a22 a23 a24
a33 a34 (aij = aji)
a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

subroutine zhpsv (character uplo, integer n, integer nrhs, complex*16,dimension( * ) ap, integer, dimension( * ) ipiv, complex*16, dimension(ldb, * ) b, integer ldb, integer info)

ZHPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Purpose:

ZHPSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N Hermitian matrix stored in packed format and X
and B are N-by-NRHS matrices.

The diagonal pivoting method is used to factor A as
A = U * D * U**H, if UPLO = ā€™Uā€™, or
A = L * D * L**H, if UPLO = ā€™Lā€™,
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, D is Hermitian and block diagonal with 1-by-1
and 2-by-2 diagonal blocks. The factored form of A is then used to
solve the system of equations A * X = B.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.

AP

AP is COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.

On exit, the block diagonal matrix D and the multipliers used
to obtain the factor U or L from the factorization
A = U*D*U**H or A = L*D*L**H as computed by ZHPTRF, stored as
a packed triangular matrix in the same storage format as A.

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D, as
determined by ZHPTRF. If IPIV(k) > 0, then rows and columns
k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
diagonal block. If UPLO = ā€™Uā€™ and IPIV(k) = IPIV(k-1) < 0,
then rows and columns k-1 and -IPIV(k) were interchanged and
D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = ā€™Lā€™ and
IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
-IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
diagonal block.

B

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.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, D(i,i) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular, so the solution could not be
computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The packed storage scheme is illustrated by the following example
when N = 4, UPLO = ā€™Uā€™:

Two-dimensional storage of the Hermitian matrix A:

a11 a12 a13 a14
a22 a23 a24
a33 a34 (aij = conjg(aji))
a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

subroutine zspsv (character uplo, integer n, integer nrhs, complex*16,dimension( * ) ap, integer, dimension( * ) ipiv, complex*16, dimension(ldb, * ) b, integer ldb, integer info)

ZSPSV computes the solution to system of linear equations A * X = B for OTHER matrices

Purpose:

ZSPSV computes the solution to a complex system of linear equations
A * X = B,
where A is an N-by-N symmetric matrix stored in packed format and X
and B are N-by-NRHS matrices.

The diagonal pivoting method is used to factor A as
A = U * D * U**T, if UPLO = ā€™Uā€™, or
A = L * D * L**T, if UPLO = ā€™Lā€™,
where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, D is symmetric and block diagonal with 1-by-1
and 2-by-2 diagonal blocks. The factored form of A is then used to
solve the system of equations A * X = B.

Parameters

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: Upper triangle of A is stored;
= ā€™Lā€™: Lower triangle of A is stored.

N

N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.

AP

AP is COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.

On exit, the block diagonal matrix D and the multipliers used
to obtain the factor U or L from the factorization
A = U*D*U**T or A = L*D*L**T as computed by ZSPTRF, stored as
a packed triangular matrix in the same storage format as A.

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D, as
determined by ZSPTRF. If IPIV(k) > 0, then rows and columns
k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1
diagonal block. If UPLO = ā€™Uā€™ and IPIV(k) = IPIV(k-1) < 0,
then rows and columns k-1 and -IPIV(k) were interchanged and
D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = ā€™Lā€™ and
IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and
-IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2-by-2
diagonal block.

B

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.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, D(i,i) is exactly zero. The factorization
has been completed, but the block diagonal matrix D is
exactly singular, so the solution could not be
computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

The packed storage scheme is illustrated by the following example
when N = 4, UPLO = ā€™Uā€™:

Two-dimensional storage of the symmetric matrix A:

a11 a12 a13 a14
a22 a23 a24
a33 a34 (aij = aji)
a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

Author

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