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---
:name: dsptrd
:md5sum: cf8f4de5c48cb0545e1cda0d8654c0d4
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- ap:
:type: doublereal
:intent: input/output
:dims:
- ldap
- d:
:type: doublereal
:intent: output
:dims:
- n
- e:
:type: doublereal
:intent: output
:dims:
- n-1
- tau:
:type: doublereal
:intent: output
:dims:
- n-1
- info:
:type: integer
:intent: output
:substitutions:
n: ((int)sqrtf(ldap*8+1.0f)-1)/2
:fortran_help: " SUBROUTINE DSPTRD( UPLO, N, AP, D, E, TAU, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DSPTRD reduces a real symmetric matrix A stored in packed form to\n\
* symmetric tridiagonal form T by an orthogonal similarity\n\
* transformation: Q**T * A * Q = T.\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)*(2*n-j)/2) = A(i,j) for j<=i<=n.\n\
* On exit, if UPLO = 'U', the diagonal and first superdiagonal\n\
* of A are overwritten by the corresponding elements of the\n\
* tridiagonal matrix T, and the elements above the first\n\
* superdiagonal, with the array TAU, represent the orthogonal\n\
* matrix Q as a product of elementary reflectors; if UPLO\n\
* = 'L', the diagonal and first subdiagonal of A are over-\n\
* written by the corresponding elements of the tridiagonal\n\
* matrix T, and the elements below the first subdiagonal, with\n\
* the array TAU, represent the orthogonal matrix Q as a product\n\
* of elementary reflectors. See Further Details.\n\
*\n\
* D (output) DOUBLE PRECISION array, dimension (N)\n\
* The diagonal elements of the tridiagonal matrix T:\n\
* D(i) = A(i,i).\n\
*\n\
* E (output) DOUBLE PRECISION array, dimension (N-1)\n\
* The off-diagonal elements of the tridiagonal matrix T:\n\
* E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.\n\
*\n\
* TAU (output) DOUBLE PRECISION array, dimension (N-1)\n\
* The scalar factors of the elementary reflectors (see Further\n\
* Details).\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* If UPLO = 'U', the matrix Q is represented as a product of elementary\n\
* reflectors\n\
*\n\
* Q = H(n-1) . . . H(2) H(1).\n\
*\n\
* Each H(i) has the form\n\
*\n\
* H(i) = I - tau * v * v'\n\
*\n\
* where tau is a real scalar, and v is a real vector with\n\
* v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP,\n\
* overwriting A(1:i-1,i+1), and tau is stored in TAU(i).\n\
*\n\
* If UPLO = 'L', the matrix Q is represented as a product of elementary\n\
* reflectors\n\
*\n\
* Q = H(1) H(2) . . . H(n-1).\n\
*\n\
* Each H(i) has the form\n\
*\n\
* H(i) = I - tau * v * v'\n\
*\n\
* where tau is a real scalar, and v is a real vector with\n\
* v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP,\n\
* overwriting A(i+2:n,i), and tau is stored in TAU(i).\n\
*\n\
* =====================================================================\n\
*\n"
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