SRC/cpbsv.f(3)

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NAME 💖

SRC/cpbsv.f

SYNOPSIS ✨

Functions/Subroutines 🎀

subroutine cpbsv (uplo, n, kd, nrhs, ab, ldab, b, ldb, info)
     CPBSV computes the solution to system of linear equations A * X = B for OTHER matrices

Function/Subroutine Documentation 🧚

subroutine cpbsv (character uplo, integer n, integer kd, integer nrhs,
    complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldb,
    * ) b, integer ldb, integer info)

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

Purpose 🎀

okay so the tea is: CPBSV computes the solution to a complex system of linear equations

A * X = B,

where A is an N-by-N Hermitian positive definite band matrix and X and B are N-by-NRHS 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 equations A * X = B.

Parameters 🌸

UPLO 💅

UPLO is CHARACTER*1

• = '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.

KD 🦋

KD is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.

NRHS 🍓

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

AB 🌈

AB is COMPLEX array, dimension (LDAB,N) On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:

if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(N,j+KD).

See below for further details.

On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H of the band matrix A, in the same storage format as A.

LDAB 💖

LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1.

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, the leading principal minor of order i of A is not positive, so the factorization could not be completed, and the solution has not been computed.

Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Further Details: 🦋

  The band storage scheme is illustrated by the following example, when
  N = 6, KD = 2, and UPLO = 'U':

  On entry:                       On exit:

      *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
      *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
     a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66

  Similarly, if UPLO = 'L' the format of A is as follows:

  On entry:                       On exit:

     a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
     a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
     a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *

  Array elements marked * are not used by the routine.

Definition at line 163 of file cpbsv.f. 💅

Author (the auto-generated one) 💀

Generated automatically by Doxygen for LAPACK from the source code.

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