hpsv(3)

📦

version 3.12.1 · 9 versions

3.12.1 · arch rolling (latest)
3.12.0 · opensuse-leap 16.0
3.12.1 · ubuntu stonking
3.12.1 · ubuntu questing
3.12.0 · ubuntu noble
3.12.0 · ubuntu noble
3.12.0 · centos-stream 10, fedora 43, fedora 44
3.12.1 · ubuntu resolute
3.12.1 · debian trixie

🌸 NAME 🌸

hpsv — {hp,sp}sv: factor and solve. Bestie, this is the hpsv(3) page from the Library Functions Manual, and it's a whole journey 💅

✨ 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 🦋

okay so real talk — the detailed description section here is basically just a vibe check before the main event. Everything juicy lives down in Function Documentation 👇

👑 Function Documentation 👑

💜 subroutine chpsv

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. periodt.

🌟 Purpose

okay so 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 = 'U', or
   A = L * D * L**H,  if UPLO = 'L',

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. iconic behaviour honestly ✨

🍓 Parameters

UPLO — UPLO is CHARACTER*1. Two moods only, bestie:
- = 'U': Upper triangle of A is stored;
- = 'L': 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 = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
  - if UPLO = 'L', 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. lowkey the receipts of the whole factorization:
- 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 = 'U' 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 = 'L' 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. glow up complete 🦋
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. 😭 tragic, no solution for you

🧚 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 = 'U':

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 ]

Definition at line 161 of file chpsv.f.

💜 subroutine cspsv

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. (yes bestie, same energy, slightly different matrix 💅)

🌟 Purpose

okay so 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 = 'U', or
   A = L * D * L**T,  if UPLO = 'L',

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.

⚠️ heads up: this one's symmetric with **T transposes, not Hermitian with **H conjugates like CHPSV. not the same thing, don't mix them up or it's giving bug report 💀

🍓 Parameters

UPLO — UPLO is CHARACTER*1. Two moods only:
- = 'U': Upper triangle of A is stored;
- = 'L': 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 = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
  - if UPLO = 'L', 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 = 'U' 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 = 'L' 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. singular D said "not today" 🙈

🧚 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 = 'U':

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 ]

Definition at line 161 of file cspsv.f.

💜 subroutine dspsv

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

DSPSV computes the solution to system of linear equations A * X = B for OTHER matrices. double precision entered the chat ✨

🌟 Purpose

…and this is exactly where the page hands off to the next part, bestie — we're literally mid-sentence, stay tuned 🫶

so DSPSV is out here doing the absolute most, solving a real system of linear equations

    A * X = B,

where A is an N-by-N symmetric matrix sitting pretty in packed format, and X and B are N-by-NRHS matrices. ✨

The diagonal pivoting method is what factors A, bestie:

    A = U * D * U**T,  if UPLO = 'U', or
    A = L * D * L**T,  if UPLO = 'L',

where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. Then the factored form of A gets used to solve A * X = B. That's the whole arc of the episode 💅

🌸 Parameters

UPLO — CHARACTER*1, and it's giving pick-a-side: = 'U' means the upper triangle of A is stored; = 'L' means the lower triangle of A is stored. Choose wisely 🎀
N — INTEGER, the number of linear equations, i.e. the order of the matrix A. Constraint: N >= 0. No cap, but also no negativity, we don't do that here ✨
NRHS — INTEGER, the number of right hand sides, i.e. the number of columns of the matrix B. Constraint: NRHS >= 0. Same energy 🦋
AP — 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 like this:

if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

See below for further details, because there ARE further details and they're cute. 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. Iconic, she reuses her own fit 🔥

IPIV — INTEGER array, dimension (N). The 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 = 'U' 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 = 'L' 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. Negative IPIV is not a red flag, it's just 2-by-2 block szn 🫶
B — 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. She goes in as B and comes out as X, main character development fr 🌈
LDB — INTEGER, the leading dimension of the array B. Constraint: LDB >= max(1,N). Respect the leading dimension or suffer 😭
INFO — INTEGER, the vibe check:
- = 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 💀 (this is the real danger, not a drill)

🎀 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 = 'U':

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 ]

Look at her, folded up like a little origami swan and still the whole matrix 🦋✨

Definition at line 161 of file dspsv.f.

💖 SSPSV

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 — that's literally the one-liner, no notes 💅

Purpose:

okay so 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 = 'U', or
    A = L * D * L**T,  if UPLO = 'L',

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, and then the factored form of A is used to solve A * X = B. Same storyline, REAL flavor 🌸

Parameters

UPLO — CHARACTER*1. = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored. Periodt 🎀
N — INTEGER, the number of linear equations, i.e. the order of the matrix A. N >= 0.
NRHS — INTEGER, the number of right hand sides, i.e. the number of columns of the matrix B. NRHS >= 0.
AP — 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 = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', 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 — 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 = 'U' 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 = 'L' 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. She's thorough, she's precise, she's booked and busy 💅
B — 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 — INTEGER, the leading dimension of the array B. LDB >= max(1,N).
INFO — 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. Sorry bestie, no solution today 💀

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 = 'U':

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 ]

Same example, same slay, different precision 🧚

Definition at line 161 of file sspsv.f.

👑 ZHPSV

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:

okay so 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 = 'U', or
    A = L * D * L**H,  if UPLO = 'L',

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. Then the factored form of A is used to solve the system of equations A * X = B. Note the **H, bestie — conjugate transpose, she's fancy like that 🦋💜

Parameters

UPLO — CHARACTER*1. = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored. Pick one, commit to it 💅
N — INTEGER, the number of linear equations, i.e. the order of the matrix A. N >= 0.
NRHS — INTEGER, the number of right hand sides, i.e. the number of columns of the matrix B. NRHS >= 0.
AP — okay so this is the array, and—
AP — okay bestie, this is a COMPLEX*16 array, dimension (N*(N+1)/2). On entry, it’s 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 AP like this:
- if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
- if UPLO = 'L', 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 — this is the drama tracker, lowkey. IPIV is an INTEGER array, dimension (N). It holds 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 = 'U' 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 = 'L' 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 a COMPLEX*16 array, dimension (LDB,NRHS). On entry, it’s the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, it’s the N-by-NRHS solution matrix X. glow-up moment fr fr 💅
LDB — LDB is INTEGER. It’s the leading dimension of the array B. LDB >= max(1,N). no cap.
INFO — INFO is INTEGER, and it’s giving status report:
- = 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. big yikes, but at least it told you

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 = 'U':

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 ]

Definition at line 161 of file zhpsv.f.

🌸 `zspsv` — symmetric packed solve, same energy 🌸

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. she’s the symmetric sibling and she ate

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 = 'U', or
A = L * D * L**T,  if UPLO = 'L',

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. literally the whole plot

Parameters 🧾

UPLO — UPLO is CHARACTER*1:
- = 'U': upper triangle of A is stored;
- = 'L': lower triangle of A is stored.
N — N is INTEGER. It’s the number of linear equations, i.e., the order of the matrix A. N >= 0.
NRHS — NRHS is INTEGER. It’s the number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
AP — AP is a COMPLEX*16 array, dimension (N*(N+1)/2). On entry, it’s 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 = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
- if UPLO = 'L', 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. same storage format, different transpose vibe
IPIV — IPIV is an INTEGER array, dimension (N). It holds 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 = 'U' 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 = 'L' 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 a COMPLEX*16 array, dimension (LDB,NRHS). On entry, it’s the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, it’s the N-by-NRHS solution matrix X.
LDB — LDB is INTEGER. It’s 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. singular D said “not today” 😭

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 = 'U':

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 ]

Definition at line 161 of file zspsv.f.

Author 📝

Generated automatically by Doxygen for LAPACK from the source code.

Okay that’s the whole manual page, bestie. The footer says LAPACK Version 3.12.0 and the page is hpsv(3) — consider this your cute little sign-off, mwah 💋✨

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms

hpsv(3)

🌸 NAME 🌸

✨ SYNOPSIS ✨

🎀 Functions

🦋 Detailed Description 🦋

👑 Function Documentation 👑

💜 subroutine chpsv

🌟 Purpose

🍓 Parameters

🧚 Author

🌈 Further Details:

💜 subroutine cspsv

🌟 Purpose

🍓 Parameters

🧚 Author

🌈 Further Details:

💜 subroutine dspsv

🌟 Purpose

🌸 Parameters

🎀 Author

⭐ Further Details:

💖 SSPSV

Purpose:

Parameters

Author

Further Details:

👑 ZHPSV

Purpose:

Parameters

Author 👑

Further Details 🔍

🌸 zspsv — symmetric packed solve, same energy 🌸

Purpose 🎯

Parameters 🧾

Author 👑

Further Details 🔍

Author 📝

🌸 `zspsv` — symmetric packed solve, same energy 🌸