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---
:name: dsptrf
:md5sum: 6ecf609969698a72de25e3e961f876f8
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- ap:
:type: doublereal
:intent: input/output
:dims:
- ldap
- ipiv:
:type: integer
:intent: output
:dims:
- n
- info:
:type: integer
:intent: output
:substitutions:
n: ((int)sqrtf(ldap*8+1.0f)-1)/2
:fortran_help: " SUBROUTINE DSPTRF( UPLO, N, AP, IPIV, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DSPTRF computes the factorization of a real symmetric matrix A stored\n\
* in packed format using the Bunch-Kaufman diagonal pivoting method:\n\
*\n\
* A = U*D*U**T or A = L*D*L**T\n\
*\n\
* where U (or L) is a product of permutation and unit upper (lower)\n\
* triangular matrices, and D is symmetric and block diagonal with\n\
* 1-by-1 and 2-by-2 diagonal blocks.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* = 'U': Upper triangle of A is stored;\n\
* = 'L': Lower triangle of A is stored.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)\n\
* On entry, the upper or lower triangle of the symmetric matrix\n\
* A, packed columnwise in a linear array. The j-th column of A\n\
* is stored in the array AP as follows:\n\
* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;\n\
* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.\n\
*\n\
* On exit, the block diagonal matrix D and the multipliers used\n\
* to obtain the factor U or L, stored as a packed triangular\n\
* matrix overwriting A (see below for further details).\n\
*\n\
* IPIV (output) INTEGER array, dimension (N)\n\
* Details of the interchanges and the block structure of D.\n\
* If IPIV(k) > 0, then rows and columns k and IPIV(k) were\n\
* interchanged and D(k,k) is a 1-by-1 diagonal block.\n\
* If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and\n\
* columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k)\n\
* is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) =\n\
* IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were\n\
* interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block.\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\n\
* > 0: if INFO = i, D(i,i) is exactly zero. The factorization\n\
* has been completed, but the block diagonal matrix D is\n\
* exactly singular, and division by zero will occur if it\n\
* is used to solve a system of equations.\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* 5-96 - Based on modifications by J. Lewis, Boeing Computer Services\n\
* Company\n\
*\n\
* If UPLO = 'U', then A = U*D*U', where\n\
* U = P(n)*U(n)* ... *P(k)U(k)* ...,\n\
* i.e., U is a product of terms P(k)*U(k), where k decreases from n to\n\
* 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1\n\
* and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as\n\
* defined by IPIV(k), and U(k) is a unit upper triangular matrix, such\n\
* that if the diagonal block D(k) is of order s (s = 1 or 2), then\n\
*\n\
* ( I v 0 ) k-s\n\
* U(k) = ( 0 I 0 ) s\n\
* ( 0 0 I ) n-k\n\
* k-s s n-k\n\
*\n\
* If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k).\n\
* If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k),\n\
* and A(k,k), and v overwrites A(1:k-2,k-1:k).\n\
*\n\
* If UPLO = 'L', then A = L*D*L', where\n\
* L = P(1)*L(1)* ... *P(k)*L(k)* ...,\n\
* i.e., L is a product of terms P(k)*L(k), where k increases from 1 to\n\
* n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1\n\
* and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as\n\
* defined by IPIV(k), and L(k) is a unit lower triangular matrix, such\n\
* that if the diagonal block D(k) is of order s (s = 1 or 2), then\n\
*\n\
* ( I 0 0 ) k-1\n\
* L(k) = ( 0 I 0 ) s\n\
* ( 0 v I ) n-k-s+1\n\
* k-1 s n-k-s+1\n\
*\n\
* If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k).\n\
* If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k),\n\
* and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1).\n\
*\n\
* =====================================================================\n\
*\n"
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